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5 - Computational Inference

from Part I - Concepts from Modeling, Inference, and Computing

Published online by Cambridge University Press:  17 August 2023

Steve Pressé
Affiliation:
Arizona State University
Ioannis Sgouralis
Affiliation:
University of Tennessee, Knoxville
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Summary

In this chapter we present computational Monte Carlo methods to sample from probability distributions, including Bayesian posteriors, that do not permit direct sampling. In doing so, we introduce the basis for Monte Carlo and Markov chain Monte Carlo sampling schemes and delve into specific methods. These include, at first, samplers such as the Metropolis–Hastings algorithms and Gibbs samplers and discuss the interpretation of the output of these samplers including the concept of burn-in and sample correlation. We also discuss more advanced sampling schemes including auxiliary variable samplers, multiplicative random walk samplers, and Hamiltonian Monte Carlo.

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Chapter
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Data Modeling for the Sciences
Applications, Basics, Computations
, pp. 163 - 212
Publisher: Cambridge University Press
Print publication year: 2023

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