Projection of a high-dimensional dataset onto a two-dimensional space is a useful tool to visualise structures and relationships in the dataset. However, a single two-dimensional visualisation may not display all the intrinsic structure. Therefore, hierarchical/multi-level visualisation methods have been used to extract more detailed understanding of the data. Here we propose a multi-level Gaussian process latent variable model (MLGPLVM). MLGPLVM works by segmenting data (with e.g. K-means, Gaussian mixture model or interactive clustering) in the visualisation space and then fitting a visualisation model to each subset. To measure the quality of multi-level visualisation (with respect to parent and child models), metrics such as trustworthiness, continuity, mean relative rank errors, visualisation distance distortion and the negative log-likelihood per point are used. We evaluate the MLGPLVM approach on the Oil Flow dataset and a dataset of protein electrostatic potentials for the Major ...

Understanding user behavior in software applications is of significant interest to software developers and companies. By having a better understanding of the user needs and usage patterns, the developers can design a more efficient workflow, add new features, or even automate the users workflow. In this thesis, I propose novel latent variable models to understand, predict and eventually automate the user interaction with a software application. I start by analyzing users clicks using time series models; I introduce models and inference algorithms for time series segmentation which are scalable to large-scale user datasets. Next, using deep generative models (e.g. conditional variational autoencoder) and some related models, I introduce a framework for automating the user interaction with a software application. I focus on photo enhancement applications, but this framework can be applied to any domain where segmentation, prediction and personalization is valuable. Finally, by combining ...

Items where Subject is "5. Quantitative Data Handling and Data Analysis , 5.10 Latent Variable Models , 5.10.7 Confirmatory factor analysis ...

Downloadable (with restrictions)! The multivariate probit model is very useful for analyzing correlated multivariate dichotomous data. Recently, this model has been generalized with a confirmatory factor analysis structure for accommodating more general covariance structure, and it is called the MPCFA model. The main purpose of this paper is to consider local influence analysis, which is a well-recognized important step of data analysis beyond the maximum likelihood estimation, of the MPCFA model. As the observed-data likelihood associated with the MPCFA model is intractable, the famous Cooks approach cannot be applied to achieve local influence measures. Hence, the local influence measures are developed via Zhu and Lees [Local influence for incomplete data model, J. Roy. Statist. Soc. Ser. B 63 (2001) 111-126.] approach that is closely related to the EM algorithm. The diagnostic measures are derived from the conformal normal curvature of an appropriate function. The building blocks are computed via a

At the crossroads between statistics and machine learning, probabilistic graphical models provide a powerful formal framework to model complex data. Probabilistic graphical models are probabilistic ... More. At the crossroads between statistics and machine learning, probabilistic graphical models provide a powerful formal framework to model complex data. Probabilistic graphical models are probabilistic models whose graphical components denote conditional independence structures between random variables. The probabilistic framework makes it possible to deal with data uncertainty while the conditional independence assumption helps process high dimensional and complex data. Examples of probabilistic graphical models are Bayesian networks and Markov random fields, which represent two of the most popular classes of such models. With the rapid advancements of high-throughput technologies and the ever decreasing costs of these next generation technologies, a fast-growing volume of biological data of ...

This MATLAB function returns a logical value (h) with the rejection decision from conducting a likelihood ratio test of model specification.

Downloadable! Monetary policy rule parameters are usually estimated at the mean of the interest rate distribution conditional on inflation and an output gap. This is an incomplete description of monetary policy reactions when the parameters are not uniform over the conditional distribution of the interest rate. I use quantile regressions to estimate parameters over the whole conditional distribution of the Federal Funds Rate. Inverse quantile regressions are applied to deal with endogeneity. Realtime data of inflation forecasts and the output gap are used. I find significant and systematic variations of parameters over the conditional distribution of the interest rate.

In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from probability + unit.[1] The purpose of the model is to estimate the probability that an observation with particular characteristics will fall into a specific one of the categories; moreover, classifying observations based on their predicted probabilities is a type of binary classification model. A probit model is a popular specification for an ordinal[2] or a binary response model. As such it treats the same set of problems as does logistic regression using similar techniques. The probit model, which employs a probit link function, is most often estimated using the standard maximum likelihood procedure, such an estimation being called a probit regression. ...

A Goodness-of-Fit Test for Multivariate Normal Distribution Using Modified Squared Distance - Multivariate normal distribution;goodness-of-fit test;empirical distribution function;modified squared distance;

Theory and lecture notes of Chi-square goodness-of-fit test all along with the key concepts of chi-square goodness-of-fit test, Interpreting the Claim. Tutorsglobe offers homework help, assignment help and tutors assistance on Chi-square goodness-of-fit test.

Analysis of potentially multimodal data is a natural application of finite mixture models. In this case, the modeling is complicated by the question of the variance for each of the components. Using identical variances for each component could obscure underlying structure, but the additional flexibility granted by component-specific variances might introduce spurious features. You can use PROC HPFMM to prepare analyses for equal and unequal variances and use one of the available fit statistics to compare the resulting models. You can use the model selection facility to explore models with varying numbers of mixture components-say, from three to seven as investigated in Roeder (1990). The following statements select the best unequal-variance model using Akaikes information criterion (AIC), which has a built-in penalty for model complexity: ...

