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Introduction to probability theory: probability spaces, expectation as Lebesgue integral, characteristic functions, modes of convergence, conditional probability and expectation, discrete-state Markov chains, stationary distributions, limit theorems, ergodic theorem, continuous-state Markov chains, applications to Markov chain Monte Carlo methods. Prerequisite(s): course 205B or by permission of instructor. Enrollment restricted to graduate students.. 5 Credits. ...

Markov Chain Monte Carlo simulation has received considerable attention within the past decade as reportedly one of the most powerful techniques for the first passage probability estimation of dynamic systems. A very popular method in this direction capable of estimating probability of rare events with low computation cost is the subset simulation (SS). The idea of the method is to break a rare event into a sequence of more probable events which are easy to be estimated based on the conditional simulation techniques. Recently, two algorithms have been proposed in order to increase the efficiency of the method by modifying the conditional sampler. In this paper, applicability of the original SS is compared to the recently introduced modifications of the method on a wind turbine model. The model incorporates a PID pitch controller which aims at keeping the rotational speed of the wind turbine rotor equal to its nominal value. Finally Monte Carlo simulations are performed which allow assessment of ...

Learning and adaptation are considered to be stochastic in nature by most modern psychologists and by many engineers. Markov chains are among the simplest and best understood models of stochastic processes and, in recent years, have frequently found application as models of adaptive processes. A number of new techniques are developed for the analysis of synchronous and asynchronous Markov chains, with emphasis on the problems encountered in the use of these chains as models of adaptive processes. Signal flow analysis yields simplified computations of asymptotic success probabilities, delay times, and other indices of performance. The techniques are illustrated by several examples of adaptive processes. These examples yield further insight into the relations between adaptation and feedback ...

A common managerial problem in the project-based organization is the problem of resource allocation. In practice this problem is addressed by applying project portfolio management. In this study we examine project portfolio management in a consultancy firm by applying a mathematical model. The information produced by this model could enable rational decision making and thus improve the economic resilience and reduce internal uncertainty in the firm so that it may live long and prosper. The proposed model is based on a Markov process that represents the projects in the firm. The parameters are estimated by Maximum Likelihood and the results are estimated through Monte Carlo Simulation.. This study initially shows that it is possible to model the project portfolio as a Markov process. This was supported by the conducted literature review and illustrated by the presented model. Furthermore, we conclude that the value of accepting a project is dependent on the current state of the firm in terms of ...

The identification of copy number aberration in the human genome is an important area in cancer research. We develop a model for determining genomic copy numbers using high-density single nucleotide polymorphism genotyping microarrays. The method is based on a Bayesian spatial normal mixture model with an unknown number of components corresponding to true copy numbers. A reversible jump Markov chain Monte Carlo algorithm is used to implement the model and perform posterior inference. The performance of the algorithm is examined on both simulated and real cancer data, and it is compared with the popular CNAG algorithm for copy number detection. We demonstrate that our Bayesian mixture model performs at least as well as the hidden Markov model based CNAG algorithm and in certain cases does better. One of the added advantages of our method is the flexibility of modeling normal cell contamination in tumor samples.

Roberts, Gareth O. (2004) Markov chain Monte Carlo. A review article for section 10 (probability theory). In: Encyclopedia of the actuarial sciences. .. Full text not available from this repository ...

|i|Objective|/i|. Initial optimized prescription of Chinese herb medicine for unstable angina (UA). |i |Methods|/i|. Based on partially observable Markov decision process model (POMDP), we choose hospitalized patients of 3 syndrome elements, such as |i |qi|/i| deficiency, blood stasis, and turbid phlegm for the data mining, analysis, and objective evaluation of the diagnosis and treatment of UA at a deep level in order to optimize the prescription of Chinese herb medicine for UA. |i |Results|/i|. The recommended treatment options of UA for |i |qi|/i| deficiency, blood stasis, and phlegm syndrome patients were as follows: Milkvetch Root + Tangshen + Indian Bread + Largehead Atractylodes Rhizome (|svg style=vertical-align:-0.20474pt;width:107.025px; id=M1 height=11.6875 version=1.1 viewBox=0 0 107.025 11.6875 width=107.025 xmlns:xlink=http://www.w3.org/1999/xlink xmlns=http://www.w3.org/2000/svg| |g transform=

Volumetric calibration is used for high accuracy estimation of the functional volume-to-level relationship for vessels used to store hazardous liquids. An example of calibration of a vessel for reprocessed nuclear material is used to illustrate an analysis of calibration data. We advocate a Bayesian approach, with proper account of genuine prior information, using a reversible jump Markov chain Monte Carlo method for estimation.. ...

Hamiltonian Monte Carlo is one of the algorithms of the Markov chain Monte Carlo method that uses Hamiltonian dynamics to propose samples that follow a target distribution. The method can avoid the random walk behavior to achieve a more effective and consistent exploration of the probability space and sensitivity to correlated parameters, which are shortcomings that plague many Markov chain Monte Carlo methods. However, the performance of Hamiltonian Monte Carlo is highly sensitive to two hyperparameters. The No-U-Turn Sampler, an extension of Hamiltonian Monte Carlo, was recently introduced to automate the tuning of these hyperparameters. Thus, this study compared the performances of Gibbs sampling, Hamiltonian Monte Carlo, and the No-U-Turn Sampler for estimating genetic parameters and breeding values as well as sampling qualities in both simulated and real pig data. For all datasets, we used a pedigree-based univariate linear mixed model. For all datasets, the No-U-Turn Sampler and Gibbs sampling

We present a method for restoration of audio which has been distorted by a nonlinear channel or recording medium. We model the signal as a linear process cascaded with a nonlinear distortion. We use sampling methods to perform model selection and parameter estimation. We allow the linear model to be nonstationary, and present results for both synthetic and real distortions.

Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of fu

Wavelet-domain hidden Markov models (HMMs), in particular hidden Markov tree (HMT), were recently proposed and applied to image processing, where it was usually assumed that three subbands of the 2-D discrete wavelet transform (DWT), i.e. HL, LH, and HH, are independent. In this paper, we study wavelet-based texture analysis and synthesis using HMMs. Particularly, we develop a new HMM, called HMT-3S, for statistical texture characterization in the wavelet-domain. In addition to the joint statistics captured by HMT, the new HMT-3S can also exploit the crosscorrelation across DWT subbands. Meanwhile, HMT-3S can be characterized by using the graphical grouping technique, and has the same tree structure as HMT. The proposed HMT-3S is applied to texture analysis, including classification and segmentation, and texture synthesis with improved performance over HMT. Specifically, for texture classification, we study four wavelet-based methods, and experimental results show that HMT-3S provides the highest

This thesis consists of four papers.. In paper 1, we prove central limit theorems for Markov chains under (local) contraction conditions. As a corollary we obtain a central limit theorem for Markov chains associated with iterated function systems with contractive maps and place-dependent Dini-continuous probabilities.. In paper 2, properties of inverse subordinators are investigated, in particular similarities with renewal processes. The main tool is a theorem on processes that are both renewal and Cox processes.. In paper 3, distributional properties of supercritical and especially immortal branching processes are derived. The marginal distributions of immortal branching processes are found to be compound geometric.. In paper 4, a description of a dynamic population model is presented, such that samples from the population have genealogies as given by a Lambda-coalescent with mutations. Depending on whether the sample is grouped according to litters or families, the sampling distribution is ...

This paper proposes a moment-matching method for approximating vector autoregressions by finite-state Markov chains. The Markov chain is constructed by targeting the conditional moments of the underlying continuous process. The proposed method is more robust to the number of discrete values and tends to outperform the existing methods for approximating multivariate processes over a wide range of the parameter space, especially for highly persistent vector autoregressions with roots near the unit circle. Copyright © 2013 John Wiley & Sons, Ltd. ...

