Markov chain Monte Carlo in the last few decades has become a very popular class of algorithms for sampling from probability distributions based on constructing a Markov chain. A special case of the Markov chain Monte Carlo is the Gibbs sampling algorithm. This algorithm can be used in such a way that it takes into account the prior distribution and likelihood function, carrying a randomly generated variable through the calculation and the simulation. In this thesis, we use the Ising model for the prior of the binary images. Assuming the pixels in binary images are polluted by random noise, we build a Bayesian model for the posterior distribution of the true image data. The posterior distribution enables us to generate the denoised image by designing a Gibbs sampling algorithm.

In this paper, we present a new fast Motion Estimation (ME) algorithm based on Markov Chain Model (MEMCM). Spatial-temporal correlation of video sequence a

While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds. Incorporating changes in theory and highlighting new applications, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition presents a concise, accessible, and comprehensive introduction to the methods of this valuable simulation technique. The second edition includes access to an internet site that provides the code, written in R and WinBUGS, used in many of the previously existing and new examples and exercises. More importantly, the self-explanatory nature of the codes will enable modification of the inputs to the codes and variation on many directions will be available for further exploration. Major changes from the previous edition:. ¿ More examples with discussion of computational details in chapters on Gibbs sampling and ...

The computation of essential dynamics of molecular systems by conformation dynamics turned out to be very successful. This approach is based on Markov chain Monte Carlo simulations. Conformation dynamics aims at decomposing the state space of the system into metastable subsets. The set‐based reduction of a Markov chain, however, destroys the Markov property. We will present an alternative reduction method that is not based on sets but on membership vectors, which are computed by the Robust Perron Cluster Analysis (PCCA+). This approach preserves the Markov property. ...

The major drawback of Markov methods is that Markov diagrams for large systems are generally exceedingly large and complicated and difficult to construct. However, Markov models may be used to analyse smaller systems with strong dependencies requiring accurate evaluation. Other analysis techniques, such as fault tree analysis, may be used to evaluate large systems using simpler probabilistic calculation techniques. Large systems which exhibit strong component dependencies in isolated and critical parts of the system may be analysed using a combination of Markov analysis and simpler quantitative models.. The state transition diagram identifies all the discrete states of the system and the possible transitions between those states. In a Markov process the transition frequencies between states depends only on the current state probabilities and the constant transition rates between states. In this way the Markov model does not need to know about the history of how the state probabilities have ...

The recent advancement in array CGH (aCGH) research has significantly improved tumor identification using DNA copy number data. A number of unsupervised learning methods have been proposed for clustering aCGH samples. Two of the major challenges for developing aCGH sample clustering are the high spatial correlation between aCGH markers and the low computing efficiency. A mixture hidden Markov model based algorithm was developed to address these two challenges. The hidden Markov model (HMM) was used to model the spatial correlation between aCGH markers. A fast clustering algorithm was implemented and real data analysis on glioma aCGH data has shown that it converges to the optimal cluster rapidly and the computation time is proportional to the sample size. Simulation results showed that this HMM based clustering (HMMC) method has a substantially lower error rate than NMF clustering. The HMMC results for glioma data were significantly associated with clinical outcomes. We have developed a fast clustering

The talk will begin by reviewing methods of specifying continuous-time Markov chains and classical limit theorems that arise naturally for chemical network models. Since models arising in molecular biology frequently exhibit multiple state and time scales, analogous limit theorems for these models will be illustrated through simple examples ...

www.MOLUNA.de Linear Algebra, Markov Chains, and Queueing Models [4196258] - Perturbation Theory and Error Analysis.- Error bounds for the computation of null vectors with Applications to Markov Chains.- The influence of nonnormality on matrix computations.- Componentwise error analysis for stationary iterative methods.- The character of a finite Markov chain.- Gaussian elimination, perturbation theory, and Markov chains.- Iterative Methods.- Algorithms for

