## 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 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

## 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

## 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

## 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

## 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

## 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