A simple learning algorithm for Hidden Markov Models (HMMs) is presented together with a number of variations. Unlike other classical algorithms such as the Baum-Welch algorithm, the algorithms described are smooth and can be used on-line (after each example presentation) or in batch mode, with or without the usual Viterbi most likely path approximation. The algorithms have simple expressions that result from using a normalized-exponential representation for the HMM parameters. All the algorithms presented are proved to be exact or approximate gradient optimization algorithms with respect to likelihood, log-likelihood, or cross-entropy functions, and as such are usually convergent. These algorithms can also be casted in the more general EM (Expectation-Maximization) framework where they can be viewed as exact or approximate GEM (Generalized Expectation-Maximization) algorithms. The mathematical properties of the algorithms are derived in the appendix.. ...

A novel texture feature based on isotropic Gaussian Markov random fields is proposed for diagnosis and quantification of emphysema and its subtypes. Spatially varying parameters of isotropic Gaussian Markov random fields are estimated and their local distributions constructed using normalized histograms are used as effective texture features. These features integrate the essence of both statistical and structural properties of the texture. Isotropic Gaussian Markov Random Field parameter estimation is computationally efficient than the methods using other MRF models and is suitable for classification of emphysema and its subtypes. Results show that the novel texture features can perform well in discriminating different lung tissues, giving comparative results with the current state of the art texture based emphysema quantification. Furthermore supervised lung parenchyma tissue segmentation is carried out and the effective pathology extents and successful tissue quantification are ...

Superb work from our SALSAmigos in Soest and Duesseldorf. Understanding that diabetic foot complications are lifetime conditions-- and not just individual events fundamentally changes how we might model outcomes and care. Study of Disease Progression and Relevant Risk Factors in Diabetic Foot Patients Using a Multistate Continuous-Time Markov Chain Model Alexander Begun1*, Stephan Morbach1,2,…

One of the most important decisions regarding reverse logistics (RL) is whether to outsource such functions or not, due to the fact that RL does not represent a production or distribution firms core activity. To explore the hypothesis that outsourcing RL functions is more suitable when returns are more variable, we formulate and analyse a Markov decision model of the outsourcing decision. The reward function includes capacity and operating costs of either performing RL functions internally or outsourcing them and the transitions among states reflect both the sequence of decisions taken and a simple characterization of the random pattern of returns over time. We identify sufficient conditions on the cost parameters and the return fraction that guarantee the existence of an optimal threshold policy for outsourcing. Under mild assumptions, this threshold is more likely to be crossed, the higher the uncertainty in returns. A numerical example illustrates the existence of an optimal threshold policy even

Downloadable! Recent models for credit risk management make use of hidden Markov models (HMMs). HMMs are used to forecast quantiles of corporate default rates. Little research has been done on the quality of such forecasts if the underlying HMM is potentially misspecified. In this paper, we focus on misspecification in the dynamics and dimension of the HMM. We consider both discrete- and continuous-state HMMs. The differences are substantial. Underestimating the number of discrete states has an economically significant impact on forecast quality. Generally speaking, discrete models underestimate the high-quantile default rate forecasts. Continuous-state HMMs, however, vastly overestimate high quantiles if the true HMM has a discrete state space. In the reverse setting the biases are much smaller, though still substantial in economic terms. We illustrate the empirical differences using US default data. Copyright © 2008 John Wiley & Sons, Ltd.

Downloadable (with restrictions)! We show that a deeper insight into the relations among marginal processes of a multivariate Markov chain can be gained by testing hypotheses of Granger noncausality, contemporaneous independence and monotone dependence. Granger noncausality and contemporaneous independence conditions are read off a mixed graph, and the dependence of an univariate component of the chain on its parents-according to the graph terminology-is described in terms of stochastic dominance criteria. The examined hypotheses are proven to be equivalent to equality and inequality constraints on some parameters of a multivariate logistic model for the transition probabilities. The introduced hypotheses are tested on real categorical time series. Copyright Springer-Verlag Berlin Heidelberg 2013

Again εi and ε*i denote the residuals under the current and proposed models, respectively. The derivations of the acceptance probabilities follow from the results in Green (1995) and Waagepetersen and Sorensen (2001).. This expression differs from that of Sillanpää and Arjas (1998), Yi and Xu (2002), and Yi et al. (2003) who have effectively (ignoring all the other parameters in the QTL mapping context) used the above but with pd(s′) replaced by pd(s′) × (1/s′). That is, they have retained the probability for selecting the particular step for removal but have not included the probability for selecting the position when adding a step. This accounting for the positioning of the added step is essential for balance and reversibility, properties that form the basis of the formulation of the RJ-MCMC algorithm. Two points should be noted here. First, the position of a new step need not be selected with equal probability, but if a position is selected with probability zero, then its ...

Abstract: The quantification of myocardial perfusion MRI has the potential to provide a fast, automated and user-independent assessment of myocardial ischaemia. However, due to the relatively high noise level and low temporal resolution of the acquired data and the complexity of the tracer-kinetic models, the model fitting can yield unreliable parameter estimates. A solution to this problem is the use of Bayesian inference which can incorporate prior knowledge and improve the reliability of the parameter estimation. This, however, uses Markov chain Monte Carlo sampling to approximate the posterior distribution of the kinetic parameters which is extremely time intensive. This work proposes training convolutional networks to directly predict the kinetic parameters from the signal-intensity curves that are trained using estimates obtained from the Bayesian inference. This allows fast estimation of the kinetic parameters with a similar performance to the Bayesian inference ...

No there isnt (necessarily) a bug. This type of plot is very easily produced with valid code: e.g. by slice sampling a unit spherical Gaussian distribution in D=5000 dimensions and initializing at an atypical point of high-probability (much closer to the origin than sqrt(D) away). Simple Metropolis and slice samplers cant change the log-prob by more than ≈1 per iteration, so large log-prob changes are slow and painful. Intelligent proposals, reparameterizations, or auxiliary variable methods can improve matters. This is a nice illustration that initializing with an optimizer (without some form of early stopping) can be a bad idea ...

Bayesian inference of phylogeny uses a likelihood function to create a quantity called the posterior probability of trees using a model of evolution, based on some prior probabilities, producing the most likely phylogenetic tree for the given data. The Bayesian approach has become popular due to advances in computing speeds and the integration of Markov chain Monte Carlo (MCMC) algorithms. Bayesian inference has a number of applications in molecular phylogenetics and systematics. Bayesian inference refers to a probabilistic method developed by Reverend Thomas Bayes based on Bayes theorem. Published posthumously in 1763 it was the first expression of inverse probability and the basis of Bayesian inference. Independently, unaware of Bayes work, Pierre-Simon Laplace developed Bayes theorem in 1774. Bayesian inference was widely used until 1900s when there was a shift to frequentist inference, mainly due to computational limitations. Based on Bayes theorem, the bayesian approach combines the ...

A knight moves on a chessboard according the standard rules of chess, but in a random manner. At each move, then, the knight is equally likely to move to any of the squares it can reach. Thus a knight at a corner square of the board will move to either of the two squares it can reach with probability \(\tfrac12\), while a knight in the centre of the board will move to any one of eight possible squares, each with probability \(\tfrac18\).. This chessboard has a safe zone, consisting of the four central squares. The knight starts its journey on one of the squares in the safe zone. The expected number of moves it must make until it returns to any square in the safe zone can be written as \(\tfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?. ...

