[PDF] Kernel Density Estimation Bayesian Inference And Random Effects Models eBook

Author : Benjamin Kedem
Publisher : World Scientific
Page : 199 pages
File Size : 40,29 MB
Release : 2017-01-24
Category : Mathematics
ISBN : 9813200200

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'The book provides a comprehensive review of the DRM approach to data fusion. It is well written and easy to follow, although the technical details are not trivial. The authors did an excellent job in making a concise introduction of the statistical techniques in data fusion. The book contains several real data … Overall, I found that the book covers an important topic and the DRM is a promising tool in this area. Researchers on data fusion will surely find this book very helpful and I will use this book in studying with my PhD students.'Journal of the American Statistical AssociationThis book comes up with estimates or decisions based on multiple data sources as opposed to more narrowly defined estimates or decisions based on single data sources. And as the world is awash with data obtained from numerous and varied processes, there is a need for appropriate statistical methods which in general produce improved inference by multiple data sources.The book contains numerous examples useful to practitioners from genomics. Topics range from sensors (radars), to small area estimation of body mass, to the estimation of small tail probabilities, to predictive distributions in time series analysis.

Author : Jihyeon Lee
Publisher :
Page : 0 pages
File Size : 13,91 MB
Release : 2022
Category : Statistics
ISBN :

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When we construct a Bayesian hierarchical model, we are required to specify a prior distribution. There are some considerations when specifying the prior distribution, such as prior misspecification, and this use of preliminary estimates. This dissertation proposes to constrain a Bayesian model on a ball centering at a preliminary estimate or the ball's complement (id est, disc). This approach extends the constrained Bayesian model in Bradley and Zong (2021) to consider the ball or the disc in specific inferential settings. In Chpater 2, we are motivated to estimate the change in the distribution of housing sale prices in the Manhattan housing market during the COVID-19 pandemic with strict COVID-19 guidelines and social distancing policies using individual transaction and property data from Zillow (ZTRAX). To improve the precision of the Dirichlet process mixture model (DPM) for density estimation, we adopt a constrained Bayes approach incorporating the kernel density estimator (KDE). Specifically, this approach constrains the joint support of the data and parameters in the DPM on either a set centered around a KDE or the complement of this set. When the KDE is a reasonable (as measured by the Kolmogorov-Smirnov statistic) preliminary estimator, we constrain the DPM to be close to the KDE and vice versa. We call our method the density-constrained Bayesian hierarchical model (D-CBHM). By doing so, we can simultaneously account for all sources of variability as well as incorporate preliminary information from the KDE. We demonstrate that the D-CBHM analytically (under reasonable conditions) and empirically outperforms the DPM in mean integrated squared error. We apply our method to our motivating dataset of Manhattan's home sales price and estimate how the COVID-19 pandemic changed the market in volume and distribution. In Chapter 3, we introduce the constrained Bayesian hierarchical model (CBM), which considers Bayesian models with both a noninformative and an informative prior distribution. Specifically, we constrain the joint support of the data and parameters in a noninformative Bayesian model on a ball centering at an informative posterior estimate, such as the posterior mean in the Bayesian model with an informative prior distribution or its complement. This approach incorporates prior sensitivity analysis by considering two different prior distributions. It also alleviates potential concerns related to prior misspecification but still uses the given prior information outside the Bayesian model whose support is constrained. We then prove that the constrained model outperforms the Bayesian model solely with the noninformative and the informative prior distributions in terms of mean squared error. In practice, the set which the Bayesian model is constrained on is determined based on the Kolmogorov-Smirnov statistic and the posterior expected mean squared error, and the Bayesian model whose support is constrained is determined based on the predictive accuracy measure such as Watanabe-Akaike information criterion. We show that the practical CBM empirically and generally outperforms the (unconstrained) Bayesian model. We apply the practical CBM to Genotype-Tissue Expression (GTEx) data to estimate the association between gene expressions and single nucleotide polymorphisms (SNPs).

Author : Anthony O'Hagan
Publisher : John Wiley & Sons
Page : 500 pages
File Size : 43,13 MB
Release : 2010-03-08
Category : Mathematics
ISBN : 0470685697

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Kendall's Advanced Theory of Statistics and Kendall's Library of Statistics The development of modern statistical theory in the past fifty years is reflected in the history of the late Sir Maurice Kenfall's volumes The Advanced Theory of Statistics. The Advanced Theory began life as a two-volume work, and since its first appearance in 1943, has been an indispensable source for the core theory of classical statistics. With Bayesian Inference, the same high standard has been applied to this important and exciting new body of theory.

Author : J.K. Ghosh
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 29,50 MB
Release : 2006-05-11
Category : Mathematics
ISBN : 0387226540

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This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. It will also appeal to statisticians in general. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian non-parametrics.

Author : Ming-Hui Chen
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 44,95 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461212766

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Dealing with methods for sampling from posterior distributions and how to compute posterior quantities of interest using Markov chain Monte Carlo (MCMC) samples, this book addresses such topics as improving simulation accuracy, marginal posterior density estimation, estimation of normalizing constants, constrained parameter problems, highest posterior density interval calculations, computation of posterior modes, and posterior computations for proportional hazards models and Dirichlet process models. The authors also discuss model comparisons, including both nested and non-nested models, marginal likelihood methods, ratios of normalizing constants, Bayes factors, the Savage-Dickey density ratio, Stochastic Search Variable Selection, Bayesian Model Averaging, the reverse jump algorithm, and model adequacy using predictive and latent residual approaches. The book presents an equal mixture of theory and applications involving real data, and is intended as a graduate textbook or a reference book for a one-semester course at the advanced masters or Ph.D. level. It will also serve as a useful reference for applied or theoretical researchers as well as practitioners.

Author : Catherine Chunling Liu
Publisher :
Page : 0 pages
File Size : 17,42 MB
Release : 2022
Category : Computers
ISBN :

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Random effects models have been widely used to analyze correlated data sets, and Bayesian techniques have emerged as a powerful tool to fit the models. However, there has been scarce literature that systematically reviews and summarizes the recent advances of Bayesian analyses of random effects models. This chapter reviews the use of the Dirichlet process mixture (DPM) prior to approximate the distribution of random errors within the general semiparametric random effects models with parametric random effects for longitudinal data setting and failure time setting separately. In a survival setting with clusters, we propose a new class of nonparametric random effects models which is motivated from the accelerated failure models. We employ a beta process prior to tact clustering and estimation simultaneously. We analyze a new data set integrated from Alzheimer,Äôs disease (AD) study to illustrate the presented model and methods.