In this work, we present a novel multiscale texture model, and a related algorithm for the unsupervised segmentation of color images. Elementary textures are characterized by their spatial interactions with neighboring regions along selected directions. Such interactions are modeled in turn by means of a set of Markov chains, one for each direction, whose parameters are collected in a feature vector that synthetically describes the texture. Based on the feature vectors, the texture are then recursively merged, giving rise to larger and more complex textures, which appear at different scales of observation: accordingly, the model is named Hierarchical Multiple Markov Chain (H-MMC). The Texture Fragmentation and Reconstruction (TFR) algorithm, addresses the unsupervised segmen- tation problem based on the H-MMC model. The

The Markov assumption (MA) is fundamental to the empirical validity of reinforcement learning. In this paper, we propose a novel Forward-Backward Learning procedure to test MA in sequential decision making. The proposed test does not assume any parametric form on the joint distribution of the observed data and plays an important role for identifying the optimal policy in high-order Markov decision processes and partially observable MDPs. We apply our test to both synthetic datasets and a real data example from mobile health studies to illustrate its usefulness.. ...

In quantitative genetics, Markov chain Monte Carlo (MCMC) methods are indispensable for statistical inference in non-standard models like generalized linear models with genetic random effects or models with genetically structured variance heterogeneity. A particular challenge for MCMC applications in quantitative genetics is to obtain efficient updates of the high-dimensional vectors of genetic random effects and the associated covariance parameters. We discuss various strategies to approach this problem including reparameterization, Langevin-Hastings updates, and updates based on normal approximations. The methods are compared in applications to Bayesian inference for three data sets using a model with genetically structured variance heterogeneity. ...

Diagnostics and prognostics are two important aspects in a condition-based maintenance (CBM) program. However, these two tasks are often separately performed. For example, data might be collected and analysed separately for diagnosis and prognosis. This practice increases the cost and reduces the efficiency of CBM and may affect the accuracy of the diagnostic and prognostic results. In this paper, a statistical modelling methodology for performing both diagnosis and prognosis in a unified framework is presented. The methodology is developed based on segmental hidden semi-Markov models (HSMMs). An HSMM is a hidden Markov model (HMM) with temporal structures. Unlike HMM, an HSMM does not follow the unrealistic Markov chain assumption and therefore provides more powerful modelling and analysis capability for real problems. In addition, an HSMM allows modelling the time duration of the hidden states and therefore is capable of prognosis. To facilitate the computation in the proposed HSMM-based ...

An essential ingredient of the statistical inference theory for hidden Markov models is the nonlinear filter. The asymptotic properties of nonlinear filters have received particular attention in recent years, and their characterization has significant implications for topics such as the convergence of approximate filtering algorithms, maximum likelihood estimation, and stochastic control. Despite much progress in specific models, however, most of the general asymptotic theory of nonlinear filters has suffered from a recently discovered gap in the fundamental work of H. Kunita (1971). In this talk, I will show that this gap can be resolved in the general setting of weakly ergodic signals with nondegenerate observations by exploiting a surprising connection with the theory of Markov chains in random environments. These results hold for both discrete and continuous time models in Polish state spaces, and shed new light on the filter stability problem. In the non-ergodic setting I will argue that a ...

The evolutionary algorithm stochastic process is well-known to be Markovian. These have been under investigation in much of the theoretical evolutionary computing research. When mutation rate is positive, the Markov chain modeling an evolutionary algorithm is irreducible and, therefore, has a unique stationary distribution, yet, rather little is known about the stationary distribution. On the other hand, knowing the stationary distribution may provide some information about the expected times to hit optimum, assessment of the biases due to recombination and is of importance in population genetics to assess whats called a ``genetic load (see the introduction for more details). In this talk I will show how the quotient construction method can be exploited to derive rather explicit bounds on the ratios of the stationary distribution values of various subsets of the state space. In fact, some of the bounds obtained in the current work are expressed in terms of the parameters involved in all the ...