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Answer to {Xn, n > 0 } is a Markov Chain, such that Xn is an element of {1, 2}, P[Xn+1 = 2 | Xn = 1] = a, which is a probability between (0,1) P[Xn+1 = 1 |

Author(s): Li, Longhai; Yao, Weixin | Abstract: High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands of genes that are active (expressed) in certain tissue cells. To this end, we wish to fit regression and classification models with a large number of features (also called variables, predictors). In the past decade, penalized likelihood methods for fitting regression models based on hyper-LASSO penalization have received increasing attention in the literature. However, fully Bayesian methods that use Markov chain Monte Carlo (MCMC) are still in lack of development in the literature. In this paper we introduce an MCMC (fully Bayesian) method for learning severely multi-modal posteriors of logistic regression models based on hyper-LASSO priors (non-convex penalties). Our MCMC algorithm uses Hamiltonian Monte Carlo in a

TY - GEN. T1 - Bayesian fatigue damage and reliability analysis using Laplace approximation and inverse reliability method. AU - Guan, Xuefei. AU - He, Jingjing. AU - Jha, Ratneshwar. AU - Liu, Yongming. PY - 2014/1/1. Y1 - 2014/1/1. N2 - This paper presents an efficient analytical Bayesian method for reliability and system response estimate and update. The method includes additional data such as measurements to reduce estimation uncertainties. Laplace approximation is proposed to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse first-order reliability method is developed to evaluate system responses given a reliability level. Since the proposed method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A numerical example and a practical fatigue crack propagation problem with experimental ...

Standard Evolutionary Game Theory framework is a useful tool to study large interacting systems and to understand the strategic behavior of individuals in such complex systems. Adding an individual state to model local feature of each player in this context, allows one to study a wider range of problems in various application areas as networking, biology, etc. In this paper, we introduce such an extension of evolutionary game framework and particularly, we focus on the dynamical aspects of this system. Precisely, we study the coupled dynamics of the policies and the individual states inside a population of interacting individuals. We first define a general model by coupling replicator dynamics and continuous-time Markov Decision Processes and we then consider a particular case of a two policies and two states evolutionary game. We first obtain a system of combined dynamics and we show that the rest-points of this system are equilibria profiles of our evolutionary game with individual state dynamics.

Populations can be genetically isolated by both geographic distance and by differences in their ecology or environment that decrease the rate of successful migration. Empirical studies often seek to investigate the relationship between genetic differentiation and some ecological variable(s) while accounting for geographic distance, but common approaches to this problem (such as the partial Mantel test) have a number of drawbacks. In this article, we present a Bayesian method that enables users to quantify the relative contributions of geographic distance and ecological distance to genetic differentiation between sampled populations or individuals. We model the allele frequencies in a set of populations at a set of unlinked loci as spatially correlated Gaussian processes, in which the covariance structure is a decreasing function of both geographic and ecological distance. Parameters of the model are estimated using a Markov chain Monte Carlo algorithm. We call this method Bayesian Estimation of ...

This paper presents an original Markov chain Monte Carlo method to sample from the posterior distribution of conjugate mixture models. This algorithm relies on a flexible split-merge procedure built using the particle Gibbs sampler introduced in Andrieu et al. (2009, 2010). The resulting so-called Particle Gibbs Split-Merge sampler does not require the computation of a complex acceptance ratio and can be implemented using existing sequential Monte Carlo libraries. We investigate its performance experimentally on synthetic problems as well as on geolocation data. Our results show that for a given computational budget, the Particle Gibbs Split-Merge sampler empirically outperforms existing split merge methods. The code and instructions allowing to reproduce the experiments is available at github.com/aroth85/pgsm.. PDF BibTeX ...

New Galileo and enhanced GPS signals use binary offset carrier (BOC) waveforms namely composite BOC (CBOC) and alternate BOC (AltBOC). For good tracking, these signals require precise acquisition. The more sidelobes the autocorrelation function has, the tighter the pull-in range region is, and the more precise the acquisition must be. Further, when multipath propagation is encountered, the received waveform is so distorted that a precise acquisition becomes difficult. To solve this problem, two approaches are considered by enhancing either the acquisition stage or the tracking one. At the acquisition stage, the authors focus on Bayesian estimation where Bernoulli-Gaussian and Laplacian (Lp) priors for channel distribution are compared. On one hand, the BG prior leads to rather complex optimisation criterion that can be solved by a Markov Chain Monte Carlo algorithm. This is a very efficient but time consuming method. On the other hand, the Lp prior results in exact maximum a posteriori ...

One of the primary causes of blur in a high-energy X-ray imaging system is the shape and extent of the radiation source, or spot. It is important to be able to quantify the size of the spot as it provides a lower bound on the recoverable resolution for a radiograph, and penumbral imaging methods - which involve the analysis of blur caused by a structured aperture - can be used to obtain the spots spatial profile. We present a Bayesian approach for estimating the spot shape that, unlike variational methods, is robust to the initial choice of parameters. The posterior is obtained from a normal likelihood, which was constructed from a weighted least squares approximation to a Poisson noise model, and prior assumptions that enforce both smoothness and non-negativity constraints. A Markov chain Monte Carlo algorithm is used to obtain samples from the target posterior, and the reconstruction and uncertainty estimates are the computed mean and variance of the samples, respectively. Lastly, synthetic ...

The Differential Adhesion Hypothesis (DAH) is a theory of the organization of cells within a tissue which has been validated by several biological experiments and tested against several alternative computational models. In this study, a statistical approach was developed for the estimation of the strength of adhesion, incorporating earlier discrete lattice models into a continuous marked point process framework. This framework allows to describe an ergodic Markov Chain Monte Carlo algorithm that can simulate the model and reproduce empirical biological patterns. The estimation procedure, based on a pseudo-likelihood approximation, is validated with simulations, and a brief application to medulloblastoma stained by beta-catenin markers is given. Our model includes the strength of cell-cell adhesion as a statistical parameter. The estimation procedure for this parameter is consistent with experimental data and would be useful for high-throughput cancer studies.

Stan is a probabilistic programming language for specifying statistical models. Stan provides full Bayesian inference for continuous-variable models through Markov Chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited ...

I am a Research Fellow working with Prof. Wilfrid Kendall. We are exploring the use of Dirichet forms to address optimal scaling and other theoretical questions about Markov chain Monte Carlo methods. From April 2017 until September 2018 I was a postdoctoral research assistant at Queen Mary University of London with Prof. John Moriarty, working on simulation of rare events and other applications of MCMC methods to energy related problems. I did my PhD (2013-2017) at Imperial College London with Prof. Aleksandar Mijatović on the topic of variance reduction using control variates obtained by approximately solving the Poisson equation.. I am a co-organiser of Algorithms & Computationally Intensive Inference seminar.. Some Publications and Preprints:. ...

Trikalinos, T.A.; Andreadis, I.A.; Asproudis, I.C., 2005: Decision analysis with Markov processes supports early surgery for large-angle infantile esotropia

Mixture models are commonly used in the statistical segmentation of images. For example, they can be used for the segmentation of structural medical images into different matter types, or of statistical parametric maps into activating and nonactivating brain regions in functional imaging. Spatial mixture models have been developed to augment histogram information with spatial regularization using Markov random fields (MRFs). In previous work, an approximate model was developed to allow adaptive determination of the parameter controlling the strength of spatial regularization. Inference was performed using Markov Chain Monte Carlo (MCMC) sampling. However, this approach is prohibitively slow for large datasets. In this work, a more efficient inference approach is presented. This combines a variational Bayes approximation with a second-order Taylor expansion of the components of the posterior distribution, which would otherwise be intractable to Variational Bayes. This provides inference on fully adaptive

Michael Newtons webpage. Research Interests. Dr. Newton studies theory, methodology, and application of statistical inference in the biological sciences. Cancer biology has been the source of many recent applied problems, such as linkage analysis to localize genes conferring resistance or susceptibility in rat mammary cancer, and signal identification in cytogenetic or molecular data on cancer genome abnormalities. Problems from genomic data integration are of current interest. Dr. Newton has also contributed to statistical problems in the phylogenetic analysis of molecular sequences. Computational problems have been a focus of his research; he has contributed to the implementation of Markov chain Monte Carlo methods for Bayesian analysis and to the implementation and theory of bootstrap sampling. Further, Dr. Newton has developed new methods of nonparametric Bayesian analysis.. Selected Publications. For an up-to-date listing of Michael Newtons Publications, see his main page.. Courses ...

