Data augmentation in multi-way contingency tables with fixed marginal totals

Gibbs Samplers for Logistic Item Response Models via the Pólya-Gamma Distribution: A Computationally Efficient Data-Augmentation Strategy

Fully Bayesian estimation of item response theory models with logistic link functions suffers from low computational efficiency due to posterior density functions that do not have known forms. To improve algorithmic computational efficiency, this paper proposes a Bayesian estimation method by adopting a new data-augmentation strategy in uni- and multidimensional IRT models. The strategy is based on the Pólya-Gamma family of distributions which provides a closed-form posterior distribution for logistic-based models. In this paper, an overview of Pólya-Gamma distributions is described within a logistic regression framework. In addition, we provide details about deriving conditional distributions of IRT, incorporating Pólya-Gamma distributions into the conditional distributions for Bayesian samplers' construction, and random drawing from the samplers such that a faster convergence can be achieved. Simulation studies and applications to real datasets were conducted to demonstrate the efficiency and utility of the proposed method.

Estimation of emigration, return migration, and transit migration between all pairs of countries

We propose a method for estimating migration flows between all pairs of countries that allows for decomposition of migration into emigration, return, and transit components. Current state-of-the-art estimates of bilateral migration flows rely on the assumption that the number of global migrants is as small as possible. We relax this assumption, producing complete estimates of all between-country migration flows with genuine estimates of total global migration. We find that the total number of individuals migrating internationally has oscillated between 1.13 and 1.29% of the global population per 5-year period since 1990. Return migration and transit migration are big parts of total migration; roughly one of four migration events is a return to an individual's country of birth. In the most recent time period, we estimate particularly large return migration flows from the United States to Central and South America and from the Persian Gulf to south Asia.

Bayes computation for ecological inference

Ecological data are available at the level of the group, rather than at the level of the individual. The use of ecological data in spatial epidemiological investigations is particularly common. Although the computational methods described are more generally applicable, this paper concentrates on the situation in which the margins of 2 × 2 tables are observed in each of n geographical areas, with a Bayesian approach to inference. We consider auxiliary schemes that impute the missing data, and compare with a previously suggested normal approximation. The analysis of ecological data is subject to ecological bias, with the only reliable means of removing such bias being the addition of auxiliary individual-level information. Various schemes have been suggested for this supplementation, and we illustrate how the computational methods may be applied to the analysis of such enhanced data. The methods are illustrated using simulated data and two examples. In the first example, the ecological data are supplemented with a simple random sample of individual-level data, and in this example the normal approximation fails. In the second example case-control sampling provides the additional information.