Earlier this week, my company, Lander Analytics, organized our first public Bayesian short course, taught by Andrew Gelman, Bob Carpenter and Daniel Lee. Needless to say the class sold out very quickly and left a long wait list. So we will schedule another public training (exactly when tbd) and will make the same course available for private training.. This was the first time we utilized three instructors (as opposed to a main instructor and assistants which we often use for large classes) and it led to an amazing dynamic. Bob laid the theoretical foundation for Markov chain Monte Carlo (MCMC), explaining both with math and geometry, and discussed the computational considerations of performing simulation draws. Daniel led the participants through hands-on examples with Stan, covering everything from how to describe a model, to efficient computation to debugging. Andrew gave his usual, crowd dazzling performance use previous work as case studies of when and how to use Bayesian methods.. It was an ...

We present an overview of the main methodological features and the goals of pharmacoeconomic models that are classified in three major categories: regression models, decision trees, and Markov models. In particular, we focus on Markov models and define a semi-Markov model on the cost utility of a vaccine for Dengue fever discussing the key components of the model and the interpretation of its results. Next, we identify some criticalities of the decision rule arising from a possible incorrect interpretation of the model outcomes. Specifically, we focus on the difference between median and mean ICER and on handling the willingness-to-pay thresholds. We also show that the life span of the model and an incorrect hypothesis specification can lead to very different outcomes. Finally, we analyse the limit of Markov model when a large number of states is considered and focus on the implementation of tools that can bypass the lack of memory condition of Markov models. We conclude that decision makers should

Clayton, D. (1996) Generalized Linear Mixed Models. In Gilks, W., et al., Eds., Markov Chain Monte Carlo in Practice, Chapman & Hall, London, 275-301.

Philosophers have been trying to understand in any branches of Artificial Intelligence since thousand years ago. Al in Bioscience was born combined with Bioinformatic and produces many kinds of research areas especially in computational problem. Hidden Markov Model is a powerful statistical tool for describing an event within hidden states (unknown condition), such as predictor for exon section at Deoxyribonucleic Acid (DNA) sequence. Number of states, transition probabilities and emission distributional oribabilities are 3 major elements of HMM. Hidden Markov Model used Forward-Backward algorithm and Viterbi algorithm for implementing the HMM basic problems and solutions, includes evaluation, training and testing. Whereas, all this functions has been planted in Single Board Computer as the embedded platform. The reason of choosing SBC was influenced by Open Source Software (OSS) development area ...

Abstract: This talk presents suffcient conditions for the existence of stationary optimal policies for average-cost Markov Decision Processes with Borel state and action sets and with weakly continuous transition probabilities. The one-step cost functions may be unbounded, and the action sets may be noncompact. The main contributions of this paper are: (i) general sufficient conditions for the existence of stationary discount-optimal and average-cost optimal policies and descriptions of properties of value functions and sets of optimal actions, (ii) a sufficient condition for the average-cost optimality of a stationary policy in the form of optimality inequalities, and (iii) approximations of average-cost optimal actions by discount-optimal actions ...

Chromosome Classification Using Continuous Hidden Markov Models - Up-to-date results on the application of Markov models to chromosome analysis are presented. On the one hand, this means using continuous Hidden Markov Models (HMMs) instead of discrete models. On the other hand, this also means to conduct empirical tests on the same large chromosome datasets that are currently used to evaluate state-ofthe-art classifiers. It is shown that the use of continuous HMMs allows to obtain error rates that are very close to those provided by the most accurate classifiers.