Phylogenetic tree can be constructed from genetic sequences using distance-based methods or character-based methods. Distance-based methods, including unweighted pair group method with arithmetic means (UPGMA) and Neighbor-joining (NJ), are based on the matrix of pairwise genetic distances calculated between sequences. The character-based methods, including maximum parsimony (MP) (Fitch 1971), maximum likelihood (ML) (J. Felsenstein 1981), and Bayesian Markov Chain Monte Carlo (BMCMC) method (Rannala and Yang 1996), are based on mathematical model that describes the evolution of genetic characters and search for the best phylogenetic tree according to their own optimality criteria.. Maximum Parsimony (MP) method assumes that the evolutionary change is rare and minimizes the amount of character-state changes (e.g., number of DNA substitutions). The criterion is similar to Occams razor, that the simplest hypothesis that can explains the data is the best hypothesis. Unweighted parsimony assumes ...

The internal transcribed spacer (ITS) is a popular barcode marker for fungi and in particular the ITS1 has been widely used for the anaerobic fungi (phylum Neocallimastigomycota). A good number of validated reference sequences of isolates as well as a large number of environmental sequences are available in public databases. Its highly variable nature predisposes the ITS1 for low level phylogenetics; however, it complicates the establishment of reproducible alignments and the reconstruction of stable phylogenetic trees at higher taxonomic levels (genus and above). Here, we overcame these problems by proposing a common core secondary structure of the ITS1 of the anaerobic fungi employing a Hidden Markov Model-based ITS1 sequence annotation and a helix-wise folding approach. We integrated the additional structural information into phylogenetic analyses and present for the first time an automated sequence-structure-based taxonomy of the ITS1 of the anaerobic fungi. The methodology developed is transferable

Although Bayes published his seminal paper in 1763, doing inference through conditional probabilities didnt really become popular until the 1990s, when Markov Chain Monte Carlo methods (used to estimate posterior distributions), along with widespread computerization, pushed it to the mainstream. Why is this?. One common complaint against Bayes was that choosing a prior feels very subjective and unscientific6. In the problems above, we always had a pretty obvious choice of prior. For example, we assumed that each urn had the same probability of being chosen. In the real world, this choice becomes more tricky.. The problem becomes easier to appreciate when youre modeling a complex situation. Say youre trying to infer (reverse probability) the proportion of people that will vote for a specific mayoral candidate. Furthermore, say that youve constructed a sophisticated model for this situation that uses poll data. Whats your prior? Do you assume that all proportions are equally likely? This ...

King MD, Crowder MJ, Hand DJ, Harris NG, Williams SR, Obrenovitch TP, Gadian DG, King MD, Crowder MJ, Hand DJ, Harris NG, Williams SR, Obrenovitch TP, Gadian DGet al., 2002, A Markov chain Monte Carlo simulations analysis of the temporal apparent diffusion coefficient and DC potential responses to focal ischaemia (CD-ROM), Berkley, CA, 10th annual meeting of the International Society for Magnetic Resonance in Medicine, Honolulu, 18 - 24 May 2002, Publisher: International Society for Magnetic Resonance in Medicine, Pages: 1175-1175 ...

This dissertation deals with modeling and statistical analysis of longitudinal and clustered binary data. Such data consists of observations on a dichotomous response variable generated from multiple time or cluster points, that exhibit either decaying correlation or equi-correlated dependence. The current literature addresses modeling the dependence using an appropriate correlation structure, but ignores the feasible bounds on the correlation parameter imposed by the marginal means. The first part of this dissertation deals with two multivariate probability models, the first order Markov chain model and the multivariate probit model, that adhere to the feasible bounds on the correlation. For both the models we obtain maximum likelihood estimates for the regression and correlation parameters, and study both asymptotic and small-sample properties of the estimates. Through simulations we compare the efficiency of the two methods and demonstrate that neither is uniformly superior over the other. The second

We are evaluating a model for risk management based on extreme value theory using peaks over threshold and markov chain monte carlo methods.. In doing this, we are firstly fitting a GARCH (we have tried GARCH(1,1), E-GARCH, Asymmetric GARCH, GJR-GARCH, ...) model in order to filter the return series.. We are encountering a problem here however, wherein our filtered return distribution is far less leptokurtic than the original one, even when we use e.g. Student T or Generalized Hyperbolic distributions for the innovations. Informally speaking, we feel the GARCH model is over-reactive and negatively affects the subsequent POT step.. Are we missing something here? Is it, in practice, better to use a simpler (e.g. EWMA) volatility model? Any insight is highly appreciated.. ...

The coalescent process is a widely used approach for inferring the demographic history of a population, from samples of its genetic diversity. Several parametric and non-parametric coalescent inference methods, involving Markov chain Monte Carlo, Gaussian processes, and other algorithms, already exist. However, these techniques are not always easy to adapt and apply, thus creating a need for alternative methodologies. We introduce the Bayesian Snyder filter as an easily implementable and flexible minimum mean square error estimator for parametric demographic functions on fixed genealogies. By reinterpreting the coalescent as a self-exciting Markov process, we show that the Snyder filter can be applied to both isochronously and heterochronously sampled datasets. We analytically solve the filter equations for the constant population size Kingman coalescent, derive expressions for its mean squared estimation error, and estimate its robustness to prior distribution specification. For populations with

Chemical reaction systems are typically regarded as having the Markov property -- they lack memory and their evolution depends only on their current state. Under a not-too-restrictive set of conditions, Markov chains will have a stationary distribution: the basic requirement seems to be that any state be reachable from any other in a finite number of steps. This seems like something that will generally be true for chemical systems, at least on the lattice of stoichiometrically-compatible states ...

The following work is devoted to investigation of the value chain of KFC company by analyzing its main peculiarities of functioning. The issue of value research papers on value chain analysis now obtains especial importance as companies try to win the rivalry and attract attention of a great number of customers. The term was introduced by Michael Porter and started its research papers on value chain analysis. Nowadays, under the term value essay writing for students 3rd edition john langan a set writing a good annotated bibliography activities which research papers on value chain analysis company performs in order to introduce a certain good to a market or a customer research papers on value chain analysis meant Manktelow, research papers on value chain analysis. Usually, using the term value chain a graduate school term paper format wants to describe the process research papers on value chain analysis advertising, manufacturing and peculiarities of delivery and image of a product.. That is why, ...

The Canary Islands have become a model region for evolutionary studies. We obtained 1.8 Kbp of mtDNA sequence from all known island forms of the endemic lizard genus Gallotia and from its sister taxon Psammodromus in order to reanalyze phylogenetic relationships within the archipelago, estimate lineage divergence times, and reconstruct the colonization history of this group. Well-supported phylogenies were obtained using maximum parsimony and Bayesian inference. Previous studies have been unable to establish the branching pattern at the base of the tree. We found evidence that G. stehlini (Gran Canaria) originated from the most basal Gallotia node and G. atlantica from the subsequent node. Divergence times were estimated under a global clock using Bayesian Markov Chain Monte Carlo methods implemented by three different programs: BEAST, MCMCTREE, MULTIDIVTIME. Node constraints were derived from subaerial island appearance data and were incorporated into the analyses as soft or hard maximal ...

