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Markov Chain Monte Carlo

N. Thompson Hobbs and Mevin B. Hooten

in Bayesian Models: A Statistical Primer for Ecologists

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691159287
eISBN:
9781400866557
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159287.003.0007
Subject:
Biology, Ecology

This chapter explains how to implement Bayesian analyses using the Markov chain Monte Carlo (MCMC) algorithm, a set of methods for Bayesian analysis made popular by the seminal paper of Gelfand and ... More


A SURVEY ON THE USE OF MARKOV CHAINS TO RANDOMLY SAMPLE COLOURINGS

Alan Frieze and Eric Vigoda

in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.003.0004
Subject:
Mathematics, Probability / Statistics

In recent years, considerable progress has been made on the analysis of Markov chains for generating a random colouring of an input graph. These improvements have come in conjunction with refinements ... More


Inference

Jesper Møller

in New Perspectives in Stochastic Geometry

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199232574
eISBN:
9780191716393
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232574.003.0009
Subject:
Mathematics, Geometry / Topology

This contribution concerns statistical inference for parametric models used in stochastic geometry and based on quick and simple simulation free procedures as well as more comprehensive methods based ... More


Monte Carlo methods

Joseph F. Boudreau and Eric S. Swanson

in Applied Computational Physics

Published in print:
2017
Published Online:
February 2018
ISBN:
9780198708636
eISBN:
9780191858598
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198708636.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Monte Carlo methods are those designed to obtain numerical answers with the use of random numbers . This chapter discusses random engines, which provide a pseudo-random pattern of bits, and their use ... More


Bayesian computation (MCMC)

Ziheng Yang

in Molecular Evolution: A Statistical Approach

Published in print:
2014
Published Online:
August 2014
ISBN:
9780199602605
eISBN:
9780191782251
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199602605.003.0007
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies, Evolutionary Biology / Genetics

This chapter provides a detailed introduction to modern Bayesian computation. The Metropolis–Hastings algorithm is illustrated using a simple example of distance estimation between two sequences. A ... More


A primer on probabilistic inference

Thomas L. Griffiths and Alan Yuille

in The Probabilistic Mind:: Prospects for Bayesian cognitive science

Published in print:
2008
Published Online:
March 2012
ISBN:
9780199216093
eISBN:
9780191695971
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199216093.003.0002
Subject:
Psychology, Cognitive Psychology

This chapter provides the technical introduction to Bayesian methods. Probabilistic models of cognition are often referred to as Bayesian models, reflecting the central role that Bayesian inference ... More


Bayesian Theory and Applications

Paul Damien, Petros Dellaportas, Nicholas G. Polson, and David A. Stephens (eds)

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.001.0001
Subject:
Mathematics, Probability / Statistics

The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances ... More


Bayesian Models: A Statistical Primer for Ecologists

N. Thompson Hobbs and Mevin B. Hooten

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691159287
eISBN:
9781400866557
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159287.001.0001
Subject:
Biology, Ecology

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This book provides a comprehensive ... More


Bayesian Inference in Dynamic Econometric Models

Luc Bauwens, Michel Lubrano, and Jean-François Richard

Published in print:
2000
Published Online:
September 2011
ISBN:
9780198773122
eISBN:
9780191695315
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198773122.001.0001
Subject:
Economics and Finance, Econometrics

This book contains an up-to-date coverage of the last twenty years of advances in Bayesian inference in econometrics, with an emphasis on dynamic models. It shows how to treat Bayesian inference in ... More


Online Bayesian learning in dynamic models: an illustrative introduction to particle methods

Hedibert F Lopes and Carlos M Carvalho

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0011
Subject:
Mathematics, Probability / Statistics

This chapter provides a step-by-step review of Monte Carlo (MC) methods for filtering in general nonlinear and non-Gaussian dynamic models, also known as state-space models or hidden Markov models. ... More