High-risk strategies would only have a modest effect on suicide prevention within a population. It is best to incorporate both high-risk and population-based strategies to prevent suicide. This study aims to compare the effectiveness of suicide prevention between high-risk and population-based strategies. A Markov chain illness and death model is proposed to determine suicide dynamic in a population and examine its effectiveness for reducing the number of suicides by modifying certain parameters of the model. Assuming a population with replacement, the suicide risk of the population was estimated by determining the final state of the Markov model. The model shows that targeting the whole population for suicide prevention is more effective than reducing risk in the high-risk tail of the distribution of psychological distress (i.e. the mentally ill). The results of this model reinforce the essence of the Rose theorem that lowering the suicidal risk in the population at large may be more effective than

Key concepts Markov chains Hidden Markov models Computing the probability of a sequence Estimating parameters of a Markov model Hidden Markov models States Emission and transition probabilities Parameter estimation Forward and backward algorithm Viterbi algorithm

AS Jean-Luc Jannink and Rohan L. Fernando (Jannink and Fernando 2004) nicely illustrated, when applying Markov chain Monte Carlo methods in a form where the dimension [the number of quantitative trait loci (QTL)] is not fixed, it can sometimes be hard to establish the correct form of the acceptance ratio for the proposals that are made. Therefore, as a safety precaution, the correct performance of the sampler should be checked also (under the prior model) without data.. We recently learned that Patrick Gaffney (Gaffney 2001) in his Ph.D. thesis had made essentially the same observation as Jannink and Fernando, correcting our mistake in Sillanpää and Arjas (1998). Somewhat earlier Vogl and Xu (2000) had expressed similar kinds of thoughts. As Gaffney (2001) explained, the acceptance ratio given in our article would correspond to an analysis, where an accelerated truncated Poisson prior (with a square term in the denominator) was assumed for the number of QTL, instead of an ordinary truncated ...

When system identification methods are used to construct mathematical models of real systems, it is important to collect data that reveal useful information about the systems dynamics. Experimental data are always corrupted by noise and this causes uncertainty in the model estimate. Therefore, design of input signals that guarantee a certain model accuracy is an important issue in system identification.. This thesis studies input design problems for system identification where time domain constraints have to be considered. A finite Markov chain is used to model the input of the system. This allows to directly include input amplitude constraints into the input model, by properly choosing the state space of the Markov chain. The state space is defined so that the model generates a binary signal. The probability distribution of the Markov chain is shaped in order to minimize an objective function defined in the input design problem.. Two identification issues are considered in this thesis: ...

We develop a new bidirectional algorithm for estimating Markov chain multi-step transition probabilities: given a Markov chain, we want to estimate the probability of hitting a given target state in $\ell$ steps after starting from a given source distribution. Given the target state $t$, we use a (reverse) local power iteration to construct an `expanded target distribution, which has the same mean as the quantity we want to estimate, but a smaller variance -- this can then be sampled efficiently by a Monte Carlo algorithm. Our method extends to any Markov chain on a discrete (finite or countable) state-space, and can be extended to compute functions of multi-step transition probabilities such as PageRank, graph diffusions, hitting/return times, etc. Our main result is that in `sparse Markov Chains -- wherein the number of transitions between states is comparable to the number of states -- the running time of our algorithm for a uniform-random target node is order-wise smaller than Monte Carlo ...

03/14/19 - We consider the recently proposed reinforcement learning (RL) framework of Contextual Markov Decision Processes (CMDP), where the ...

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Ellibs Ebookstore - Ebook: Markov Decision Processes: Discrete Stochastic Dynamic Programming - Author: Puterman, Martin L. - Price: 122,75€

In the runup to PyconUK 2014, I made the following ill-advised statement in an IRC channel: I feel like I should find something to talk about at PyconUK. I wish I had something interesting to talk about. Nine seconds later someone replied create a markov chain to generate a talk from the names of the talks at pycon and europython, then talk about how you did that, using a title it generates as the title of the talk.. Challenge accepted. This is that talk, admittedly one year late.. In this talk I will briefly describe Markov Chains as a means to simulate conversations and graph databases as a means to store Markov Chains. After this, I will discuss various considerations for creating interesting candidate responses in conversations, along with the challenges of too little and too much data. Finally, I will demonstrate my implementation and generate the title of this talk.. ...