Modern general-purpose speech recognition systems are based on Hidden Markov Models. These are statistical models that output a sequence of symbols or quantities. HMMs are used in speech recognition because a speech signal can be viewed as a piecewise stationary signal or a short-time stationary signal. In a short time-scale (e.g., 10 milliseconds), speech can be approximated as a stationary process. Speech can be thought of as a Markov model for many stochastic purposes. Another reason why HMMs are popular is because they can be trained automatically and are simple and computationally feasible to use. In speech recognition, the hidden Markov model would output a sequence of n-dimensional real-valued vectors (with n being a small integer, such as 10), outputting one of these every 10 milliseconds. The vectors would consist of cepstral coefficients, which are obtained by taking a Fourier transform of a short time window of speech and decorrelating the spectrum using a cosine transform, then ...

Two treatment regimens for malaria are compared in their abilities to cure and combat reinfection. Bayesian analysis techniques are used to compare two typical treatment therapies for uncomplicated malaria in children under five years, not only in their power to resist recrudescence, but also how long they can postpone recrudescence or reinfection in case of failure. We present a new way of analysing this type of data using Markov Chain Monte Carlo techniques. This is done using data from clinical trials at two different centres. The results which give the full posterior distributions show that artemisinin-based combination therapy is more efficacious than sulfadoxine-pyrimethamine. It both reduced the risk of recrudescence and delayed the time until recrudescence.. ...

Abstract: In this study, we introduce a novel machine learning model hidden Markov support vector machine for protein binding site prediction. The model treats the protein binding site prediction as a sequential labelling task based on the maximum margin criterion. Common features derived from protein sequences and structures, including protein sequence profile and residue accessible surface area, are used to train hidden Markov support vector machine. When tested on six data sets, the method based on hidden Markov support vector machine shows better performance than some state-of-the-art methods, including artificial neural networks, support vector machines and conditional random field. Furthermore, its running time is several orders of magnitude shorter than that of the compared methods.The improved prediction performance and computational efficiency of the method based on hidden Markov support vector machine can be attributed to the following three factors. Firstly, the relation between ...

This is part of the Quantifying Output Uncertainty in Models used for Climatic Change Research Seminars.. How can we tractably and rigorously combine data from observations and computationally expensive earth system models/simulators to infer past and future climate/earth system evolution with appropriate uncertainty estimation? I will present an evolving methodology that relies on brute force Markov Chain Monte Carlo sampling to generate a posterior distribution for model parameters given observational constraints. Bayesian artificial neural network emulators of the simulator provide computational tractability for such sampling. Through two concrete examples (reconstruction of deglacial ice sheet evolution and general circulation climate model calibration), I will illustrate the strengths and ongoing challenges in the application of the methodology, especially within the context of trying to quantify the structural contribution to uncertainty.. Contact [email protected] for more ...

Multiple linear regression and model building. Exploratory data analysis techniques, variable transformations and selection, parameter estimation and interpretation, prediction, Bayesian hierarchical models, Bayes factors and intrinsic Bayes factors for linear models, and Bayesian model averaging. The concepts of linear models from Bayesian and classical viewpoints. Topics in Markov chain Monte Carlo simulation introduced as required. Prerequisite: Statistical Science 611 and 601 or equivalent.. ...

A Bayesian meta-analysis method for studying cross-phenotype genetic associations. It uses summary-level data across multiple phenotypes to simultaneously measure the evidence of aggregate-level pleiotropic association and estimate an optimal subset of traits associated with the risk locus. CPBayes is based on a spike and slab prior and is implemented by Markov chain Monte Carlo technique Gibbs sampling.. ...

On November 6, the National Council on Disability (NCD) released a report titled Quality-Adjusted Life Years and the Devaluation of Life with Disability. The report details the use of quality-adjusted life years (QALYs) in the evaluation of treatment coverage. QALYs are based on the premise that the value of one year of the life of a person with a disability is less than the value of one year of the life of a person without a disability. The report recommends, among other things, prohibiting the use of QALYs in Medicare and Medicaid.. ...

The majority of automatic speech recognition (ASR) systems rely on hidden Markov models (HMM), in which the output distribution associated with each state is modelled by a mixture of diagonal covariance Gaussians. Dynamic information is typically included by appending time-derivatives to feature vectors. This approach, whilst successful, makes the false assumption of framewise independence of the augmented feature vectors and ignores the spatial correlations in the parametrised speech signal. This dissertation seeks to address these shortcomings by exploring acoustic modelling for ASR with an application of a form of state-space model, the linear dynamic model (LDM). Rather than modelling individual frames of data, LDMs characterize entire segments of speech. An auto-regressive state evolution through a continuous space gives a Markovian model of the underlying dynamics, and spatial correlations between feature dimensions are absorbed into the structure of the observation process. LDMs have been ...

Lipoproteins are of great interest in understanding the molecular pathogenesis of spirochaetes. Because spirochaete lipobox sequences exhibit more plasticity than those of other bacteria, application of existing prediction algorithms to emerging sequence data has been problematic. In this paper a novel lipoprotein prediction algorithm is described, designated SpLip, constructed as a hybrid of a lipobox weight matrix approach supplemented by a set of lipoprotein signal peptide rules allowing for conservative amino acid substitutions. Both the weight matrix and the rules are based on a training set of 28 experimentally verified spirochaetal lipoproteins. The performance of the SpLip algorithm was compared to that of the hidden Markov model-based LipoP program and the rules-based algorithm Psort for all predicted protein-coding genes of Leptospira interrogans sv. Copenhageni, L. interrogans sv. Lai, Borrelia burgdorferi, Borrelia garinii, Treponema pallidum and Treponema denticola. Psort sensitivity (13-35

BACKGROUND:Melioidosis is an infectious disease that is transmitted mainly through contact with contaminated soil or water, and exhibits marked seasonality in most settings, including Southeast Asia. In this study, we used mathematical modelling to examine the impacts of such demographic changes on melioidosis incidence, and to predict the disease burden in a developing country such as Thailand. METHODOLOGY/PRINCIPAL FINDINGS:A melioidosis infection model was constructed which included demographic data, diabetes mellitus (DM) prevalence, and melioidosis disease processes. The model was fitted to reported melioidosis incidence in Thailand by age, sex, and geographical area, between 2008 and 2015, using a Bayesian Markov Chain Monte Carlo (MCMC) approach. The model was then used to predict the disease burden and future trends of melioidosis incidence in Thailand. Our model predicted two-fold higher incidence rates of melioidosis compared with national surveillance data from 2015. The estimated incidence

In stochastic frontier analysis, firm-specific efficiencies and their distribution are often main variables of interest. If firms fall into several groups, it is natural to allow each group to have its own distribution. This paper considers a method for nonparametrically modelling these distributions using Dirichlet processes. A common problem when applying nonparametric methods to grouped data is small sample sizes for some groups which can lead to poor inference. Methods that allow dependence between each groups distribution are one set of solutions. The proposed model clusters the groups and assumes that the unknown distribution for each group in a cluster are the same. These clusters are inferred from the data. Markov chain Monte Carlo methods are necessary for model-fitting and efficient methods are described. The model is illustrated on a cost frontier application to US hospitals.. ...

Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian nonparametric noise model based on Dirichlet process mixtures is introduced. Efficient Markov chain Monte Carlo and Sequential Monte Carlo methods are then developed to perform optimal batch and sequential estimation in such contexts. The algorithms are applied to blind deconvolution and change point detection. Experimental results on synthetic and real data demonstrate the efficiency of this approach in various contexts.

This paper shows how to use adaptive particle filtering and Markov chain Monte Carlo methods to estimate quadratic term structure models (QTSMs) by likelihood inference. The procedure is applied to a quadratic model for the United States during the recent financial crisis.

Methods A compartmental mathematical Markov state model was used over a 20-year time horizon (1995-2015) to estimate the cost effectiveness of FSW targeted interventions, with a health system perspective. The incremental costs and effects of FSW targeted interventions were compared against a baseline scenario of mass media for the general population alone. The incremental cost-effectiveness ratio was computed at a 3% discount rate using HIV infections averted and disability-adjusted life-years (DALY) as benefit measures. It was assumed that the transmission of the HIV virus moves from a high-risk group (FSW) to the client population and finally to the general population (partners of clients). ...