As you have described it, there is not enough information to know how to conditional probability of the child from the parents. You have described that you have the marginal probabilities of each node; this tells you nothing about the relationship between nodes. For example, if you observed that 50% of people in a study take a drug (and the others take placebo), and then you later note that 20% of the people in the study had an adverse outcome, you do not have enough information to know how the probability of the child (adverse outcome) depends on the probability of the parent (taking the drug). You need to know the joint distribution of the parents and child to learn the conditional distribution. The joint distribution requires that you know the probability of the combination of all possible values for the parents and the children. From the joint distribution, you can use the definition of conditional probability to find the conditional distribution of the child on the parents.. ...

BACKGROUND: In addition to their use in detecting undesired real-time PCR products, melting temperatures are useful for detecting variations in the desired target sequences. Methodological improvements in recent years allow the generation of high-resolution melting-temperature (Tm) data. However, there is currently no convention on how to statistically analyze such high-resolution Tm data. RESULTS: Mixture model analysis was applied to Tm data. Models were selected based on Akaikes information criterion. Mixture model analysis correctly identified categories in Tm data obtained for known plasmid targets. Using simulated data, we investigated the number of observations required for model construction. The precision of the reported mixing proportions from data fitted to a preconstructed model was also evaluated. CONCLUSION: Mixture model analysis of Tm data allows the minimum number of different sequences in a set of amplicons and their relative frequencies to be determined. This approach allows Tm data

div class=share-contianer, ,ul class=social-icons social-icons-color custom-share-buttons, ,li, ,a href=https://www.facebook.com/sharer/sharer.php?u=https://ei.is.tuebingen.mpg.de/~janzing/janzingmzlzdss2012 onclick=popupCenter($(this).attr(href), , 580, 470); return false; class=popup social_facebook,,/a, ,!-- ,a href=https://www.facebook.com/sharer/sharer.php?s=100&p[title]=While conventional approaches to causal inference are mainly based on conditional (in)dependences, recent methods also account for the shape of (conditional) distributions. The idea is that the causal hypothesis "X causes Y" imposes that the marginal distribution PX and the conditional distribution PY,X represent independent mechanisms of nature. Recently it has been postulated that the shortest description of the joint distribution PX,Y should therefore be given by separate descriptions of PX and PY,X. Since description length in the sense of Kolmogorov complexity is uncomputable, practical implementations ...

Abstract: Estimating survival functions has interested statisticians for numerous years. A survival function gives information on the probability of a time-to-event of interest. Research in the area of survival analysis has increased greatly over the last several decades because of its large usage in areas related to biostatistics and the pharmaceutical industry. Among the methods which estimate the survival function, several are widely used and available in popular statistical software programs. One purpose of this research is to compare the efficiency between competing estimators of the survival function. Results are given for simulations which use nonparametric and parametric estimation methods on censored data. The simulated data sets have right-, left-, or interval-censored time points. Comparisons are done on various types of data to see which survival function estimation methods are more suitable. We consider scenarios where distributional assumptions or censoring type assumptions are ...

Longitudinal and time-to-event data are often observed together. Finite mixture models are currently used to analyze nonlinear heterogeneous longitudinal data, which, by releasing the homogeneity restriction of nonlinear mixed-effects (NLME) models, can cluster individuals into one of the pre-specified classes with class membership probabilities. This clustering may have clinical significance, and be associated with clinically important time-to-event data. This article develops a joint modeling approach to a finite mixture of NLME models for longitudinal data and proportional hazard Cox model for time-to-event data, linked by individual latent class indicators, under a Bayesian framework ...

I have some tips :. (1) How residuals ought to compare to fits isnt always all that obvious, so its good to be familiar with diagnostics for particular models. In logistic regression models, for example, the Hosmer-Lemeshow statistic is used to assess goodness of fit; leverage values tend to be small where the estimated odds are very large, very small or about even; & so on.. (2) Sometimes one family of models can be seen as a special case of another, so you can use a hypothesis test on a parameter to help you choose. Exponential vs Weibull, for example.. (3) Akaikes Information Criterion is useful in choosing between different models, which includes choosing between different families.. (4) Theoretical/empirical knowledge about what youre modelling narrows the field of plausible models.. But theres no automatic way of finding the right family; real-life data can come from distributions as complicated as you like, & the complexity of models that are worth trying to fit increases with the ...

The primary area of statistical expertise in the Qian-Li Xue Lab is the development and application of statistical methods for: (1) handling the truncation of information on underlying or unobservable outcomes (e.g., disability) as a result of screening, (2) missing data, including outcome (e.g., frailty) censoring by a competing risk (e.g., mortality) and (3) trajectory analysis of multivariate outcomes. Other areas of methodologic research interests include multivariate, latent variable models. In Womens Health and Aging Studies, we have closely collaborated with scientific investigators on the design and analysis of longitudinal data relating biomarkers of inflammation, hormonal dysregulation and micronutrient deficiencies to the development and progression of frailty and disability, as well as characterizing the natural history of change in cognitive and physical function over time.. Research Areas: epidemiology, disabilities, longitudinal data, hormonal dysregulation, womens health, ...

THE CHI-SQUARE GOODNESS-OF-FIT TEST The chi-square goodness-of-fit test is used to analyze probabilities of multinomial distribution trials along a single

Latent variable models have a broad set of applications in domains such as social networks, natural language processing, computer vision and computational biology. Training them on a large scale is challenging due to non-convexity of the objective function. We propose a unified framework that exploits tensor algebraic constraints of the (low order) moments of the models.

