Diffusive nested sampling

We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested probability distributions, each successive distribution occupying ∼e ⁻¹ times the enclosed prior mass of the previous distribution. While NS technically requires independent generation of particles, Markov Chain Monte Carlo (MCMC) exploration fits naturally into this technique. We illustrate the new method on a test problem and find that it can achieve four times the accuracy of classic MCMC-based Nested Sampling, for the same computational effort; equivalent to a factor of 16 speedup. An additional benefit is that more samples and a more accurate evidence value can be obtained simply by continuing the run for longer, as in standard MCMC.     

Modeling heavy-tailed,skewed and peaked uncertainty phenomena with bounded support

A prevalence of heavy-tailed, peaked and skewed uncertainty phenomena have been cited in literature dealing with economic, physics, and engineering data. This fact has invigorated the search for continuous distributions of this nature. In this paper we shall generalize the two-sided framework presented in Kotz and van Dorp (Beyond beta: other continuous families of distributions with bounded support and applications. World Scientific Press, Singapore, 2004) for the construction of families of distributions with bounded support via a mixture technique utilizing two generating densities instead of one. The family of Elevated Two-Sided Power (ETSP) distributions is studied as an instance of this generalized framework. Through a moment ratio diagram comparison, we demonstrate that the ETSP family allows for a remarkable flexibility when modeling heavy-tailed and peaked, but skewed, uncertainty phenomena. We shall demonstrate its applicability via an illustrative example utilizing 2008 US income data.     

Estimating the prevalence of sensitive behaviour and cheating with a dual design for direct questioning and randomized response

Randomized response is a misclassification design to estimate the prevalence of sensitive behaviour. Respondents who do not follow the instructions of the design are considered to be cheating. A mixture model is proposed to estimate the prevalence of sensitive behaviour and cheating in the case of a dual sampling scheme with direct questioning and randomized response. The mixing weight is the probability of cheating, where cheating is modelled separately for direct questioning and randomized response. For Bayesian inference, Markov chain Monte Carlo sampling is applied to sample parameter values from the posterior. The model makes it possible to analyse dual sample scheme data in a unified way and to assess cheating for direct questions as well as for randomized response questions. The research is illustrated with randomized response data concerning violations of regulations for social benefit.     

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.     

Bayesian and likelihood-based inference for the bivariate normal correlation coefficient

The paper develops some objective priors for correlation coefficient of the bivariate normal distribution. The criterion used is the asymptotic matching of coverage probabilities of Bayesian credible intervals with the corresponding frequentist coverage probabilities. The paper uses various matching criteria, namely, quantile matching, highest posterior density matching, and matching via inversion of test statistics. Each matching criterion leads to a different prior for the parameter of interest. We evaluate their performance by comparing credible intervals through simulation studies. In addition, inference through several likelihood-based methods have been discussed.     

Density estimation using asymmetric kernels and Bayes bandwidths with censored data

We propose a modification to the regular kernel density estimation method that use asymmetric kernels to circumvent the spill over problem for densities with positive support. First a pivoting method is introduced for placement of the data relative to the kernel function. This yields a strongly consistent density estimator that integrates to one for each fixed bandwidth in contrast to most density estimators based on asymmetric kernels proposed in the literature. Then a data-driven Bayesian local bandwidth selection method is presented and lognormal, gamma, Weibull and inverse Gaussian kernels are discussed as useful special cases. Simulation results and a real-data example illustrate the advantages of the new methodology.     

Dealing with noncompliance and missing outcomes in a randomized trial using Bayesian technology: Prevention of perinatal sepsis clinical trial,Soweto, South Africa

The success of interventions designed to address important issues in social and medical science is best addressed by randomized experiments. With human beings there are often complications, however, such as noncompliance and missing data. Such complications are often addressed by statistically invalid methods of analysis, in particular, intention-to-treat and per-protocol analyses. Here we address these two complications using a statistically valid approach based on principal stratification with a fully Bayesian analysis. This analysis is applied to a randomized trial of a potentially important intervention designed to reduce the transmission of bacterial colonization between mothers and their infants through vaginal delivery in South Africa: the Prevention of Perinatal Sepsis (PoPs).