Exact Markov Chain Monte Carlo with Likelihood Approximations for Functional Linear Models

Exact Markov Chain Monte Carlo with Likelihood Approximations for Functional Linear Models
Author: Corey James Smith
Publisher:
Total Pages:
Release: 2018
Genre: Bayesian statistical decision theory
ISBN:

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Functional data analysis is a branch of statistics that deals with the theory and analysis of data which may be comprised of functions in addition to scalar values. Here we consider the linear model that relates functional covariates to scalar responses. We introduce an exact MCMC algorithm which does not rely on likelihood evaluations to estimate the parameter function. The proposed method uses Barker's algorithm (as opposed to Metropolis-Hastings). Though Barker's has been shown to be asymptotically less efficient than Metropolis-Hastings, the form of its acceptance probability allows us to make the accept/reject decision efficiently without needing to evaluate the likelihood function. We utilize unbiased estimates of the log-likelihood function along with two nested Bernoulli factories to accomplish this. In addition, exact MCMC methods for logistic and Poisson regression settings with functional predictors are provided. These latter two models again feature Bernoulli factories and Barker's algorithm while also making use of debiasing techniques to aid in log-likelihood estimation.

Markov Chain Monte Carlo

Markov Chain Monte Carlo
Author: Dani Gamerman
Publisher: CRC Press
Total Pages: 342
Release: 2006-05-10
Genre: Mathematics
ISBN: 148229642X

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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 Simul

Monte Carlo Methods

Monte Carlo Methods
Author: Neal Noah Madras
Publisher: American Mathematical Soc.
Total Pages: 238
Release: 2000
Genre: Mathematics
ISBN: 0821819925

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This volume contains the proceedings of the Workshop on Monte Carlo Methods held at The Fields Institute for Research in Mathematical Sciences (Toronto, 1998). The workshop brought together researchers in physics, statistics, and probability. The papers in this volume - of the invited speakers and contributors to the poster session - represent the interdisciplinary emphasis of the conference. Monte Carlo methods have been used intensively in many branches of scientific inquiry. Markov chain methods have been at the forefront of much of this work, serving as the basis of many numerical studies in statistical physics and related areas since the Metropolis algorithm was introduced in 1953. Statisticians and theoretical computer scientists have used these methods in recent years, working on different fundamental research questions, yet using similar Monte Carlo methodology. This volume focuses on Monte Carlo methods that appear to have wide applicability and emphasizes new methods, practical applications and theoretical analysis. It will be of interest to researchers and graduate students who study and/or use Monte Carlo methods in areas of probability, statistics, theoretical physics, or computer science.

Handbook of Markov Chain Monte Carlo

Handbook of Markov Chain Monte Carlo
Author: Steve Brooks
Publisher: CRC Press
Total Pages: 620
Release: 2011-05-10
Genre: Mathematics
ISBN: 1420079425

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Since their popularization in the 1990s, Markov chain Monte Carlo (MCMC) methods have revolutionized statistical computing and have had an especially profound impact on the practice of Bayesian statistics. Furthermore, MCMC methods have enabled the development and use of intricate models in an astonishing array of disciplines as diverse as fisherie

Advanced Markov Chain Monte Carlo Methods

Advanced Markov Chain Monte Carlo Methods
Author: Faming Liang
Publisher: John Wiley & Sons
Total Pages: 308
Release: 2011-07-05
Genre: Mathematics
ISBN: 1119956803

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Markov Chain Monte Carlo (MCMC) methods are now an indispensable tool in scientific computing. This book discusses recent developments of MCMC methods with an emphasis on those making use of past sample information during simulations. The application examples are drawn from diverse fields such as bioinformatics, machine learning, social science, combinatorial optimization, and computational physics. Key Features: Expanded coverage of the stochastic approximation Monte Carlo and dynamic weighting algorithms that are essentially immune to local trap problems. A detailed discussion of the Monte Carlo Metropolis-Hastings algorithm that can be used for sampling from distributions with intractable normalizing constants. Up-to-date accounts of recent developments of the Gibbs sampler. Comprehensive overviews of the population-based MCMC algorithms and the MCMC algorithms with adaptive proposals. This book can be used as a textbook or a reference book for a one-semester graduate course in statistics, computational biology, engineering, and computer sciences. Applied or theoretical researchers will also find this book beneficial.

Introducing Monte Carlo Methods with R

Introducing Monte Carlo Methods with R
Author: Christian Robert
Publisher: Springer Science & Business Media
Total Pages: 297
Release: 2010
Genre: Computers
ISBN: 1441915753

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This book covers the main tools used in statistical simulation from a programmer’s point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison.

Markov Chain Monte Carlo Simulations and Their Statistical Analysis

Markov Chain Monte Carlo Simulations and Their Statistical Analysis
Author: Bernd A Berg
Publisher: World Scientific Publishing Company
Total Pages: 380
Release: 2004-10-01
Genre: Science
ISBN: 9813106379

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This book teaches modern Markov chain Monte Carlo (MC) simulation techniques step by step. The material should be accessible to advanced undergraduate students and is suitable for a course. It ranges from elementary statistics concepts (the theory behind MC simulations), through conventional Metropolis and heat bath algorithms, autocorrelations and the analysis of the performance of MC algorithms, to advanced topics including the multicanonical approach, cluster algorithms and parallel computing. Therefore, it is also of interest to researchers in the field. The book relates the theory directly to Web-based computer code. This allows readers to get quickly started with their own simulations and to verify many numerical examples easily. The present code is in Fortran 77, for which compilers are freely available. The principles taught are important for users of other programming languages, like C or C++.

Bayesian Filtering and Smoothing

Bayesian Filtering and Smoothing
Author: Simo Särkkä
Publisher: Cambridge University Press
Total Pages: 255
Release: 2013-09-05
Genre: Computers
ISBN: 110703065X

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A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.

Foundations of Linear and Generalized Linear Models

Foundations of Linear and Generalized Linear Models
Author: Alan Agresti
Publisher: John Wiley & Sons
Total Pages: 480
Release: 2015-01-15
Genre: Mathematics
ISBN: 1118730305

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A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding. The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. Focusing on the theoretical underpinnings of these models, Foundations ofLinear and Generalized Linear Models also features: An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods An overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problems Numerous examples that use R software for all text data analyses More than 400 exercises for readers to practice and extend the theory, methods, and data analysis A supplementary website with datasets for the examples and exercises An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.