Parametric statistical methods are traditionally employed in functional magnetic resonance imaging (fMRI) for identifying areas in the brain that are active with a certain degree of statistical significance. These parametric methods, however, have two major drawbacks. First, it isassumed that the observed data are Gaussian distributed and independent; assumptions that generally are not valid for fMRI data. Second, the statistical test distribution can be derived theoretically only for very simple linear detection statistics. In this work it is shown how the computational power of the Graphics Processing Unit (GPU) can be used to speedup non-parametric tests, such as random permutation tests. With random permutation tests it is possible to calculate significance thresholds for any test statistics. As an example, fMRI activity maps from the General Linear Model (GLM) and Canonical Correlation Analysis (CCA) are compared at the same significance level.. ...

Sufficient replication within subpopulations is required to make the Pearson and deviance goodness-of-fit tests valid. When there are one or more continuous predictors in the model, the data are often too sparse to use these statistics. Hosmer and Lemeshow (2000) proposed a statistic that they show, through simulation, is distributed as chi-square when there is no replication in any of the subpopulations. This test is available only for binary response models. First, the observations are sorted in increasing order of their estimated event probability. The event is the response level specified in the response variable option EVENT= , or the response level that is not specified in the REF= option, or, if neither of these options was specified, then the event is the response level identified in the "Response Profiles" table as "Ordered Value 1". The observations are then divided into approximately 10 groups according to the following scheme. Let N be the total number of subjects. Let M be the ...

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentlers (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in ...

Mayo and Gray introduced the leverage residual-weighted elemental (LRWE) classification of regression estimators and a new method of estimation called trimmed elemental estimation (TEE), showing the efficiency and robustness of TEE point estimates. Using bootstrap methods, properties of various trimmed elemental estimator interval estimates to allow for inference are examined and estimates with ordinary least squares (OLS) and least sum of absolute values (LAV) are compared. Confidence intervals and coverage probabilities for the estimators using a variety of error distributions, sample sizes, and number of parameters are examined. To reduce computational intensity, randomly selecting elemental subsets to calculate the parameter estimates were investigated. For the distributions considered, randomly selecting 50% of the elemental regressions led to highly accurate estimates.

The aim of this thesis is to extend some methods of change-point analysis, where classically, measurements in time are examined for structural breaks, to random field data which is observed over a grid of points in multidimensional space. The thesis is concerned with the a posteriori detection and estimation of changes in the marginal distribution of such random field data. In particular, the focus lies on constructing nonparametric asymptotic procedures which take the possible stochastic dependence into account. In order to avoid having to restrict the results to specific distributional assumptions, the tests and estimators considered here use a nonparametric approach where the inference is justified by the asymptotic behavior of the considered procedures (i.e. their behavior as the sample size goes towards infinity). This behavior can often be derived from functional central limit theorems which make it possible to write the limit variables of the statistics as functionals of Wiener processes, ...

I am always struck by this same issue. Heres what I think is going on:. 1. What goes in a paper is up to the author. If the author struggled with a step or found it a bit tricky to think about themselves, then the struggle goes into the paper. Even if it might be obvious to someone with more experience in a field. I was just reading a paper with a very detailed exposition of EM for a latent logistic regression problem with conditional probability derivations, etc. (JMLR paper Learning from Crowds by Raykar et al., which is an awesome paper, even if it suffers from this flaw and number 3.). 2. What goes in a paper is up to editors. If the editors dont understand something, theyll ask for details, even if they should be obvious to the entire field. This is agreeing with Roberts point, I think. Editors like to see the author sweat, because of some kind of no-pain, no-gain esthetic that seems to permeate academic journal publishing. Its so hard to boil something down, then when you do, you get ...

By. G. Jogesh Babu and C.R. Rao, The Pennsylvania State University, University Park, USA. SUMMARY. Several nonparametric goodness-of-fit tests are based on the empirical distribution function. In the presence of nuisance parameters, the tests are generally constructed by first estimating these nuisance parameters. In such a case, it is well known that critical values shift, and the asymptotic null distribution of the test statistic may depend in a complex way on the unknown parameters. In this paper we use bootstrap methods to estimate the null distribution. We shall consider both parametric and nonparametric bootstrap methods. We shall first demonstrate that, under very general conditions, the process obtained by subtracting the population distribution function with estimated parameters from the empirical distribution has the same weak limit as the corresponding bootstrap version. Of course in the nonparametric bootstrap case a bias correction is needed. This result is used to show that the ...

We evaluate data on choices made from Convex Time Budgets (CTB) in Andreoni and Sprenger (2012a) and Augenblick et al (2015), two influential studies that proposed and applied this experimental technique. We use the Weak Axiom of Revealed Preference (WARP) to test for external consistency relative to pairwise choice, and demand, wealth and impatience monotonicity to test for internal consistency. We find that choices made by subjects in the original Andreoni and Sprenger (2012a) paper violate WARP frequently; violations of all three internal measures of monotonicity are concentrated in subjects who take advantage of the novel feature of CTB by making interior choices. Wealth monotonicity violations are more prevalent and pronounced than either demand or impatience monotonicity violations. We substantiate the importance of our desiderata of choice consistency in examining effort allocation choices made in Augenblick et al (2015), where we find considerably more demand monotonicity violations, as ...

Non-parametric smoothers can be used to test parametric models. Forms of tests: differences in in-sample performance; differences in generalization performance; whether the parametric models residuals have expectation zero everywhere. Constructing a test statistic based on in-sample performance. Using bootstrapping from the parametric model to find the null distribution of the test statistic. An example where the parametric model is correctly specified, and one where it is not. Cautions on the interpretation of goodness-of-fit tests. Why use parametric models at all? Answers: speed of convergence when correctly specified; and the scientific interpretation of parameters, if the model actually comes from a scientific theory. Mis-specified parametric models can predict better, at small sample sizes, than either correctly-specified parametric models or non-parametric smoothers, because of their favorable bias-variance characteristics; an example. Reading: Notes, chapter 10 Advanced Data Analysis ...