Content characterization of sport videos is a subject of great interest to researchers working on the analysis of multimedia documents. In this paper, we propose a semantic indexing algorithm which uses both audio and visual information for salient event detection in soccer. The video signal is processed first by extracting low-level visual descriptors directly from an MPEG-2 bitstream. It is assumed that any instance of an event of interest typically affects two consecutive shots and is characterized by a different temporal evolution of the visual descriptors in the two shots. This motivates the introduction of a controlled Markov chain to describe such evolution during an event of interest, with the control input modeling the occurrence of a shot transition. After adequately training different controlled Markov chain models, a list of video segments can be extracted to represent a specific event of interest using the maximum likelihood criterion. To reduce the presence of false alarms, ...

Atomistic simulations have the potential to elucidate the molecular basis of biological processes such as protein misfolding in Alzheimers disease or the conformational changes that drive transcription or translation. However, most simulations can only capture the nanosecond to microsecond timescale, whereas most biological processes of interest occur on millisecond and longer timescales. Also, even with an infinitely fast computer, extracting meaningful insight from simulations is difficult because of the complexity of the underlying free energy landscapes. Fortunately, Markov State Models (MSMs) can help overcome these limitations.. MSMs may be used to model any random process where the next state depends solely on the current state. For example, imagine exploring New York City by rolling a die to randomly select which direction to go in each time you came to an intersection. Such a process could be described by an MSM with a state for each intersection. Each state might have a probability of ...

Read the book An Introduction To Markov State Models And Their Application To Long Timescale Molecular Simulation by Gregory R. Bowman ; Vijay S. Pande ; Frank Noé, Ed online or Preview the book. Please wait while, the book is loading ...

In this article, we present a modification of the popular Bayesian clustering program STRUCTURE (Pritchard et al. 2000) for inferring population substructure and self-fertilization simultaneously. Using extensive simulations with four distinct demographic models (K = 1, 2, 3, 6), we demonstrate that our method can accurately estimate selfing rates in the presence of population structure in the data. Additionally it can classify individuals into their appropriate subpopulations without the assumption of Hardy-Weinberg equilibrium within subpopulations.. It is important to note that the accuracy of selfing rate estimation is influenced by multiple factors, including sample size and number of loci, with decreased precision when they are small, as is illustrated in Table 2. Likewise, we find that the complexity of the true demographic history underlying data (e.g., the number of subpopulations derived from a common ancestral population) also influences accuracy. In general, more complicated models ...

Hi. For a project I am using a Markov Chain model with 17 states. I have used data to estimate transition probabilities. From these transition

Downloadable (with restrictions)! While the literature has established that there is substantial and highly selective return migration, the growing importance of repeat migration has been largely ignored. Using Markov chain analysis, this paper provides a modeling framework for repeated moves of migrants between the host and home countries. The Markov transition matrix between the states in two consecutive periods is parameterized and estimated using a logit specification and a large panel data with 14 waves. The analysis for Germany, the largest European immigration country, shows that more than 60% of the migrants are indeed repeat migrants. The out-migration per year is low, about 10%. Migrants are more likely to leave again early after their arrival in Germany, and when they have social and familial bonds in the home country, but less likely when they have a job in Germany and speak the language well. Once out-migrated from Germany, the return probability is about 80% and guided mainly by

The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant additivity properties: (i) existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii) existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i) and (ii) are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the Markov order). The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally most random distributions ...

Designers often search for new solutions by iteratively adapting a current design. By engaging in this search, designers not only improve solution quality but also begin to learn what operational patterns might improve the solution in future iterations. Previous work in psychology has demonstrated that humans can fluently and adeptly learn short operational sequences that aid problem-solving. This paper explores how designers learn and employ sequences within the realm of engineering design. Specifically, this work analyzes behavioral patterns in two human studies in which participants solved configuration design problems. Behavioral data from the two studies is first analyzed using Markov chains to determine how much representation complexity is necessary to quantify the sequential patterns that designers employ during solving. It is discovered that first-order Markov chains are capable of accurately representing designers sequences. Next, the ability to learn first-order sequences is ...

