Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC gives information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.Comment: 26 pages, 9 figure

Present and future evidence for evolving dark energy

We compute the Bayesian evidences for one- and two-parameter models of evolving dark energy, and compare them to the evidence for a cosmological constant, using current data from Type Ia supernova, baryon acoustic oscillations, and the cosmic microwave background. We use only distance information, ignoring dark energy perturbations. We find that, under various priors on the dark energy parameters, LambdaCDM is currently favoured as compared to the dark energy models. We consider the parameter constraints that arise under Bayesian model averaging, and discuss the implication of our results for future dark energy projects seeking to detect dark energy evolution. The model selection approach complements and extends the figure-of-merit approach of the Dark Energy Task Force in assessing future experiments, and suggests a significantly-modified interpretation of that statistic.Comment: 10 pages RevTex4, 3 figures included. Minor changes to match version accepted by PR

Forecasting in dynamic factor models using Bayesian model averaging

This paper considers the problem of forecasting in dynamic factor models using Bayesian model averaging. Theoretical justifications for averaging across models, as opposed to selecting a single model, are given. Practical methods for implementing Bayesian model averaging with factor models are described. These methods involve algorithms which simulate from the space defined by all possible models. We discuss how these simulation algorithms can also be used to select the model with the highest marginal likelihood (or highest value of an information criterion) in an efficient manner. We apply these methods to the problem of forecasting GDP and inflation using quarterly U.S. data on 162 time series. For both GDP and inflation, we find that the models which contain factors do out-forecast an AR(p), but only by a relatively small amount and only at short horizons. We attribute these findings to the presence of structural instability and the fact that lags of dependent variable seem to contain most of the information relevant for forecasting. Relative to the small forecasting gains provided by including factors, the gains provided by using Bayesian model averaging over forecasting methods based on a single model are appreciable

Measuring the health effects of air pollution : to what extent can we really say people are dying from bad air?

Estimation of the effects of environmental impacts is a major focus of current theoretical and policy research in environmental economics. Such estimates are used to set regulatory standards for pollution exposure; design appropriate environmental protection and damage mitigation strategies; guide the assessment of environmental impacts; and measure public willingness to pay for environmental amenities. It is a truism that the effectiveness of such strategies depends crucially on the quality of the estimates used to inform them. However, this paper argues that in respect to at least one area of the empirical literature - the estimation of the health impacts of air pollution using daily time series data - existing estimates are questionable and thus have limited relevance for environmental decision-making. By neglecting the issue of model uncertainty - or which models, among the myriad of possible models researchers should choose from to estimate health effects - most studies overstate confidence in their chosen model and underestimate the evidence from other models, thereby greatly enhancing the risk of obtaining uncertain and inaccurate results. This paper discusses the importance of model uncertainty for accurate estimation of the health effects of air pollution and demonstrates its implications in an exercise that models pollution-mortality impacts using a new and comprehensive data set for Toronto, Canada. The main empirical finding of the paper is that standard deviations for air pollution-mortality impacts become very large when model uncertainty is incorporated into the analysis. Indeed they become so large as to question the plausibility of previously measured links between air pollution and mortality. Although applied to the estimation of the effects of air pollution, the general message of this paper - that proper treatment of model uncertainty critically determines the accuracy of the resulting estimates - applies to many studies that seek to estimate environmental effects