Get network security expert advice on VPN risk analysis and learn the risk estimation model necessary to assess SSL VPN implementation.

KernelMixtureDistribution[{x1, x2, ...}] represents a kernel mixture distribution based on the data values xi. KernelMixtureDistribution[{{x1, y1, ...}, {x2, y2, ...}, ...}] represents a multivariate kernel mixture distribution based on data values {xi, yi, ...}. KernelMixtureDistribution[..., bw] represents a kernel mixture distribution with bandwidth bw. KernelMixtureDistribution[..., bw, ker] represents a kernel mixture distribution with bandwidth bw and smoothing kernel ker.

Courvoisier, D. S., Eid, M., & Nussbeck, F. W. (2007). Mixture distribution latent state-trait analysis: Basic ideas and applications. Psychological Methods, 12(1), 80-104. doi:10.1037/1082-989X.12.1. ...

This talk will focus on the use of advanced multivariate latent variable models to aid the accelerated development of the product and the process, as

Motivated by problems in molecular biology and molecular physics, we propose a five-parameter torus analogue of the bivariate normal distribution for modelling the distribution of two circular random variables. The conditional distributions of the proposed distribution are von Mises. The marginal distributions are symmetric around their means and are either unimodal or bimodal. The type of shape d

The naive Bayes model is a simple model that has been used for many decades, often as a baseline, for both supervised and unsupervised learning. With a latent class variable it is one of the simplest latent variable models ...

The bootstrap method for estimating the standard error of the kappa statistic in the presence of clustered data is evaluated. depicted in a 2 Il1a × 2 table. Let denotes the number of subjects under study. Define and introduced by Cohen [1] is calculated as follows: of the kappa statistic can be estimated by method since bootstrap sampling is conducted on clusters only [24 25 26 In our study a cluster is a physician and observations within the cluster are patients. 2.2 Bootstrap sampling of clusters (physicians) 1. Assume that there are clusters (physicians) and they are indexed by {1 … clusters with replacement from the original data. The selected clusters are indexed by {1* 2 … * (= 1 … and … times to generate independent bootstrap samples Z1 … ZB. Calculate the kappa statistic corresponding to each bootstrap sample Zb following formula (1). Calculate bootstrap estimate by denotes bootstrap standard error estimate of is the 100(1 ? confidence interval following [23] with some ...

Solution for A joint probability density function is given by f(x,y) = x+y, 0|=x,y|=1. Find conditional expectation of y, given x = 0.5.

Zhang, X., Hauck, K. and Zhao, X. (2013), PATIENT SAFETY IN HOSPITALS - A BAYESIAN ANALYSIS OF UNOBSERVABLE HOSPITAL AND SPECIALTY LEVEL RISK FACTORS. Health Econ., 22: 1158-1174. doi: 10.1002/hec.2972 ...

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Hi, I have two DLM model specifications (x[t] and y[t] are univariate): MODEL1: y[t] = b[t]x[t]+e[t], e[t] ~ N(0,v1^2) b[t] = b[t-1]+eta[t], eta[t] ~ N(0,w1^2) MODEL2: y[t] = a[t]+e[t], e[t] ~ N(0,v2^2) a[t] = a[t-1]+eta[t], eta[t] ~ N(0,w2^2) I run the filter through data recursively to obtain state variables for each model. However, how do I know if b[t]x[t] in MODEL1 is different from MODEL2? In other words, how do I know if x[t] makes a difference in explaining dynamic of y[t]? Another question is that how do I compare MODEL1 and MODEL2? From model specification point of view, how can one say that MODEL1 is better than MODEL2? Any suggestion/reference would be greatly appreciated. Thank you. ac ...

The Object Management Group® (OMG®) is an international, open membership, not-for-profit technology standards consortium.. Founded in 1989, OMG standards are driven by vendors, end-users, academic institutions and government agencies. OMG Task Forces develop enterprise integration standards for a wide range of technologies and an even wider range of industries.. Learn More ...

Prediction models are increasingly used to complement clinical reasoning and decision making in modern medicine in general, and in the cardiovascular domain in particular. Developed models first and foremost need to provide accurate and (internally and externally) validated estimates of probabilities of specific health conditions or outcomes in targeted patients. The adoption of such models must guide physicians decision making and an individuals behaviour, and consequently improve individual outcomes and the cost-effectiveness of care. In a series of two articles we review the consecutive steps generally advocated for risk prediction model research. This first article focuses on the different aspects of model development studies, from design to reporting, how to estimate a models predictive performance and the potential optimism in these estimates using internal validation techniques, and how to quantify the added or incremental value of new predictors or biomarkers (of whatever type) to existing

Scatterplots of the count (z) against the covariates (Figure 2) showed that that some of the potential covariates were strongly correlated: vill and cvill; guard and patrol. There is little point in including both of these pairs, so we dropped vill and guard from the analysis.. In the first stage of the modelling several models were constructed using the covariates and the best model was selected. In the second stage dung counts were predicted over the area of interest.. We used a generalized additive model (GAM) approach. This type of modelling allows for smooth non-linear relationships between covariates and the dependent variable (dung counts). The modelling was done with S-plus software.. We started by fitting a full model that included all selected covariates. However some variables did not contribute significantly to the fit. To reduce the number of variables, an automated stepwise regression was used, using the Akaike Information Criterion (AIC) as the model selection criterion.. AIC is a ...

