There are many hierarchical clustering algorithms available, but these lack a firm statistical basis. Here we set up a hierarchical probabilistic mixture model, where data is generated in a hierarchical tree-structured manner. Markov chain Monte Carlo (MCMC) methods are demonstrated which can be used to sample from the posterior distribution over trees containing variable numbers of hidden units.

This note concerns the use of parametric bootstrap sampling to carry out Bayesian inference calculations. This is only possible in a subset of those problems amenable to Markov-Chain Monte Carlo (MCMC) analysis, but when feasible the bootstrap approach offers both computational and theoretical advantages. The discussion here is in terms of a simple example, with no attempt at a general analysis.

Usually in multivariate regression problem it is assumed that residuals of outputs are independent of each other. In many applications a more realistic model would allow dependencies between the outputs. In this paper we show how a Bayesian treatment using Markov Chain Monte Carlo (MCMC) method can allow for a full covariance matrix with Multi Layer Perceptron (MLP) neural networks.

Models are developed to adjust for measurement errors in normally distributed predictor and response variables and categorical predictors with misclassification errors. The models allow for a hierarchical data structure and for correlations among the errors and misclassifications. Markov Chain Monte Carlo (MCMC) estimation is used and implemented in a set of MATLAB macros.

f dπ. From the weak law of large numbers we know that the empirical mean nSn = n −1∑n k=1 f(Xk) converges to μ in probability. This result is the working principle behind all Markov chain Monte Carlo (MCMC) integration techniques. The basis of MCMC dates back to the 50’s with the article of Metropolis, Rosenbluth, Rosenbluth, Teller and Teller (1953), but it is only with today’s computing power...

Multimodal, high-dimension posterior distributions are well known to cause mixing problems for standard Markov chain Monte Carlo (MCMC) procedures; unfortunately such functional forms readily occur in empirical political science. This is a particularly important problem in applied Bayesian work because inferences are made from finite intervals of the Markov chain path. To address this issue, we...

A hierarchical Bayesian approach is developed to estimate parameters at both the individual and the population level in a HIV model, with the implementation carried out by Markov Chain Monte Carlo (MCMC) techniques. Sample numerical simulations and statistical results are provided to demonstrate the feasibility of this approach.

A fully Bayesian approach is proposed to the analysis of accuracy and mutuality in interpersonal perceptions. The Bayesian analysis is based on social relations model (SRM) formulation. Inference is straightforward using Markov chain Monte Carlo (MCMC) methods as implemented in the software package WinBUGS. An Example is provided to highlight the use of Bayesian analysis of interpersonal attrac...

We introduce the Weibull distributions in presence of cure fraction, censored data and covariates. Twomodels are explored in this paper: mixture and non-mixture models. Inferences for the proposed models are obtained under the Bayesian approach, using standard MCMC (Markov Chain Monte Carlo) methods. An illustration of the proposed methodology is given considering a lifetime data set.

I describe the design of NooShare, a decentralised ledger similar to Bitcoin [11] with the novel feature that its proofs of work are iterations of essentially arbitrary Markov-Chain Monte-Carlo (MCMC) chains, the scheduling of which can be purchased using the currency itself. It is a novel economic basis for sharing fallow computational resources.