Markov chain Monte Carlo methods in corporate finance

ARTHUR KORTEWEG

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0026
Subject:
Mathematics, Probability / Statistics

This chapter introduces Markov chain Monte Carlo (MCMC) methods and provides a hands-on guide to writing algorithms. It also illustrates some of the many applications of MCMC in corporate finance. ... More


Markov Chain Monte Carlo sampling of graphs

A.C.C. Coolen, A. Annibale, and E.S. Roberts

in Generating Random Networks and Graphs

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198709893
eISBN:
9780191780172
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198709893.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter looks at Markov Chain Monte Carlo techniques to generate hard- and soft-constrained exponential random graph ensembles. The essence is to define a Markov chain based on ergodic ... More


A brief guide to computer intensive statistics

Odo Diekmann, Hans Heesterbeek, and Tom Britton

in Mathematical Tools for Understanding Infectious Disease Dynamics

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691155395
eISBN:
9781400845620
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691155395.003.0015
Subject:
Biology, Disease Ecology / Epidemiology

Chapters 5, 13 and 14 presented methods for making inference about infectious diseases from available data. This is of course one of the main motivations for modeling: learning about important ... More


Modelling bivariate processes

Eric Renshaw

in Stochastic Population Processes: Analysis, Approximations, Simulations

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199575312
eISBN:
9780191728778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199575312.003.0007
Subject:
Mathematics, Applied Mathematics, Mathematical Biology

This chapter examines the general bivariate process, and illustrates the basic approaches involved by first developing a simple process for which the preceding methods of solution do carry across. ... More


Monte Carlo computational approaches in Bayesiancodon-substitution modelling

Nicolas Rodrigue and Nicolas Lartillot

in Codon Evolution: Mechanisms and Models

Published in print:
2012
Published Online:
May 2015
ISBN:
9780199601165
eISBN:
9780191810114
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:osobl/9780199601165.003.0004
Subject:
Biology, Evolutionary Biology / Genetics

This chapter reviews Markov Chain Monte Carlo (MCMC) approaches in codon-substitution modelling. It outlines the process of data analysis using the Bayesian framework. It describes the algorithms for ... More


Introduction

Paul Damien, Petros Dellaportas, Nicholas G. Polson, and David A. Stephens

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0034
Subject:
Mathematics, Probability / Statistics

This introductory chapter begins by noting how the three key ideas in this volume — hierarchical models, Markov chain Monte Carlo, and sequential Monte Carlo — that have revolutionized Bayesian ... More


Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

Ludwig Fahrmeir and Thomas Kneib

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199533022
eISBN:
9780191728501
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199533022.001.0001
Subject:
Mathematics, Probability / Statistics, Biostatistics

Several recent advances in smoothing and semiparametric regression are presented in this book from a unifying, Bayesian perspective. Simulation-based full Bayesian Markov chain Monte Carlo (MCMC) ... More


Inverse problems

Fox Colin, Haario Heikki, and Christen J Andrés

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0031
Subject:
Mathematics, Probability / Statistics

This chapter discusses the features that are characteristic for the problems most typically treated under the umbrella of inverse problems. It begins by listing representative examples of inverse ... More


Molecular Evolution: A Statistical Approach

Ziheng Yang

Published in print:
2014
Published Online:
August 2014
ISBN:
9780199602605
eISBN:
9780191782251
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199602605.001.0001
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies, Evolutionary Biology / Genetics

This book summarizes the statistical models and computational algorithms for comparative analysis of genetic sequence data in the fields of molecular evolution, molecular phylogenetics, and ... More


Frailty‐Induced Correlation *

Darrell Duffie

in Measuring Corporate Default Risk

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199279234
eISBN:
9780191728419
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199279234.003.0006
Subject:
Economics and Finance, Financial Economics

This chapter presents the foundations for frailty modeling of correlated default in a setting of stochastic intensities. The approach is to assume that default times are jointly doubly stochastic ... More


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