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TY - JOUR. T1 - Robust regression analysis for non-normal situations under symmetric distributions arising in medical research. AU - Ganguly, S. S.. PY - 2014. Y1 - 2014. N2 - In medical research, while carrying out regression analysis, it is usually assumed that the independent (covariates) and dependent (response) variables follow a multivariate normal distribution. In some situations, the covariates may not have normal distribution and instead may have some symmetric distribution. In such a situation, the estimation of the regression parameters using Tikus Modified Maximum Likelihood (MML) method may be more appropriate. The method of estimating the parameters is discussed and the applications of the method are illustrated using real sets of data from the field of public health.. AB - In medical research, while carrying out regression analysis, it is usually assumed that the independent (covariates) and dependent (response) variables follow a multivariate normal distribution. In some ...

Estimates non-Gaussian mixture models of case-control data. The four types of models supported are binormal, two component constrained, two component unconstrained, and four component. The most general model is the four component model, under which both cases and controls are distributed according to a mixture of two unimodal distributions. In the four component model, the two component distributions of the control mixture may be distinct from the two components of the case mixture distribution. In the two component unconstrained model, the components of the control and case mixtures are the same; however the mixture probabilities may differ for cases and controls. In the two component constrained model, all controls are distributed according to one of the two components while cases follow a mixture distribution of the two components. In the binormal model, cases and controls are distributed according to distinct unimodal distributions. These models assume that Box-Cox transformed case and ...

Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; Fall, 2007 Outline Statistical Models Structure of models in R Model Assessment (Part IA) Anova

Hi everyone, I have the following exercise: Given img.top {vertical-align:15%;} , a) Consider the following decomposition img.top {vertical-align:15%;}

Evaluation of model fit is an important step in any statistical modeling. When continuous covariates are present, classical Pearson and deviance goodness-of-fit tests to assess logistic or proportional odds model fit break down. We present in this paper an easy-to-implement SAS macro for testing goodness-of-fit for logistic or proportional odds model, when continuous covariates are present. Computational methods and program description are provided. Application of the macro is shown in a real clinical trial model testing. The macro presented can be readily called for immediate use and has been structured for easy modification ...

Understanding the impact of production, environmental exposure and age characteristics on the reliability of a population is frequently based on underlying science and empirical assessment. When there is incomplete science to prescribe which inputs should be included in a model of reliability to predict future trends, statistical model/variable selection techniques can be leveraged on a stockpile or population of units to improve reliability predictions as well as suggest new mechanisms affecting reliability to explore. We describe a five-step process for exploring relationships between available summaries of age, usage and environmental exposure and reliability. The process involves first identifying potential candidate inputs, then second organizing data for the analysis. Third, a variety of models with different combinations of the inputs are estimated, and fourth, flexible metrics are used to compare them. As a result, plots of the predicted relationships are examined to distill leading ...

The local dependence function is constant for the bivariate normal distribution. Here we identify all other distributions which also have constant local dependence. The key property is exponential family conditional distributions and a linear conditional mean. When given two marginal distributions only, this characterisation is not very helpful, and numerical solutions are necessary.. ...

High-dimensional regression problems which reveal dynamic behavior are typically analyzed by time propagation of a few number of factors. The inference on the whole system is then based on the low-dimensional time series analysis. Such highdimensional problems occur frequently in many different fields of science. In this paper we address the problem of inference when the factors and factor loadings are estimated by semiparametric methods. This more flexible modelling approach poses an important question: Is it justified, from inferential point of view, to base statistical inference on the estimated times series factors? We show that the difference of the inference based on the estimated time series and true unobserved time series is asymptotically negligible. Our results justify fitting vector autoregressive processes to the estimated factors, which allows one to study the dynamics of the whole high-dimensional system with a low-dimensional representation. We illustrate the theory with a ...

The paper presents a new concept of parallel bivariate marginal distribution algorithm using the stepping stone based model of communication with the unidirectional ring topology. The traditional migration of individuals is compared with a newly proposed technique of probability model migration. The idea of the new xBMDA algorithms is to modify the learning of classic probability model (applied in the sequential BMDA). In the first strategy, the adaptive learning of the resident probability model is used. The evaluation of pair dependency, using Pearsons chi-square statistics is influenced by the relevant immigrant pair dependency according to the quality of resident and immigrant subpopulation. In the second proposed strategy, the evaluation metric is applied for the diploid mode of the aggregated resident and immigrant subpopulation. Experimental results show that the proposed adaptive BMDA outperforms the traditional concept of individual migration ...

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Short answer: to know a MVN distribution you need to know the mean vector and the covariance matrix. If you dont know a distribution you cannot simulate from it. So you need to know the marginal variances (the diagonal of the covariance matrix). If you have those, you can form the covariance matrix and use rmvnorm or mvrnorm. If you are willing to assume they are one, you have the covariance (= correlation matrix). If you dont know the marginal variances the problem is incompletely specified. On Fri, 25 Jun 2004, Matthew David Sylvester wrote: , Hello, , I would like to simulate randomly from a multivariate normal distribution using a correlation , matrix, rho. I do not have sigma. I have searched the help archive and the R documentation as , well as doing a standard google search. What I have seen is that one can either use rmvnorm in , the package: mvtnorm or mvrnorm in the package: MASS. I believe I read somewhere that the latter , was more robust. I have seen conflicting (or at least ...