Anopheles gambiae Gene finding parameters for FGENESH the program with parameters for major model organisms is available for on line usage at: http://www.softberry.com/berry.phtml?topic=gfind Method description: A new parameter set for gene prediction Anopheles gambiae is developed for FGENESH program. Accuracy of prediction of Plasmodium falciparum protein coding genes is about 98% on the nucleotide level. The FGENESH algorithm is based on pattern recognition of different types of signals and Markov chain models of coding regions. Optimal combination of these features is then found by dynamic programming and a set of gene models is constructed along given sequence. FGENESH is the fastest and most accurate ab initio gene prediction program available. Fgenesh output: fgenesh Tue Nov 5 16:23:15 EST 2002 FGENESH 1.1 Prediction of potential genes in Anopheles_gambiae genomic DNA Time : Tue Nov 5 16:23:16 2002 Seq name: Softberry SERVER PAST Sequence Length of sequence: 1542 Number of predicted genes ...

Breast cancer is the most common cancer among women in China. Amplification of the Human epidermal growth factor receptor type 2 (HER2) gene is present and overexpressed in 18-20% of breast cancers and historically has been associated with inferior disease-related outcomes. There has been increasing interest in de-escalation of therapy for low-risk disease. This study analyzes the cost-effectiveness of Doxorubicin/ Cyclophosphamide/ Paclitaxel/ Trastuzumab (AC-TH) and Docetaxel/Carboplatin/Trastuzumab(TCH) from payer perspective over a 5 year time horizon. A half-cycle corrected Markov model was built to simulate the process of breast cancer events and death occurred in both AC-TH and TCH armed patients. Cost data came from studies based on a Chinese hospital. One-way sensitivity analyses as well as second-order Monte Carlo and probabilistic sensitivity analyses were performed.The transition probabilities and utilities were extracted from published literature, and deterministic sensitivity analyses were

Life is extremely complex and amazingly diverse; it has taken billions of years of evolution to attain the level of complexity we observe in nature now and ranges from single-celled prokaryotes to multi-cellular human beings. With availability of molecular sequence data, algorithms inferring homology and gene families have emerged and similarity in gene content between two genes has been the major signal utilized for homology inference. Recently there has been a significant rise in number of species with fully sequenced genome, which provides an opportunity to investigate and infer homologs with greater accuracy and in a more informed way. Phylogeny analysis explains the relationship between member genes of a gene family in a simple, graphical and plausible way using a tree representation. Bayesian phylogenetic inference is a probabilistic method used to infer gene phylogenies and posteriors of other evolutionary parameters. Markov chain Monte Carlo (MCMC) algorithm, in particular using ...

Background: We describe an approach to estimating the cost-effectiveness of an intervention that changes health behaviour. The method captures the lifetime costs and benefits incurred by participants in an ongoing cluster-randomized controlled trial of an intervention that aims to change health behaviour. The existing literature only captures short-term economic and health outcomes. Methods: We develop a state-transition Markov model of how individuals move between different health behaviour states over time. We simulate hypothetical data to describe the costs and health benefits of the intervention, illustrate how the data collected in the ongoing randomized controlled trial can be used and demonstrate how incremental cost-effectiveness ratios are estimated. Results: On the basis of the simulated (i.e. hypothetical) data, we estimate the cost per quality-adjusted life year. The estimate reflects the lifetime health and economic consequences of the intervention. Discussion: The method used for ...

New Plasmodium falciparum finding Genes parameters for FGENESH the program with parameters for major model organisms, viruses and bacteria is available for on line usage at: http://www.softberry.com/berry.phtml?topic=gfind Method description: A new parameter set for gene prediction Plasmodium falciparum is developed for FGENESH program. Accuracy of prediction of Plasmodium falciparum protein coding genes is about 98% on the nucleotide level. Exact exon prediction accuracy ~80%. The FGENESH algorithm is based on pattern recognition of different types of signals and Markov chain models of coding regions. Optimal combination of these features is then found by dynamic programming and a set of gene models is constructed along given sequence. FGENESH is the fastest and most accurate ab initio gene prediction program available. Fgenesh output: fgenesh Wed Oct 30 23:05:15 EST 2002 FGENESH 1.1 Prediction of potential genes in Plasmodium genomic DNA Time : Wed Oct 30 23:05:15 2002 Seq name: MAL7P1.27 chr7 ...

TY - JOUR. T1 - A markov clustering based link clustering method to identify overlapping modules in protein-protein interaction networks. AU - Wang, Yan. AU - Wang, Guishen. AU - Meng, Di. AU - Huang, Lan. AU - Blanzieri, Enrico. AU - Cui, Juan. PY - 2016/4/1. Y1 - 2016/4/1. N2 - Previous studies indicated that many overlapping structures exist among the modular structures in protein-protein interaction (PPI) networks, which may reflect common functional components shared by different biological processes. In this paper, a Markov clustering based Link Clustering (MLC) method for the identification of overlapping modular structures in PPI networks is proposed. Firstly, MLC method calculates the extended link similarity and derives a similarity matrix to represent the relevance among the protein interactions. Then it employs markov clustering to partition the link similarity matrix and obtains overlapping network modules with significantly less parameters and threshold constraints compared to most ...

Gaussian processes provide a powerful Bayesian approach to many machine learning tasks. Unfortunately, their application has been limited by the cubic computational complexity of inference. Mixtures of Gaussian processes have been used to lower the computational costs and to enable inference on more complex data sets. In this thesis, we investigate a certain finite Gaussian process mixture model and its applicability to clustering and prediction tasks. We apply the mixture model on a multidimensional data set that contains multiple groups. We perform Bayesian inference on the model using Markov chain Monte Carlo. We find the predictive performance of the model satisfactory. Both the variances and the trends of the groups are estimated well, bar the issues caused by poor clustering. The model is unable to cluster some of the groups properly and we suggest improving the prior of the mixing proportions or incorporating more prior information as remedies for the issues in clustering ...

Identifying functional elements, such as transcriptional factor binding sites, is a fundamental step in reconstructing gene regulatory networks and remains a challenging issue, largely due to limited availability of training samples. We introduce a novel and flexible model, the O ptimized Mi xture Ma rkov model (OMiMa), and related methods to allow adjustment of model complexity for different motifs. In comparison with other leading methods, OMiMa can incorporate more than the NNSplices pairwise dependencies; OMiMa avoids model over-fitting better than the Permuted Variable Length Markov Model (PVLMM); and OMiMa requires smaller training samples than the Maximum Entropy Model (MEM). Testing on both simulated and actual data (regulatory cis-elements and splice sites), we found OMiMas performance superior to the other leading methods in terms of prediction accuracy, required size of training data or computational time. Our OMiMa system, to our knowledge, is the only motif finding tool that incorporates

The aim of this study was to assess the cost-effectiveness, from a health care perspective, of adding rituximab to fludarabine and cyclophosphamide scheme (FCR versus FC) for treatment-naïve and refractory/relapsed Ukrainian patients with chronic lymphocytic leukemia. A decision-analytic Markov cohort model with three health states and 1-month cycle time was developed and run within a life time horizon. Data from two multinational, prospective, open-label Phase 3 studies were used to assess patients survival. While utilities were generalized from UK data, local resource utilization and disease-associated treatment, hospitalization, and side effect costs were applied. The alternative scenario was performed to assess the impact of lower life expectancy of the general population in Ukraine on the incremental cost-effectiveness ratio (ICER) for treatment-naïve patients. One-way, two-way, and probabilistic sensitivity analyses were conducted to assess the robustness of the results. The ICER (in US ...

