Using Simulation-Based Inference with Panel Data in Health Economics

Panel datasets provide a rich source of information for health economists, offering the scope to control for individual heterogeneity and to model the dynamics of individual behaviour. However the qualitative or categorical measures of outcome often used in health economics create special problems for estimating econometric models. Allowing a flexible specification of individual heterogeneity leads to models involving higher order integrals that cannot be handled by conventional numerical methods. The dramatic growth in computing power over recent years has been accompanied by the development of simulation estimators that solve this problem. This review uses binary choice models to show what can be done with conventional methods and how the range of models can be expanded by using simulation methods. Practical applications of the methods are illustrated using on health from the British Household Panel Survey (BHPS)Econometrics, panel data, simulation methods, determinants of health

Using Simulation-based Inference with Panel Data in Health Economics

Panel datasets provide a rich source of information for health economists, offering the scope to control for individual heterogeneity and to model the dynamics of individual behaviour. However the qualitative or categorical measures of outcome often used in health economics create special problems for estimating econometric models. Allowing a flexible specification of the autocorrelation induced by individual heterogeneity leads to models involving higher order integrals that cannot be handled by conventional numerical methods. The dramatic growth in computing power over recent years has been accompanied by the development of simulation-based estimators that solve this problem. This review uses binary choice models to show what can be done with conventional methods and how the range of models can be expanded by using simulation methods. Practical applications of the methods are illustrated using data on health from the British Household Panel Survey (BHPS).

Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation

There is increasing consensus in the hydrologic literature that an appropriate framework for streamflow forecasting and simulation should include explicit recognition of forcing and parameter and model structural error. This paper presents a novel Markov chain Monte Carlo (MCMC) sampler, entitled differential evolution adaptive Metropolis (DREAM), that is especially designed to efficiently estimate the posterior probability density function of hydrologic model parameters in complex, high-dimensional sampling problems. This MCMC scheme adaptively updates the scale and orientation of the proposal distribution during sampling and maintains detailed balance and ergodicity. It is then demonstrated how DREAM can be used to analyze forcing data error during watershed model calibration using a five-parameter rainfall-runoff model with streamflow data from two different catchments. Explicit treatment of precipitation error during hydrologic model calibration not only results in prediction uncertainty bounds that are more appropriate but also significantly alters the posterior distribution of the watershed model parameters. This has significant implications for regionalization studies. The approach also provides important new ways to estimate areal average watershed precipitation, information that is of utmost importance for testing hydrologic theory, diagnosing structural errors in models, and appropriately benchmarking rainfall measurement devices

Conjugate Bayes for probit regression via unified skew-normal distributions

Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve also as building blocks in more complex formulations, such as density regression, nonparametric classification and graphical models. Within the Bayesian framework, inference proceeds by updating the priors for the coefficients, typically set to be Gaussians, with the likelihood induced by probit or logit regressions for the responses. In this updating, the apparent absence of a tractable posterior has motivated a variety of computational methods, including Markov Chain Monte Carlo routines and algorithms which approximate the posterior. Despite being routinely implemented, Markov Chain Monte Carlo strategies face mixing or time-inefficiency issues in large p and small n studies, whereas approximate routines fail to capture the skewness typically observed in the posterior. This article proves that the posterior distribution for the probit coefficients has a unified skew-normal kernel, under Gaussian priors. Such a novel result allows efficient Bayesian inference for a wide class of applications, especially in large p and small-to-moderate n studies where state-of-the-art computational methods face notable issues. These advances are outlined in a genetic study, and further motivate the development of a wider class of conjugate priors for probit models along with methods to obtain independent and identically distributed samples from the unified skew-normal posterior