sdunbarne

SpectralBounds

Section 15 of proposed book on Markov chains. This section examines the spectral approach to convergence of Markov chains. The focus is on two-component Gibbs samplers, with applications to the Beta/Binomial and Poisson/Gamma Gibbs samplers.

AnalysisPopulationDeviationNebr

ApplicationsMetropolis

Section 11 of tentative book on Markov chains, with application of Monte Carlo Markov chain methods to the Ising model, image reconstruction with Gibbs sampling, and Bayesian hierarchical statistical models.

Baseball

Section 5 of tentative book on theory and examples of Markov Chains

CardShuffling

Section 9 of tentative book on Markov chains, modeling card-shuffling as a Markov chain leading to mixing.

ConvergenceStationary

Section 15.5 of proposed book on Markov chains. This section examines a general approach to convergence of Markov chains. The section has examples for finite-state chains, and continuous state spaces and a detailed look at random walk on the hypercube.

Epidemics

Section 8 of a tentative book on Markov chains, modeling epidemics as Markov chains with the Greenwood and Reed-Frost formulations.

FastestMixing

Section 14 of a tentative book on Markov chains with detailed analysis of eigenvalues of Markov chains of random walks.

Games

Section 7 of a tentative book with four board games, of increasing size, modeled as Markov chains.

ggplot2Exercises

My solutions to the on-line version of the work-in-progress 3rd edition of /ggplot2: elegant graphics for data analysis/ by Hadley Wickham, Danielle Navarro and Thomas Lin Pedersen, as of about March 2021.

GibbsSampler

Section 12 of a tentative book on Markov chains with examples of application of Gibbs sampling

IntroCoupling

Section 15.2 of a proposed book on Markov chains. \emph{Coupling} means the joint construction of two or more random variables or processes to deduce properties of the individual variables or gain insight into distributional similarities or relations between them.

IsingModel

Section 11 of tentative book on Markov chains, Description of Ising Model and Metropolis, Glauber Algorithms

LumpedChains

Tentative Section 4.7 of book on Markov chains

MarkovChain

This section is a survey of basic concepts and facts about Markov processes and Markov chains.

MonopolyGame

Section 6 of a tentative book, detailing the board game of Monopoly modeled as a Markov chain.

MonteCarlo

Section 10 of tentative book on Markov chains, with motivation for the Metropolis and Metropolis-Hastings algorithms for Markov Chain Monte Carlo, along with some theory.

MotivationMetropolis

NebraskaRedistrictingTalk

openelections-data-ne

Raw election results for Nebraska elections

ParallelSignificance

Section 17 of a tentative book on Markov chains. This section derives improved statistical tests to detect that a given state from a stationary distribution of a reversible Markov chain is unusual.

ReversibleMarkovChains

Tentative Section 4.5 of proposed book on Markov Chains and Theory

RiskGame

sdunbarne.github.io

Personal webpage for Steve Dunbar with information, writing, talks, research, code, and so on.

SerialSignificance

Section 16 of a tentative book on Markov chains. This section derives statistical tests to detect that a given state from a stationary distribution of a reversible Markov chain is unusual.

Sports

Section 5.5 of potnetial book on Markov chains and applications

StandardExamples

Section 4 of tentative book on theory and examples of Markov Chains

StationaryDistributions

Section 3 of a tentative book on theory and examples of Markov Chains

StirlingsFormulaSequences

Rigorous mathematical proofs of Stirling's Formula

WaitingTimeAbsorption

Section 2 of tentative book on theory and examples of Markov Chains