A tutorial on bridge sampling Gronau, Quentin F.; Sarafoglou, Alexandra; Matzke, Dora ...
Journal of mathematical psychology,
December 2017, 2017-Dec, 2017-12-00, 20171201, Letnik:
81
Journal Article
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The marginal likelihood plays an important role in many areas of Bayesian statistics such as parameter estimation, model comparison, and model averaging. In most applications, however, the marginal ...likelihood is not analytically tractable and must be approximated using numerical methods. Here we provide a tutorial on bridge sampling (Bennett, 1976; Meng & Wong, 1996), a reliable and relatively straightforward sampling method that allows researchers to obtain the marginal likelihood for models of varying complexity. First, we introduce bridge sampling and three related sampling methods using the beta-binomial model as a running example. We then apply bridge sampling to estimate the marginal likelihood for the Expectancy Valence (EV) model—a popular model for reinforcement learning. Our results indicate that bridge sampling provides accurate estimates for both a single participant and a hierarchical version of the EV model. We conclude that bridge sampling is an attractive method for mathematical psychologists who typically aim to approximate the marginal likelihood for a limited set of possibly high-dimensional models.
•We provide a tutorial on bridge sampling for estimating marginal likelihoods.•We use the beta-binomial model as a running example.•We estimate the marginal likelihood for the Expectancy Valence (EV) model.•We obtain accurate results for individual-level and hierarchical EV model versions.
Abstract
Fertility projections are vital to anticipate demand for maternity and childcare services, among other uses. Models typically use aggregate population-level data alone, ignoring the richness ...of individual-level data. We hence develop a Bayesian parity-specific projection model combining such data sources. We apply our method to England and Wales, using individual-level data from Understanding Society. Fitting generalised additive models gives smooth projections across age, cohort, and time since last birth. We also incorporate prior beliefs about the relative importance of the data sources. Our approach generates plausible forecasts by individual-level variables including educational qualification, despite their absence in the population-level data.
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, hi 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.
Integrated Modeling of European Migration Raymer, James; Wiśniowski, Arkadiusz; Forster, Jonathan J ...
Journal of the American Statistical Association,
09/2013, Letnik:
108, Številka:
503
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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.
Discrete-time event history analysis (EHA) is the standard approach taken when modelling fertility histories collected in surveys, where the date of birth is often recorded imprecisely. This method ...is commonly used to investigate the factors associated with the time to a first or subsequent conception or birth. Although there is an emerging trend towards the smooth incorporation of continuous covariates in the broader literature, this is yet to be formally embraced in the context of birth events. We investigate the formal application of smooth methods implemented via generalized additive models (GAMs) to the analysis of fertility histories. We also determine whether and where GAMs offer a practical improvement over existing approaches. We fit parity-specific logistic GAMs to data from the UK Household Longitudinal Study, learning about the effects of age, period, time since last birth, educational qualification, and country of birth. First, we select the most parsimonious GAMs that fit the data sufficiently well. Then we compare them with corresponding models that use the existing methods of categorical, polynomial, and piecewise linear spline representations in terms of fit, complexity, and substantive insights gained. We find that smooth terms can offer considerable improvements in precision and efficiency, particularly for highly non-linear effects and interactions between continuous variables. Their flexibility enables the detection of important features that are missed or estimated imprecisely by comparator methods.
Summary
Fertility projections are a key determinant of population forecasts, which are widely used by government policy makers and planners. In keeping with the recent literature, we propose an ...intuitive and transparent hierarchical Bayesian model to forecast cohort fertility. Using Hamiltonian Monte Carlo methods and a data set from the human fertility database, we obtain fertility forecasts for 30 countries. We use scoring rules to assess the predictive accuracy of the forecasts quantitatively; these indicate that our model predicts with an accuracy comparable with that of the best‐performing models in the current literature overall, with stronger performance for countries without a recent structural shift. Our findings support the position of hierarchical Bayesian modelling at the forefront of population forecasting methods.
We provide forecasts for mortality rates by using two different approaches. First we employ dynamic non-linear logistic models based on the Heligman–Pollard formula. Second, we assume that the ...dynamics of the mortality rates can be modelled through a Gaussian Markov random field. We use efficient Bayesian methods to estimate the parameters and the latent states of the models proposed. Both methodologies are tested with past data and are used to forecast mortality rates both for large (UK and Wales) and small (New Zealand) populations up to 21 years ahead. We demonstrate that predictions for individual survivor functions and other posterior summaries of demographic and actuarial interest are readily obtained. Our results are compared with other competing forecasting methods.
Bayesian model comparison for mortality forecasting Wong, Jackie S T; Forster, Jonathan J; Smith, Peter W F
Applied statistics/Journal of the Royal Statistical Society. Series C, Applied statistics,
06/2023, Letnik:
72, Številka:
3
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Abstract
Stochastic models are appealing for mortality forecasting in their ability to generate intervals that quantify uncertainties underlying the forecasts. We present a fully Bayesian ...implementation of the age-period-cohort-improvement (APCI) model with overdispersion, which is compared with the Lee–Carter model with cohorts. We show that naive prior specification can yield misleading inferences, where we propose Laplace prior as an elegant solution. We also perform model averaging to incorporate model uncertainty. Our findings indicate that the APCI model offers better fit and forecast for England and Wales data spanning 1961–2002. Our approach also allows coherent inclusion of multiple sources of uncertainty, producing well-calibrated probabilistic intervals.
We consider the specification of prior distributions for Bayesian model comparison, focusing on regression-type models. We propose a particular joint specification of the prior distribution across ...models so that sensitivity of posterior model probabilities to the dispersion of prior distributions for the parameters of individual models (Lindley's paradox) is diminished. We illustrate the behavior of inferential and predictive posterior quantities in linear and log-linear regressions under our proposed prior densities with a series of simulated and real data examples.
Asylum-related migration is highly complex, uncertain, and volatile, which precludes using standard model-based predictions to inform policy and operational decisions. At the same time, asylum's ...potentially high societal impacts on receiving countries and the resource implications of asylum processes call for more proactive approaches for assessing current and future migration flows. In this article, we propose an alternative approach to asylum modeling, based on the detection of early warning signals by using models originating from statistical control theory. Our empirical analysis of several asylum flows into Europe in 2010–2016 demonstrates the approach's utility and potential in aiding the management of mixed migration flows, while also shedding more light on the work needed to make better use of the “big data” and scenario-based methods for comprehensive and systematic examination of risk, uncertainty, and emerging trends.
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