The marginal likelihood plays an important role in many areas of Bayesian statistics such as parameter estimation, model comparison, and averaging. In most applications, however, the is not analytically tractable must be approximated using numerical methods. Here we provide a tutorial on bridge sampling (Bennett, 1976; Meng & Wong, 1996), reliable relatively straightforward method that allows researchers to obtain for models varying complexity. First, introduce three related methods...

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

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

Abstract Migration is one of the most unpredictable demographic processes. The aim this article to provide a blueprint for assessing various possible forecasting approaches in order help safeguard producers and users official migration statistics against misguided forecasts. To achieve that, we first evaluate existing modelling international flows. Subsequently, present an empirical comparison ex post performance methods, applied from United Kingdom. overarching goal assess uncertainty...

Asylum-related migration is highly complex, uncertain, and volatile, which precludes using standard model-based predictions to inform policy operational decisions. At the same time, asylum's potentially high societal impacts on receiving countries resource implications of asylum processes call for more proactive approaches assessing current future flows. In this article, we propose an alternative approach modeling, based detection early warning signals by models originating from statistical...

Summary We consider non-response models for a single categorical response with covariates whose values are always observed. present Bayesian methods ignorable and particular non-ignorable model, we argue that standard of model comparison inappropriate comparing models. Uncertainty about ignorability is incorporated by introducing parameters describing the extent non-ignorability into pattern mixture specification integrating over prior uncertainty associated these parameters. Our approach...

SUMMARY The form of the exact conditional distribution a sufficient statistic for interest parameters, given nuisance is derived generalized linear model with canonical link. General results log-linear and logistic models are given. A Gibbs sampling approach generating from proposed, which enables Monte Carlo tests to be performed. Examples include goodness fit all-two-way interaction 28-table simple model. Tests against non-saturated alternatives also considered.

Abstract In this article, we first discuss the need to augment reported flows of international migration in Europe with additional knowledge gained from experts on measurement, quality and coverage. Second, present our method for eliciting information. Third, describe how information is converted into prior distributions subsequent use a Bayesian model estimating amongst countries European Union (EU) Free Trade Association (EFTA). The article concludes an assessment importance expert...

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

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

Summary Forecasts of mortality provide vital information about future populations, with implications for pension and healthcare policy as well decisions made by private companies life insurance annuity pricing. The paper presents a Bayesian approach to the forecasting that jointly estimates generalized additive model (GAM) majority age range parametric older ages where data are sparser. GAM allows smooth components be estimated age, cohort age-specific improvement rates, together...

We provide forecasts for mortality rates by using two different approaches. First we employ dynamic non-linear logistic models based on Heligman-Pollard formula. Second, assume that the dynamics of can be modelled through a Gaussian Markov random field. use efficient Bayesian methods to estimate parameters and latent states proposed models. Both methodologies are tested with past data used forecast both large (UK Wales) small (New Zealand) populations up 21 years ahead. demonstrate...

Summary Age and sex patterns of migration are essential for understanding drivers population change heterogeneity migrant groups. We develop a hierarchical Bayesian model to estimate such international in the European Union Free Trade Association from 2002 2008, which was period time when number members expanded 19 31 countries. Our corrects inadequacies inconsistencies available data estimates missing patterns. The posterior distributions age profiles then combined with matrix...

The marginal likelihood plays an important role in many areas of Bayesian statistics such as parameter estimation, model comparison, and averaging. In most applications, however, the is not analytically tractable must be approximated using numerical methods. Here we provide a tutorial on bridge sampling (Bennett, 1976; Meng & Wong, 1996), reliable relatively straightforward method that allows researchers to obtain for models varying complexity. First, introduce three related methods...