Honest Exploration of Intractable Probability Distributions via Markov Chain Monte Carlo

By Galin L. Jones, James P. Hobert. 2001

335 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3cc6c2774e9bd8a4f8fdda8e352a0ee268708a5b

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Citations in the corpus

The Markov chain Monte Carlo revolution (2008, background): “A splendid introduction to Harris recurrence is in [53].”
Markov chain Monte Carlo: Can we trust the third significant figure? (2007, background): “Let the initial value for the simulation be (λ1, µ1) = (1,1).”
Sufficient burn-in for Gibbs samplers for a hierarchical random effects model (2004, methodology): “robability distribution associated with the density in (2).] Expectations with respect to π h are typically ratios of intractable integrals, the numerators of which can have dimension as high as K+3 [Jones and Hobert (2001)]. Thus, to make inferences using π h, we must resort to (possibly) high dime”
On the Markov chain central limit theorem (2004, positive): “ar X iv :m at h/ 04 09 11 2v 2 [ m at h. PR ] 1 0 M ar 2 00 5 On theM arkov Chain CentralLimitTheorem Galin L.Jones SchoolofStatistics University ofM innesota M inneapolis,M N,USA galin@stat.umn.edu October25,2021”
Asymptotic Variance and Convergence Rates of Nearly-Periodic Markov Chain Monte Carlo Algorithms (2003, background): “On the other hand, there is also a great deal of interest in convergence rates for nonuniformly ergodic chains (see, e.g., Meyn and Tweedie 1994; Rosenthal 1995b; Roberts and Tweedie 1999; Jones and Hobert 2001) corresponding results about P for nonuniform chains will be considered in subsequent res”
A Hierarchical Bayesian Approach to Seasonal Hurricane Modeling (2004, background): “Developing rigorous criteria for deciding chain length and burn-in requires a detailed study of the convergence properties of the chain (Jones and Hobert 2001) that goes beyond the scope of the present work.”
Batch means and spectral variance estimators in Markov chain Monte Carlo (2008, neutral): “(2) Received November 2008; revised April 2009.”
Revisiting the Gelman–Rubin Diagnostic (2018, background): “n the starting distribution of X i1 is far away from F. Determining how many samples to retain is a challenging problem that often involves a detailed study of the specic Markov chain kernel, P. See Jones and Hobert (2001); Rosenthal (1995) for a theoretical exposition. Convergence diagnostics that ”
Explaining the Perfect Sampler (2001, background): “A serious practical problem is determining the “burn-in” time T ; see Jones and Hobert (2001).”
RATES OF CONVERGENCE OF SOME MULTIVARIATE MARKOV CHAINS WITH POLYNOMIAL EIGENFUNCTIONS (2009, methodology): “So far, probabilists have come up with various techniques of finding rates of convergence of Markov chains, which can be roughly grouped under five headings: (a) using the spectral decomposition of a Markov chain, (b) using Harris recurrence techniques (see [33]), (c) using probabilistic techniques ”
Geometric Ergodicity of van Dyk and Meng's Algorithm for the Multivariate Student's t Model (2004, background): “For a more general discussion of the ideas described in this section, see Jones and Hobert (2001).”
Quantitative bounds on convergence of time-inhomogeneous Markov chains (2004, background): “The problem of getting explicit bounds on ‖Pn(x, ·)− π‖f has received much attention in recent years, motivated by control of convergence for Markov chain Monte Carlo and operation research problems [see, e.g., Jones and Hobert (2001)].”
On Convergence Properties of the Monte Carlo EM Algorithm (2012, background): “In fact the result holds more generally under Markov chain Monte Carlo methods, assuming the underlying Markov transition kernel is uniformly ergodic (see, for example, Jones and Hobert, 2001).”