Advanced Statistics Assignment Help, Quality-adjusted survival analysis, Quality-adjusted survival analysis is a method for evaluating the effects of treatment on survival which allows the consideration of quality of life as well as the quantity of life. For instance, a highly toxic treatment with number of side effects

We present an application of ABS algorithms for multiple sequence alignment (MSA). The Markov decision process (MDP) based model leads to a linear programming problem (LPP), whose solution is linked to a suggested alignment. The important features of our work include the facility of alignment of multiple sequences simultaneously and no limit ...

Preface. 1. Introduction.. 1.1 Two Examples.. 1.1.1 Public School Class Sizes.. 1.1.2 Value at Risk.. 1.2 Observables, Unobservables, and Objects of Interest.. 1.3 Conditioning and Updating.. 1.4 Simulators.. 1.5 Modeling.. 1.6 Decisionmaking.. 2. Elements of Bayesian Inference.. 2.1 Basics.. 2.2 Sufficiency, Ancillarity, and Nuisance Parameters.. 2.2.1 Sufficiency.. 2.2.2 Ancillarity.. 2.2.3 Nuisance Parameters.. 2.3 Conjugate Prior Distributions.. 2.4 Bayesian Decision Theory and Point Estimation.. 2.5 Credible Sets.. 2.6 Model Comparison.. 2.6.1 Marginal Likelihoods.. 2.6.2 Predictive Densities.. 3. Topics in Bayesian Inference.. 3.1 Hierarchical Priors and Latent Variables.. 3.2 Improper Prior Distributions.. 3.3 Prior Robustness and the Density Ratio Class.. 3.4 Asymptotic Analysis.. 3.5 The Likelihood Principle.. 4. Posterior Simulation.. 4.1 Direct Sampling,.. 4.2 Acceptance and Importance Sampling.. 4.2.1 Acceptance Sampling.. 4.2.2 Importance Sampling.. 4.3 Markov Chain Monte ...

The hepatitis E virus (HEV) is the causative pathogen of hepatitis E, a global public health concern. HEV comprises 8 genotypes with a wide host range and geographic distribution. This study aims to determine the genetic factors influencing the molecular adaptive changes of HEV open reading frames (ORFs) and estimate the HEV origin and evolutionary history. Sequences of HEV strains isolated between 1982 and 2017 were retrieved and multiple analyses were performed to determine overall codon usage patterns, effects of natural selection and/or mutation pressure and host influence on the evolution of HEV ORFs. Besides, Bayesian Coalescent Markov Chain Monte Carlo (MCMC) Analysis was performed to estimate the spatial-temporal evolution of HEV. The results indicated an A/C nucleotide bias and ORF-dependent codon usage bias affected mainly by natural selection. The adaptation of HEV ORFs to their hosts was also ORF-dependent, with ORF1 and ORF2 sharing an almost similar adaptation profile to the different

Background It has been suggested that efforts to identify genetic risk markers of autism spectrum disorder (ASD) would benefit from the analysis of more narrowly defined ASD phenotypes. software program MCLINK, a Markov chain Monte Carlo (MCMC) method that allows for multilocus linkage analysis on large extended pedigrees. Results Genome-wide significance was observed for IS at 2q37.1-q37.3 (dominant model heterogeneity lod score (hlod) 3.42) and for RSMA at 15q13.1-q14 (recessive model hlod 3.93). We found some linkage signals that overlapped and others that were not observed in our previous linkage analysis of the ASD phenotype in the same pedigrees, and regions varied in the range of phenotypes with which they were linked. A new finding with respect to Is Apilimod supplier usually was that it is positively associated with IQ if the IS-RSMA correlation is usually statistically controlled. Conclusions The finding that Is usually and Apilimod supplier RSMA are linked to different regions that ...

Brownian download statistical physics of fracture breakdown and earthquake effects, Beautiful &, Markov Chain Monte Carlo, texts. topicsPerfumeOildoTerraNaturalYoung download statistical physics of fracture breakdown and earthquake effects of disorder: February 15, 2014. awesome Laboratories in Probability and Statistics.

Introduction: The Nature of Probability Theory. The Sample Space. Elements of Combinatorial Analysis. Fluctuations in Coin Tossing and Random Walks. Combination of Events. Conditional Probability. Stochastic Independence. The Binomial and Poisson Distributions. The Normal Approximation to the Binomial Distribution. Unlimited Sequences of Bernoulli Trials. Random Variables; Expectation. Laws of Large Numbers. Integral Valued Variables. Generating Functions. Compound Distributions. Branching Processes. Recurrent Events. Renewal Theory. Random Walk and Ruin Problems. Markov Chains. Algebraic Treatment of Finite Markov Chains. The Simplest Time-Dependent Stochastic Processes. Answers to Problems.William Feller is the author of An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition with ISBN 9780471257080 and ISBN 0471257087. [read more] ...

1. Suppose that shocks occur according to a Poisson process with rate A| 0. Also suppose that each shock independently causes the system to fail with probability 0 | p | 1. Let N denote the number of shocks that it takes for the.

With a lack of economic assessments of these interventions, the researchers conducted a cost-effectiveness analysis using a Markov model, a mathematical method for finding patterns and making predictions. Based on results from the Frontier of Renal Outcome Modifications in Japan (FROM-J) study, which found success in dietitian-led education and lifestyle advice, along with periodic check-ups, they projected how such intervention would perform economically.. Naturally, a host of factors, such as disease progression and drug costs, play into this complex modeling. Key here was whether the incremental cost-effectiveness ratio (ICER), which shows the unit cost of gaining 1 extra healthy life year among the patients via the intervention, gave sufficient worth for that amount. The estimated ICER of about US$1,324 per quality-adjusted life year (QALY) was compared with the suggested social willingness to pay about US$45,455 for a 1-QALY gain. This demonstrates considerable ...

Course Description A comprehensive introduction to calculus based probability. Basics: sample space, conditional probability, Bayes Theorem. Univariate distributions: mass functions and density, expectation and variance, binomial, Poisson, normal, and gamma distributions. Multivariate distributions: joint and conditional distribution, independence, transformation, multivariate normal and related distributions. Limit laws: probability inequalities, law of large numbers, central limit theorem. Monte Carlo (simulation) methods. Markov chains: transition probability, stationary distribution and convergence. Announcements Final Exam The final exam will be held in Science Center 222 on Wednesday, August 16th at 9:00. This 3 hour exam will be comprehensive, though will be weighted a bit towards material covered after the midterm. You may bring 2 pages of notes to the exam and a calculator. As with earlier exams, any tables that might be needed will be supplied with the exam. Exam Week Office Hours ...

In this paper, we present a novel method to explore semantically meaningful visual information and identify the discriminative spatiotemporal relationships between them for real-time activity recognition. Our approach infers human activities using continuous egocentric (first-person-view) videos of object manipulations in an industrial setup. In order to achieve this goal, we propose a random forest that unifies randomization, discriminative relationships mining and a Markov temporal structure. Discriminative relationships mining helps us to model relations that distinguish different activities, while randomization allows us to handle the large feature space and prevents over-fitting. The Markov temporal structure provides temporally consistent decisions during testing. The proposed random forest uses a discriminative Markov decision tree, where every nonterminal node is a discriminative classifier and the Markov structure is applied at leaf nodes. The proposed approach outperforms the ...

I dont have that book on me (I am saving up to get it!), but if you are mentioning this algorithm then it seems that the convergence rate is simply the convergence of the path to its stable distribution itself. Indeed, the proof in a nutshell is that the EM algorithm works for finding the steady state distribution is simply that the algorithm follows the actual path close enough to approximate the same distribution. Finding results about convergence rate and the like would be tough because it has adaptive timesteps and the like.. For an intuition on the rate of convergence of SDEs to their steady state distribution, you can look at Maos SDE book in Chapter 5. It seems as though solutions converge in p-norms exponentially (this tends to be a general property of Markov processes), but I might be mistaken.. For details on why the algorithm works, Mao has a paper on Euler methods for SDEs with Markovian Switching. Here he shows that the EM method converges with order 1/2 in the $L^2$ sense. The ...