Video created by Universidad de Míchigan for the course Fitting Statistical Models to Data with Python. In this second week, well introduce you to the basics of two types of regression: linear regression and logistic regression. Youll get ...

Suryanarayana Employee health and safety are the areas of major the ability to enjoy leisure time and a sense of peace with the environment, preparedness the ability to over come or avoid emergencies. Hypothesis test: Age coefficient: Null hypothesis: B2 = 0, alternative hypothesis B2 ? 0 Given that the T statistics value > T critical value, then the null hypothesis is rejected, this means the age coefficient is statistically significant Constant value: Null hypothesis: a1 = 0, alternative hypothesis a1 ? 0 Given that the T statistics value > T critical value, then the null hypothesis is rejected, Alex Simring means the constant is statistically significant Multiple regressions: This section estimates a multiple regression model where age and gender are independent variables and health status is the dependent variable; Model specification; Models are specified with reference to existing theories, using our discussion on theories that depict the relationship status, Simring categories are ...

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Iranian Journal of Epidemiology covers all different fields of epidemiology, as a multidisciplinary science. The journal publish original articles form all divisions of Epidemiology in its diverse contexts & its primary focus is on clinical medicine, public health, and health care delivery.

Perception & Psychophysics 28, 7 (2), doi:.3758/pp Type I error rates and power analyses for single-point sensitivity measures Caren M. Rotello University of Massachusetts, Amherst, Massachusetts

An implementation of sequential testing that uses evidence ratios computed from the weights of a set of models. These weights correspond either to Akaike weights computed from the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) and following Burnham & Anderson (2004, ,doi:10.1177/0049124104268644,) recommendations, or to pseudo-BMA weights computed from the WAIC or the LOO-IC of models fitted with brms and following Yao et al. (2017, ,arXiv:1704.02030v3,).. ...

Author Summary In order to most effectively control the spread of an infectious disease, we need to better understand how pathogens spread within a host population, yet this is something we know remarkably little about. Cases close together in their locations and timing are often thought to be linked, but timings and locations alone are usually consistent with many different scenarios of who-infected-who. The genome of many pathogens evolves so quickly relative to the rate that they are transmitted, that even over single short epidemics we can identify which hosts contain pathogens that are most closely related to each other. This information is valuable because when combined with the spatial and timing data it should help us infer more reliably who-transmitted-to-who over the course of a disease outbreak. However, doing this so that these three different lines of evidence are appropriately weighted and interpreted remains a major statistical challenge. In our paper we present a new statistical method

Author Summary In order to most effectively control the spread of an infectious disease, we need to better understand how pathogens spread within a host population, yet this is something we know remarkably little about. Cases close together in their locations and timing are often thought to be linked, but timings and locations alone are usually consistent with many different scenarios of who-infected-who. The genome of many pathogens evolves so quickly relative to the rate that they are transmitted, that even over single short epidemics we can identify which hosts contain pathogens that are most closely related to each other. This information is valuable because when combined with the spatial and timing data it should help us infer more reliably who-transmitted-to-who over the course of a disease outbreak. However, doing this so that these three different lines of evidence are appropriately weighted and interpreted remains a major statistical challenge. In our paper we present a new statistical method

Vol 15: Gene set analysis methods: statistical models and methodological differences.. . Biblioteca virtual para leer y descargar libros, documentos, trabajos y tesis universitarias en PDF. Material universiario, documentación y tareas realizadas por universitarios en nuestra biblioteca. Para descargar gratis y para leer online.

Diagnostic accuracy can be improved considerably by combining multiple biomarkers. Although the likelihood ratio provides optimal solution to combination of biomarkers, the method is sensitive to distributional assumptions which are often difficult to justify. Alternatively simple linear combinations can be considered whose empirical solution may encounter intensive computation when the number of biomarkers is relatively large. Moreover, the optimal linear combinations derived under multivariate normality may suffer substantial loss of efficiency if the distributions are apart from normality. In this paper, we propose a new approach that linearly combines the minimum and maximum values of the biomarkers. Such combination only involves searching for a single combination coefficient that maximizes the area under the receiver operating characteristic (ROC) curves and is thus computation-effective. Simulation results show that the min-max combination may yield larger partial or full area under the ...

A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems a

Univariate linkage analysis is used routinely to localise genes for human complex traits. Often, many traits are analysed but the significance of linkage for each trait is not corrected for multiple trait testing, which increases the experiment-wise type-I error rate. In addition, univariate analyses do not realise the full power provided by multivariate data sets. Multivariate linkage is the ideal solution but it is computationally intensive, so genome-wide analysis and evaluation of empirical significance are often prohibitive. We describe two simple methods that efficiently alleviate these caveats by combining P-values from multiple univariate linkage analyses. The first method estimates empirical pointwise and genome-wide significance between one trait and one marker when multiple traits have been tested. It is as robust as an appropriate Bonferroni adjustment, with the advantage that no assumptions are required about the number of independent tests performed. The second method estimates the ...

I did an advanced search of all articles for "p value" and for "Akaike Information Criterion" (the most popular one), looking at 5-year intervals just to save me some time and to smooth out the year-to-year variation. I start when the AIC is first mentioned. For the prevalence of each, I end in 2003, since theres typically a 5-year lag before articles end up in JSTOR, and estimating the prevalence requires a good guess about the population size. For the ratio of the size of one group to the other, I go up through 2008, since this ratio does not depend an accurate estimate of the total number of articles. From 2004 to 2008, there are 4132 articles with "p value" and 927 with "Akaike Infomration Criterion," so the estimate of the ratio isnt going to be bad even with fewer articles available during this time ...