0040] FIG. 1 shows a schematic diagram of a sequence generator 100 according to an embodiment. In particular, FIG. 1 shows the details of a processing part 10 of the sequence generator 100 (e.g. a processor or other suitable processing part). The sequence generator 100 creates a non-homogenous Markov process M that generates sequences, wherein each sequence has a finite length L, comprises items from a set of a specific number n of items, and satisfies one or more control constraints specifying one or more requirements on the sequence. As an example, at least one of the control constraints can require a specific item to be at a specific position within the sequence, or can require a specific transition between two positions within the sequence. Each sequence can for example comprise items of music notes, text components or drawings, or any other suitable type of items. The sequence generator 100 comprises a Markov process unit 11 adapted to provide data defining an initial Markov process M of a ...

We present a discriminative learning method for pattern discovery of binding sites in nucleic acid sequences based on hidden Markov models. Sets of positive and negative example sequences are mined for sequence motifs whose occurrence frequency varies between the sets. The method offers several objective functions, but we concentrate on mutual information of condition and motif occurrence. We perform a systematic comparison of our method and numerous published motif-finding tools. Our method achieves the highest motif discovery performance, while being faster than most published methods. We present case studies of data from various technologies, including ChIP-Seq, RIP-Chip and PAR-CLIP, of embryonic stem cell transcription factors and of RNA-binding proteins, demonstrating practicality and utility of the method. For the alternative splicing factor RBM10, our analysis finds motifs known to be splicing-relevant. The motif discovery method is implemented in the free software package Discrover. It ...

Free The Markov Chain Algorithm Download,The Markov Chain Algorithm 1.2 is A classic algorithm which can produce entertaining output, given a sufficiently

Markov Chains, part I December 8, Introduction A Markov Chain is a sequence of random variables X 0, X 1,, where each X i S, such that P(X i+1 = s i+1 X i = s i, X i 1 = s i 1,, X 0 = s 0 ) = P(X

We study asynchronous SSMA communication systems using binary spreading sequences of Markov chains and prove the CLT (central limit theorem) for the empirical distribution of the normalized MAI (multiple-access interference). We also prove that the distribution of the normalized MAI for asynchronous systems can never be Gaussian if chains are irreducible and aperiodic. Based on these results, we propose novel theoretical evaluations of bit error probabilities in such systems based on the CLT and compare these and conventional theoretical estimations based on the SGA (standard Gaussian approximation) with experimental results. Consequently we confirm that the proposed theoretical evaluations based on the CLT agree with the experimental results better than the theoretical evaluations based on the SGA. Accordingly, using the theoretical evaluations based on the CLT, we give the optimum spreading sequences of Markov chains in terms of bit error probabilities. ...

Linear Models and Markov Chain MBA Assignment Help, Online MBA Assignment Writing Service and Homework Help Linear Models and Markov Chain Assignment Help Linear models explain a constant reaction variable as a function of several predictor variables. They can he

TY - BOOK. T1 - Limiting conditional distributions for transient Markov chains on the nonnegative integers conditioned on recurrence to zero. AU - Coolen-Schrijner, Pauline. PY - 1994. Y1 - 1994. KW - METIS-142900. M3 - Report. T3 - Memorandum Faculty of Mathematical Sciences. BT - Limiting conditional distributions for transient Markov chains on the nonnegative integers conditioned on recurrence to zero. PB - University of Twente, Faculty of Mathematical Sciences. ER - ...

