Nowadays, many biological data are acquired via images. In this article, we study the pathological images scanned from 205 patients with lung cancer with the goal to find out the relationship between the survival time and the spatial distribution of different types of cells, including lymphocyte, stroma, and tumor cells. Toward this goal, we model the spatial distribution of different types of ...

We propose a split-merge Markov chain algorithm to address the problem of inee-cient sampling for conjugate Dirichlet process mixture models. Traditional Markov chain Monte Carlo methods for Bayesian mixture models, such as Gibbs sampling, can become trapped in isolated modes corresponding to an inappropriate clustering of data points. This article describes a Metropolis-Hastings procedure that...

Despite a few notable uses of simulation of random processes in the pre-computer era (Hammersley and Handscomb, 1964, Section 1.2; Stigler, 2002, Chapter 7), practical widespread use of simulation had to await the invention of computers. Almost as soon as computers were invented, they were used for simulation (Hammersley and Handscomb, 1964, Section 1.2). The name “Monte Carlo” started as cuten...

We apply a linear mixed-effects model to multivariate failure time data. Computation of the regression parameters involves the Buckley-James method in an iterated Monte Carlo expectation-maximization algorithm, wherein the Monte Carlo E-step is implemented using the Metropolis-Hastings algorithm. From simulation studies, this approach compares favorably with the marginal independence approach, ...

A novel fully automatic Bayesian procedure for variable selection in normal regression models is proposed, along with computational strategies for model posterior evaluation. A stochastic search algorithm is given, based on the Metropolis-Hastings Algorithm, that has a stationary distribution proportional to the model posterior probabilities. The procedure is illustrated on both simulated and r...

Markov Chain Monte Carlo (MCMC) methods are well-known Monte Carlo methodologies, widely used in different fields for statistical inference and stochastic optimization. The Multiple Try Metropolis (MTM) algorithm is an extension of the standard Metropolis-Hastings (MH) algorithm in which the next state of the chain is chosen among a set of candidates, according to certain weights. The Particle ...