Jonathan J. Forster

Bayesian variable and link determination for generalised linear models

In this paper, we describe full Bayesian inference for generalised linear models where uncertainty exists about the structure of the linear predictor, the linear parameters and the link function. Choice of suitable prior distributions is discussed in detail and we propose an efficient reversible jump Markov chain Monte-Carlo algorithm for calculating posterior summaries. We illustrate our method with two data examples.

Model‐based inference for categorical survey data subject to non‐ignorable non‐response

We consider non-response models for a single categorical response with categorical covariates whose values are always observed. We present Bayesian methods for ignorable models and a particular non-ignorable model, and we argue that standard methods of model comparison are inappropriate for comparing ignorable and non-ignorable models. Uncertainty about ignorability of non-response is incorporated by introducing parameters describing the extent of non-ignorability into a pattern mixture specification and integrating over the prior uncertainty associated with these parameters. Our approach is illustrated using polling data from the 1992 British general election panel survey. We suggest sample size adjustments for surveys when non-ignorable non-response is expected.

Monte Carlo exact tests for square contingency tables

Square contingency tables arise frequently in social research. Typically, many of the off‐diagonal cell counts are small because of the social processes involved. This causes concern about the validity of using asymptotic tests and an exact test should be considered. We develop Markov chain Monte Carlo methods for estimating the exact conditional p‐value for various complex log‐linear models that are useful for the analysis of square contingency tables. These methods are used to analyse a sparse 8×8 intermarriage table.

Integrated Modeling of European Migration

International migration data in Europe are collected by individual countries with separate collection systems and designs. As a result, reported data are inconsistent in availability, definition, and quality. In this article, we propose a Bayesian model to overcome the limitations of the various data sources. The focus is on estimating recent international migration flows among 31 countries in the European Union and European Free Trade Association from 2002 to 2008, using data collated by Eurostat. We also incorporate covariate information and information provided by experts on the effects of undercount, measurement, and accuracy of data collection systems. The methodology is integrated and produces a synthetic database with measures of uncertainty for international migration flows and other model parameters. Supplementary materials for this article are available online.

Estimation of Wind Speed Distribution Using Markov Chain Monte Carlo Techniques

The Weibull distribution is the most commonly used statistical distribution for describing wind speed data. Maximum likelihood has traditionally been the main method of estimation for Weibull parameters. In this paper, Markov chain Monte Carlo techniques are used to carry out a Bayesian estimation procedure using wind speed data obtained from the Observatory of Hong Kong. The method is extremely flexible. Inference for any quantity of interest is routinely available, and it can be adapted easily when data are truncated.

Bayesian model determination for multivariate ordinal and binary data

Different conditional independence specifications for ordinal categorical data are compared by calculating a posterior distribution over classes of graphical models. The approach is based on the multivariate ordinal probit model where the data are considered to have arisen as truncated multivariate normal random vectors. By parameterising the precision matrix of the associated multivariate normal in Cholesky form, ordinal data models corresponding to directed acyclic conditional independence graphs for the latent variables can be specified and conveniently computed. Where one or more of the variables are binary this parameterisation is particularly compelling, as necessary constraints on the latent variable distribution can be imposed in such a way that a standard, fully normalised, prior can still be adopted. For comparing different directed graphical models a reversible jump Markov chain Monte Carlo (MCMC) approach is proposed. Where interest is focussed on undirected graphical models, this approach is augmented to allow switches in the orderings of variables of associated directed graphs, hence allowing the posterior distribution over decomposable undirected graphical models to be computed. The approach is illustrated with several examples, involving both binary and ordinal variables, and directed and undirected graphical model classes.

Stochastic search variable selection for log-linear models

We develop a Markov chain Monte Carlo algorithm, based on ‘stochastic search variable selection’ (George and McCuUoch, 1993), for identifying promising log-linear models. The method may be used in the analysis of multi-way contingency tables where the set of plausible models is very large.

Bayesian population forecasting: extending the Lee-Carter Method

In this article, we develop a fully integrated and dynamic Bayesian approach to forecast populations by age and sex. The approach embeds the Lee-Carter type models for forecasting the age patterns, with associated measures of uncertainty, of fertility, mortality, immigration, and emigration within a cohort projection model. The methodology may be adapted to handle different data types and sources of information. To illustrate, we analyze time series data for the United Kingdom and forecast the components of population change to the year 2024. We also compare the results obtained from different forecast models for age-specific fertility, mortality, and migration. In doing so, we demonstrate the flexibility and advantages of adopting the Bayesian approach for population forecasting and highlight areas where this work could be extended.

Default Bayesian model determination methods for generalised linear mixed models

A default strategy for fully Bayesian model determination for generalised linear mixed models (GLMMs) is considered which addresses the two key issues of default prior specification and computation. In particular, the concept of unit-information priors is extended to the parameters of a GLMM. A combination of Markov chain Monte Carlo (MCMC) and Laplace approximations is used to compute approximations to the posterior model probabilities to find a subset of models with high posterior model probability. Bridge sampling is then used on the models in this subset to approximate the posterior model probabilities more accurately. The strategy is applied to four examples.

Markov chain Monte Carlo exact inference for binomial and multinomial logistic regression models

We develop Metropolis-Hastings algorithms for exact conditional inference, including goodness-of-fit tests, confidence intervals and residual analysis, for binomial and multinomial logistic regression models. We present examples where the exact results, obtained by enumeration, are available for comparison. We also present examples where Monte Carlo methods provide the only feasible approach for exact inference.