Artificial Intelligence has made tremendous progress in industry in terms of problem solving pattern recognition. Mirror neuron systems (MNS), a new branch in intention recognition, has been successful in human robot interface, but with some limitations. First, it is a cognitive function in relation to the basic research limited. Second, it lacks an experimental paradigm. Therefore MNS requires a firm mathematical modeling. If we design engineering modeling based on mathematical, we will be able to apply mirror neuron system to brain-computer interface. This paper proposes a hybrid model-based classification of the action for brain-computer interface, a combination of Hidden Markov Model and Gaussian Mixture Model. Both models are possible to collect specific information. This hybrid model has been compared with Hidden Markov Model-based classification. The recognition rates achieved by Hidden Markov Model were 76.62% and the proposed model showed 84.38 ...

TY - GEN. T1 - Contextual Image Segmentation based on AdaBoost and Markov Random Fields. AU - Nishii, Ryuei. PY - 2003. Y1 - 2003. N2 - AdaBoost, one of machine learning algorithms, is employed for classification of land-cover categories of geostatistical data. We assume that the posterior probability is given by the odds ratio due to loss functions. Further, landcover categories are assumed to follow Markov random fields (MRF). Then, we derive a classifier by combining two posteriors based on AdaBoost and MRF through the iterative conditional modes. Our procedure is applied to benchmark data sets provided by IEEE GRSS Data Fusion Committee and shows an excellent performance.. AB - AdaBoost, one of machine learning algorithms, is employed for classification of land-cover categories of geostatistical data. We assume that the posterior probability is given by the odds ratio due to loss functions. Further, landcover categories are assumed to follow Markov random fields (MRF). Then, we derive a ...

The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity computation reduces to finding a model of a specification with highest entropy. Entropy maximization for probabilistic process specifications has not been studied before, even though it is well known in Bayesian inference for discrete distributions. We give a characterization of global entropy of a process as a reward function, a polynomial algorithm to verify the existence of a system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the

Background:Natural history models of breast cancer progression provide an opportunity to evaluate and identify optimal screening scenarios. This paper describes a detailed Markov model characterising breast cancer tumour progression.Methods:Breast cancer is modelled by a 13-state continuous-time Markov model. The model differentiates between indolent and aggressive ductal carcinomas in situ tumours, and aggressive tumours of different sizes. We compared such aggressive cancers, that is, which are non-indolent, to those which are non-growing and regressing. Model input parameters and structure were informed by the 1978-1984 Ostergotland county breast screening randomised controlled trial. Overlaid on the natural history model is the effect of screening on diagnosis. Parameters were estimated using Bayesian methods. Markov chain Monte Carlo integration was used to sample the resulting posterior distribution.Results:The breast cancer incidence rate in the Ostergotland population was 21 (95% CI: ...

Title: Approximate conditional independence of separated subtrees and phylogenetic inference Abstract: Bayesian methods to reconstruct evolutionary trees from aligned DNA sequence data from different species depend on Markov chain Monte Carlo sampling of phylogenetic trees from a posterior distribution. The probabilities of tree topologies are typically estimated with the simple relative frequencies of the trees in the sample. When the posterior distribution is spread thinly over a very large number of trees, the simple relative frequencies from finite samples are often inaccurate estimates of the posterior probabilities for many trees. We present a new method for estimating the posterior distribution on the space of trees from samples based on the approximation of conditional independence between subtrees given their separation by an edge in the tree. This approximation procedure effectively spreads the estimated posterior distribution from the sampled trees to the larger set of trees that ...

Title: Approximate conditional independence of separated subtrees and phylogenetic inference Abstract: Bayesian methods to reconstruct evolutionary trees from aligned DNA sequence data from different species depend on Markov chain Monte Carlo sampling of phylogenetic trees from a posterior distribution. The probabilities of tree topologies are typically estimated with the simple relative frequencies of the trees in the sample. When the posterior distribution is spread thinly over a very large number of trees, the simple relative frequencies from finite samples are often inaccurate estimates of the posterior probabilities for many trees. We present a new method for estimating the posterior distribution on the space of trees from samples based on the approximation of conditional independence between subtrees given their separation by an edge in the tree. This approximation procedure effectively spreads the estimated posterior distribution from the sampled trees to the larger set of trees that ...