An introduction to the core ideas in probability and statistics. Computation of probabilities using, for instance, counting techniques and Bayes rule. Introduction to discrete and continuous random variables, joint and conditional distributions, expectation, variance and correlation, random sampling from populations, hypothesis tests and confidence intervals, and least squares ...

Descriptive statistics provide important information about variables to be analyzed. Mean, median, and mode measure central tendency of a variable. Measures of dispersion include variance, standard deviation, range, and interquantile range (IQR). Researchers may draw a histogram, stem-and-leaf plot, or box plot to see how a variable is distributed. Statistical methods are based on various underlying assumptions. One common assumption is that a random variable is normally distributed. In many statistical analyses, normality is often conveniently assumed without any empirical evidence or test. But normality is critical in many statistical methods. When this assumption is violated, interpretation and inference may not be reliable or valid. The t-test and ANOVA (Analysis of Variance) compare group means, assuming a variable of interest follows a normal probability distribution. Otherwise, these methods do not make much sense. Figure 1 illustrates the standard normal probability distribution and a ...

This paper documents the development and application of a general statistical methodology to assess the accuracy of baseline energy models, focusing on its application to Measurement and Verification (M&V) of whole--building energy savings. The methodology complements the principles addressed in resources such as ASHRAE Guideline 14 and the International Performance Measurement and Verification Protocol. It requires fitting a baseline model to data from a ``training period and using the model to predict total electricity consumption during a subsequent ``prediction period. We illustrate the methodology by evaluating five baseline models using data from 29 buildings. The training period and prediction period were varied, and model predictions of daily, weekly, and monthly energy consumption were compared to meter data to determine model accuracy. Several metrics were used to characterize the accuracy of the predictions, and in some cases the best--performing model as judged by one metric was ...

In this study, we will examine the Bayesian Dynamic Survival Models, time-varying coefficients models from a Bayesian perspective, and their applications in the aging setting. The specific questions we are interested in are: Do the relative importance of characteristics measured at a particular age, such as blood pressure, smoking, and body weight, with respect to heart diseases or death change as people age? If they do, how can we model the change? And, how does the change affect the analysis results if fixed-effect models are applied? In the epidemiological and statistical literature, the relationship between a risk factor and the risk of an event is often described in terms of the numerical contribution of the risk factor to the total risk within a follow-up period, using methods such as contingency tables and logistic regression models. With the development of survival analysis, another method named the Proportional Hazards Model becomes more popular. This model describes the relationship ...

Statistical models seem to be the sort that the most people are most familiar with. My note Does CO2 correlate with temperature arrives at a statistical model, for instance -- that for each 100 ppm CO2 rises, temperature rises by 1 K. Its an only marginally useful model, but useful enough to show a connection between the two variables, and an approximate order of magnitude of the size. As I mentioned then, this is not how the climate really is modelled. A good statistical model is the relationship between exercise and heart disease. A statistical model, derived from a long term study of people over decades, showed that the probability of heart disease declined as people did more aerobic exercise. Being statistical, it cant guarantee that if you walk 5 miles a week instead of 0 youll decrease your heart disease chances by exactly X%. But it does provide strong support that youre better off if you cover 5 miles instead of 0. Digressing a second: Same study was (and is still part of) the ...

Presents novel research in the field of statistical models for data analysis Offers statistical solutions for relevant problems Contains explicit

Exponential distribution [r]: Class of continuous probability distributions that describe the times between events in a Poisson process, i.e. a process in which events occur continuously and independently at a constant average rate. [e] ...

Evolutionary divergence of humans from chimpanzees likely occurred some 8 million years ago rather than the 5 million year estimate widely accepted by scientists, a new statistical model suggests.

I have this Joint Probability table: I need to figure out a) E[X] (given Y=30) b) E[Y] (given X=5) I have worked something out, Im not certain it is

The paper introduces a new simple semiparametric estimator of the conditional variance-covariance and correlation matrix (SP-DCC). While sharing a similar sequential approach to existing dynamic conditional correlation (DCC) methods, SP-DCC has the advantage of not requiring the direct parameterization of the conditional covariance or correlation processes, therefore also avoiding any assumption on their long-run target. In the proposed framework, conditional variances are estimated by univariate GARCH models, for actual and suitably transformed series, in the first step; the latter are then nonlinearly combined in the second step, according to basic properties of the covariance and correlation operator, to yield nonparametric estimates of the various conditional covariances and correlations. Moreover, in contrast to available DCC methods, SP-DCC allows for straightforward estimation also for the non-symultaneous case, i.e. for the estimation of conditional cross-covariances and correlations, displaced

Multivariate time series with definite harmonic structure is considered, in the special case when the marginal univariate time series are independent and asymptotically stationary to second order. The asymptotic distribution of the estimators of a harmonic component under $m$-dependence is found. ...

A semiparametric models combines parametric and nonparametric components, where the later are functions whose shapes are not confined to a low-dimensional family. Penalized splines model these nonparametric components using a fixed, pre-determined basis. Overfitting is prevented by a roughness penalty, and penalized splines include classical smoothing splines as a special case. A penalized splines can be viewed as a BLUP in a mixed model or as an empirical Bayes estimator. The mixed mixed viewpoint is especially convenient for applications because of its conceptual simplicity and because it allows use of readily available software ...