South Africa has the largest worldwide HIV/AIDS population with 5.6 million people infected and at least 2 million people on antiretroviral therapy. The majority of these infections are caused by HIV-1 subtype C. Using genotyping methods we characterized HIV-1 subtypes of the gag p24 and pol PR and RT fragments, from a cohort of female participants in the Western Cape Province, South Africa. These participants were recruited as part of a study to assess the combined brain and behavioural effects of HIV and early childhood trauma. The partial HIV-1 gag and pol fragments of 84 participants were amplified by PCR and sequenced. Different online tools and manual phylogenetic analysis were used for HIV-1 subtyping. Online tools included: REGA HIV Subtyping tool version 3; Recombinant Identification Program (RIP); Context-based Modeling for Expeditious Typing (COMET); jumping profile Hidden Markov Models (jpHMM) webserver; and subtype classification using evolutionary algorithms (SCUEAL). HIV-1 subtype ...

The enzymatic O-18-labeling is a useful quantification technique to account for between-spectrum variability of the results of mass spectrometry experiments. One of the important issues related to the use of the technique is the problem of incomplete labeling of peptide molecules, which may result in biased estimates of the relative peptide abundance. In this manuscript, we propose a Markov-chain model, which takes into account the possibility of incomplete labeling in the estimation of the relative abundance from the observed data. This allows for the use of less precise but faster labeling strategies, which should better fit in the high-throughput proteomic framework. Our method does not require extra experimental steps, as proposed in the approaches developed by Mirgorodskaya et al. (2000), Lopez-Ferrer et al. (2006) and Rao et al. (2005), while it includes the model proposed by Eckel-Passow et al. (2006) as a special case. The method estimates information about the isotopic distribution ...

Background Plasmodium vivax continues to be the most widely distributed malarial parasite species in tropical and sub-tropical areas, causing high morbidity indices around the world. Better understanding of the proteins used by the parasite during the invasion of red blood cells is required to obtain an effective vaccine against this disease. This study describes characterizing the P. vivax asparagine-rich protein (PvARP) and examines its antigenicity in natural infection. Methods The target gene in the study was selected according to a previous in silico analysis using profile hidden Markov models which identified P. vivax proteins that play a possible role in invasion. Transcription of the arp gene in the P. vivax VCG-1 strain was here evaluated by RT-PCR. Specific human antibodies against PvARP were used to confirm protein expression by Western blot as well as its subcellular localization by immunofluorescence. Recognition of recombinant PvARP by sera from P. vivax-infected individuals was ...

Description: The course material changes with each occurrence of the course and may be taken for credit repeatedly with the instructors permission. Continuous time random processes, Kolmogorovs continuity theorem. Brownian Motion: the Donsker invariance principle, Holder continuity, quadratic variation. Continuous-time martingales and square integrable martingales. Markov processes and the strong Markov property. Properties of Brownian Motion: strong Markov property, Blumenthal zero-one law, Law of Iterated Logarithm. Stochastic integration with respect to continuous local martingales, Itos formula, Levys Characterization of Brownian motion, Girsanov transformation, Stochastic Differential Equations with Lipschitz Coefficients. Other topics in probability theory and stochastic processes at the choice of the instructor (e.g. connection to PDEs, local time, Skorokhods embedding theorem, zeros of the BM, empirical processes, concentration inequalities and applications in non-parametric ...

If you have a question about this talk, please contact Rachel Fogg.. Great technological and experimental advances have recently facilitated the imaging neural activity both in live animals. We describe a sequential Monte Carlo (SMC) expectation maximization algorithm that both infers the posterior distributions of the hidden states, and finds the maximum likelihood estimates of the parameters. Using such an approach enables us to (i) incorporate errorbars on the estimate of the hidden states, (ii) allow for nonlinearities in the observation and transition distributions, and (iii) consider Markov priors governing neural activity. This strategy works in real time for each observable neuron. We show how this method can condition the inferred spike trains on external stimuli, and achieve superresolution, i.e., infer not just whether a spike occurred within a stimulus frame, but when within that frame. Furthermore, our model has a relatively small number of parameters, and each of the parameters may ...

Rosss classic bestseller, Introduction to Probability Models, has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. It provides an introduction to elementary probability theory and stochastic processes, and shows how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries. A new section (3.7) on COMPOUND RANDOM VARIABLES, that can be used to establish a recursive formula for computing probability mass functions for a variety of common compounding distributions. A new section (4.11) on HIDDDEN MARKOV CHAINS, including the forward and backward approaches for computing the joint probability mass function of the signals, as well as the Viterbi algorithm for determining the most likely

Author: Körmann, F. et al.; Genre: Journal Article; Published in Print: 2010-04-19; Title: Rescaled Monte Carlo approach for magnetic systems: Ab initio thermodynamics of bcc iron

Bayesian survival model using Weibull regression on both scale and shape parameters. Dependence of shape parameter on covariates permits deviation from proportional-hazard assumption, leading to dynamic - i.e. non-constant with time - hazard ratios between subjects. Bayesian Lasso shrinkage in the form of two Laplace priors - one for scale and one for shape coefficients - allows for many covariates to be included. Cross-validation helper functions can be used to tune the shrinkage parameters. Monte Carlo Markov Chain (MCMC) sampling using a Gibbs wrapper around Radford Neals univariate slice sampler (R package MfUSampler) is used for coefficient estimation.. ...

This paper demonstrates how economic modelling can be used to derive estimates of the cost-effectiveness of prognostic markers in the management of clinically localised and moderately graded prostate cancer. The model uses a Markov process and is populated using published evidence and local data. The robustness of the results has been tested using sensitivity analysis. Three treatment policies of monitoring (observation), radical prostatectomy, or a selection-based management policy using DNA-ploidy as an experimental marker, have been evaluated. Modelling indicates that a policy of managing these tumours utilising experimental markers has an estimated cost per quality-adjusted life year (QALY) of pound 12 068. Sensitivity analysis shows the results to be relatively sensitive to quality-of-life variables. If novel and experimental markers can achieve specificity in excess of 80%, then a policy of radical surgery for those identified as being at high risk and conservative treatment for the remainder

This paper demonstrates how economic modelling can be used to derive estimates of the cost-effectiveness of prognostic markers in the management of clinically localised and moderately graded prostate cancer. The model uses a Markov process and is populated using published evidence and local data. The robustness of the results has been tested using sensitivity analysis. Three treatment policies of monitoring (observation), radical prostatectomy, or a selection-based management policy using DNA-ploidy as an experimental marker, have been evaluated. Modelling indicates that a policy of managing these tumours utilising experimental markers has an estimated cost per quality-adjusted life year (QALY) of pound 12 068. Sensitivity analysis shows the results to be relatively sensitive to quality-of-life variables. If novel and experimental markers can achieve specificity in excess of 80%, then a policy of radical surgery for those identified as being at high risk and conservative treatment for the remainder

Based on the concept of Kolmogorov complexity, algorithmic statistics in a form of a computer program is proposed as an unified way of computing unknown probabilistic or non-probabilistic dynamic structures of high frequency time series data. Popular model selection techniques, such as AIC, BIC and MDL, all are shown not algorithmic statistics due to their computational infeasibility. We then address a fundamental question: Is there an algorithmic statistic that can extract more computable information of dynamic structure than maximum likelihood approach can? We address this question by comparing two algorithmic statistics: Viterbi and Hierarchical Factor Segmentation (HFS) algorithms, for decoding state-space vector under Hidden Markov Model and beyond. We discuss how to apply HFS algorithm to resolve parametric/non-parametric change-point problems without prior knowledge of number of changes as an example of non-probabilistic dynamic structure. We present applications of HFS algorithm on ...