Search results for "Gibbs sampling"
showing 8 items of 18 documents
Bayesian Smoothing in the Estimation of the Pair Potential Function of Gibbs Point Processes
1999
A flexible Bayesian method is suggested for the pair potential estimation with a high-dimensional parameter space. The method is based on a Bayesian smoothing technique, commonly applied in statistical image analysis. For the calculation of the posterior mode estimator a new Monte Carlo algorithm is developed. The method is illustrated through examples with both real and simulated data, and its extension into truly nonparametric pair potential estimation is discussed.
Uniform ergodicity of the iterated conditional SMC and geometric ergodicity of particle Gibbs samplers
2018
We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers. Our main findings are that the essential boundedness of potential functions associated with the i-cSMC algorithm provide necessary and sufficient conditions for the uniform ergodicity of the i-cSMC Markov chain, as well as quantitative bounds on its (uniformly geometric) rate of convergence. Furthermore, we show that the i-cSMC Markov chain cannot even be geometrically ergodic if this essential boundedness does not hold in many applications of interest. Our sufficiency and quantitative bounds rely on…
A Bayesian comparison of cluster, strata, and random samples
1999
When sampling from finite populations, simple random sampling (SRS) is rarely used in practice, due to either high cost or information to be gained from more efficient designs. Bayesian hierarchical models are a natural framework to model the non-randomness in the sample. This paper concentrates on the effects that the design has on inference about characteristics of the finite population, and makes a critical comparison among some common designs.
On implementation of the Gibbs sampler for estimating the accuracy of multiple diagnostic tests
2010
Implementation of the Gibbs sampler for estimating the accuracy of multiple binary diagnostic tests in one population has been investigated. This method, proposed by Joseph, Gyorkos and Coupal, makes use of a Bayesian approach and is used in the absence of a gold standard to estimate the prevalence, the sensitivity and specificity of medical diagnostic tests. The expressions that allow this method to be implemented for an arbitrary number of tests are given. By using the convergence diagnostics procedure of Raftery and Lewis, the relation between the number of iterations of Gibbs sampling and the precision of the estimated quantiles of the posterior distributions is derived. An example conc…
Contributed discussion on article by Pratola
2016
The author should be commended for his outstanding contribution to the literature on Bayesian regression tree models. The author introduces three innovative sampling approaches which allow for efficient traversal of the model space. In this response, we add a fourth alternative.
Multi-label Classification Using Stacked Hierarchical Dirichlet Processes with Reduced Sampling Complexity
2018
Nonparametric topic models based on hierarchical Dirichlet processes (HDPs) allow for the number of topics to be automatically discovered from the data. The computational complexity of standard Gibbs sampling techniques for model training is linear in the number of topics. Recently, it was reduced to be linear in the number of topics per word using a technique called alias sampling combined with Metropolis Hastings (MH) sampling. We propose a different proposal distribution for the MH step based on the observation that distributions on the upper hierarchy level change slower than the document-specific distributions at the lower level. This reduces the sampling complexity, making it linear i…
Online Sparse Collapsed Hybrid Variational-Gibbs Algorithm for Hierarchical Dirichlet Process Topic Models
2017
Topic models for text analysis are most commonly trained using either Gibbs sampling or variational Bayes. Recently, hybrid variational-Gibbs algorithms have been found to combine the best of both worlds. Variational algorithms are fast to converge and more efficient for inference on new documents. Gibbs sampling enables sparse updates since each token is only associated with one topic instead of a distribution over all topics. Additionally, Gibbs sampling is unbiased. Although Gibbs sampling takes longer to converge, it is guaranteed to arrive at the true posterior after infinitely many iterations. By combining the two methods it is possible to reduce the bias of variational methods while …
Bayesian Hierarchical Models for Random Routes in Finite Populations
1996
In many practical situations involving sampling from finite populations, it is not possible (or it is prohibitely expensive) to access, or to even produce, a listing of all of the units in the population. In these situations, inferences can not be based on random samples from the population. Random routes are widely used procedures to collect data in absence of well defined sampling frames, and they usually have either been improperly analyzed as random samples, or entirely ignored as useless. We present here a Bayesian analysis of random routes that incorporates the information provided but carefully takes into account the non- randomness in the selection of the units.