Estimates of the parameters in a linear model are considered based upon the minimization of a dispersion function of the residuals. The dispersion function used depends on Walsh averages of pairs of residuals. Results similar to those arising with signed rank statistics can be obtained as a special case. Trimming and weighting of the Walsh averages can occur with a suitable choice of dispersion function. Asymptotic properties of this type of dispersion function and its derivatives are developed and used to determine the large sample distribution of the estimates. Some discussion appears on the practical application of this methodology. (Author)*Walsh functions

Dear Experts, I need an example which will facilitate the programming of t-Statistics for the various regression coefficients in multiple regression. The specific part of this task that I am having...

Broadband semi-parametric estimation of long-memory time series by fractional exponential models.[Journal of Time Series Analysis,32(2),(2011),175-193]Narukawa, M. and Matsuda, Y ...

Explains the concepts and use of univariate Box-Jenkins/ARIMA analysis and forecasting through 15 case studies. Cases show how to build good ARIMA models in a step-by-step manner using real data. Also includes examples of model misspecification. Provides guidance to alternative models and discusses reasons for choosing one over another ...

Formalized rules for protein-protein interactions have recently been introduced to represent the binding and enzymatic activities of proteins in cellular signaling. Rules encode an understanding of how a system works in terms of the biomolecules in the system and their possible states and interactions. A set of rules can be as easy to read as a diagrammatic interaction map, but unlike most such maps, rules have precise interpretations. Rules can be processed to automatically generate a mathematical or computational model for a system, which enables explanatory and predictive insights into the systems behavior. Rules are independent units of a model specification that facilitate model revision. Instead of changing a large number of equations or lines of code, as may be required in the case of a conventional mathematical model, a protein interaction can be introduced or modified simply by adding or changing a single rule that represents the interaction of interest. Rules can be defined and ...

This function computes the bivariate marginal density function f(x_q, x_r) from a k-dimensional Truncated Multivariate Normal density function (k|=2).
The bivariate marginal density is obtained by integrating out (k-2) dimensions as proposed by Tallis (1961).
This function is basically an extraction of the Leppard and Tallis (1989) Fortran code for moments calculation,
but extended to the double truncated case.

123. semPLS - This package offers an implementation to fit structural equatation models (SEM) by the partial least squares (PLS) algorithm. The PLS approach is referred to as soft-modeling technique and requires no distributional assumptions on the observed data ...

The DatabaseConnector and SqlRender packages require Java. Java can be downloaded from http://www.java.com. Once Java is installed, ensure that Java is being pathed correctly. Under environment variables in the control panel, ensure that the jvm.dll file is added correctly to the path ...

Goodness-of-Fit Tests QTM1310/ Sharpe Goodness-of-Fit Tests Given the following… 1) Counts of items in each of several categories 2) A model that predicts the distribution of the relative frequencies …this question naturally arises:

View Notes - Lecture16 from AMS 312 at SUNY Stony Brook. AMS312 Spring_ 2010 April 19th Chapter 7 (Section 7.5): Two-sample problems: Review: Inference on two population means, paired samples: the

A method and system are presented in which statistical predictions are generated to indicate whether an individual has or will acquire an attribute designated in a query. The predictions are generated based on a first set of attributes associated with the individual and a second set of attribute combinations and statistical results that indicate the strength of association of each attribute combination with the query attribute.

After 33 volumes, Statistical Methodology will be discontinued as of 31st December 2016. At this point the possibility to submit manuscripts has been...

The precise contents of this course may vary from occasion to occasion, but will consist of selected themes of contemporary research interest in statistics methodology, depending on both demands from students and the availability of appropriate course leaders. Examples include parametric lifetime modelling, experimental design, extreme value statistics, advanced stochastic simulation, graphical modelling. The course will be of interest to students who want to develop their basic knowledge of statistics methodology. See the specific semester page for a more detailed description of the course.. Spring 2014: Parametric Lifetime Modeling. The course gives an introduction to modeling and statistical analysis of lifetimes, with emphasis on parametric models and estimation techniques, and applications in technical reliability and medicine. Topics in lifetime modeling include: the survival function; the hazard function; the mean residual life function, as well as different types of censoring of ...

The frequency of occurence of a given amplitude (or value) from a finite number of realizations of a random variable can be displayed by dividing the range of possible values of the random variables into a number of slots (or windows). Since all possible values are covered, each realization fits into only one window. For every realization a count is entered into the appropriate window. When all the realizations have been considered, the number of counts in each window is divided by the total number of realizations. The result is called the histogram (or frequency of occurence diagram). From the definitioin it follows immediately that the sum of the values of all the windows is exactly one. The shape of a histogram depends on the statistical distribution of the random variable, but it also depends on the total number of realizations, N, and the size of the slots ...

The frequency of occurence of a given amplitude (or value) from a finite number of realizations of a random variable can be displayed by dividing the range of possible values of the random variables into a number of slots (or windows). Since all possible values are covered, each realization fits into only one window. For every realization a count is entered into the appropriate window. When all the realizations have been considered, the number of counts in each window is divided by the total number of realizations. The result is called the histogram (or frequency of occurence diagram). From the definitioin it follows immediately that the sum of the values of all the windows is exactly one. The shape of a histogram depends on the statistical distribution of the random variable, but it also depends on the total number of realizations, N, and the size of the slots ...

A combination of exponential and log - logistic failure rate model is considered and named it as exponential log-logistic additive failure rate model. An attempt is made to present the distributional properties, estimation of parameters, testing of hypothesis and the power of likelihood ratio criterion about the proposed model.

Validation of risk predictions obtained from survival models and
competing risk models based on censored data using inverse weighting and
cross-validation.