Bayesian inference for pairwise interacting point processes

Pairwise interacting point processes are commonly used to model spatial point patterns. To perform inference, the established frequentist methods can produce good point estimates when the interaction in the data is moderate, but some methods may produce severely biased estimates when the interaction in strong. Furthermore, because the sampling distributions of the estimates are unclear, interval estimates are typically obtained by parametric bootstrap methods. In the current setting however, the behavior of such estimates is not well understood. In this article we propose Bayesian methods for obtaining inferences in pairwise interacting point processes. The requisite application of Markov chain Monte Carlo (MCMC) techniques is complicated by an intractable function of the parameters in the likelihood. The acceptance probability in a Metropolis-Hastings algorithm involves the ratio of two likelihoods evaluated at differing parameter values. The intractable functions do not cancel, and hence an intractable ratio r must be estimated within each iteration of a Metropolis-Hastings sampler. We propose the use of importance sampling techniques within MCMC to address this problem. While r may be estimated by other methods, these, in general, are not readily applied in a Bayesian setting. We demonstrate the validity of our importance sampling approach with a small simulation study. Finally, we analyze the Swedish pine sapling dataset (Strand 1972) and contrast the results with those in the literature.     

When a loved one has AIDS: care for the significant other

1. The significant others of persons with AIDS, whether they assume the role of primary caregiver or not, have a number of unique experiences, concerns, and needs specifically related to their situations. 2. During the initial period following the diagnosis of a loved one, the significant others indicated their primary needs as sensitivity to their situations, assistance in securing appropriate information, and psychological support in dealing with uncertainty, and a general sense of dread. 3. Other common concerns and needs expressed by the significant others included support and reassurance, assistance in adjusting to a myriad of personal relationship changes, and help in meeting needs for active involvement in some form of AIDS-related work.     

Accelerating Monte Carlo Markov chain convergence for cumulative-link generalized linear models

The ordinal probit, univariate or multivariate, is a generalized linear model (GLM) structure that arises frequently in such disparate areas of statistical applications as medicine and econometrics. Despite the straightforwardness of its implementation using the Gibbs sampler, the ordinal probit may present challenges in obtaining satisfactory convergence.We present a multivariate Hastings-within-Gibbs update step for generating latent data and bin boundary parameters jointly, instead of individually from their respective full conditionals. When the latent data are parameters of interest, this algorithm substantially improves Gibbs sampler convergence for large datasets. We also discuss Monte Carlo Markov chain (MCMC) implementation of cumulative logit (proportional odds) and cumulative complementary log-log (proportional hazards) models with latent data.     

Parallelizing MCMC for Bayesian spatiotemporal geostatistical models

When MCMC methods for Bayesian spatiotemporal modeling are applied to large geostatistical problems, challenges arise as a consequence of memory requirements, computing costs, and convergence monitoring. This article describes the parallelization of a reparametrized and marginalized posterior sampling (RAMPS) algorithm, which is carefully designed to generate posterior samples efficiently. The algorithm is implemented using the Parallel Linear Algebra Package (PLAPACK). The scalability of the algorithm is investigated via simulation experiments that are implemented using a cluster with 25 processors. The usefulness of the method is illustrated with an application to sulfur dioxide concentration data from the Air Quality System database of the U.S. Environmental Protection Agency.     

Correlating point-referenced radon and areal uranium data arising from a common spatial process

Summary.  Because exposure to radon gas in buildings is a likely risk factor for lung cancer, estimation of residential radon levels is an important public health endeavour. Radon originates from uranium, and therefore data on the geographical distribution of uranium in the Earth's surface may inform about radon levels. We fit a Bayesian geostatistical model that appropriately combines data on uranium with measurements of indoor home radon in the state of Iowa, thereby obtaining more accurate and precise estimation of the geographic distribution of average residential radon levels than would be possible by using radon data alone.     

MCMC Sampler Convergence Rates for Hierarchical Normal Linear Models: A Simulation Approach

This paper presents a straightforward method of approximating theoretical bounds on burn-in time for MCMC samplers for hierarchical normal linear models. An extension and refinement of Cowles and Rosenthal's (1998) simulation approach, it exploits Hodges's (1998) reformulation of hierarchical normal linear models. The method is illustrated with three real datasets, involving a one-way variance components model, a growth-curve model, and a spatial model with a pairwise-differences prior. In all three cases, when the specified priors produce proper, unimodal posterior distributions, the method provides very reasonable upper bounds on burn-in time. In contrast, when the posterior distribution for the variance-components model can be shown to be improper or bimodal, the new method correctly identifies convergence failure while several other commonly-used diagnostics provide false assurance that convergence has occurred.