Renate Meyer

Deviance Information Criterion for Comparing Stochastic Volatility Models

Bayesian methods have been efficient in estimating parameters of stochastic volatility models for analyzing financial time series. Recent advances made it possible to fit stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components, and heavy-tailed distributions. However, a formal model comparison via Bayes factors remains difficult. The main objective of this article is to demonstrate that model selection is more easily performed using the deviance information criterion (DIC). It combines a Bayesian measure of fit with a measure of model complexity. We illustrate the performance of DIC in discriminating between various different stochastic volatility models using simulated data and daily returns data on the Standard & Poors (S&P) 100 index.

Bayesian methods for cosmological parameter estimation from cosmic microwave background measurements

We present a strategy for a statistically rigorous Bayesian approach to the problem of determining cosmological parameters from the results of observations of anisotropies in the cosmic microwave background. Our strategy relies on Markov chain Monte Carlo methods, specifically the Metropolis-Hastings algorithm, to perform the necessary high-dimensional integrals. We describe the Metropolis-Hastings algorithm in detail and discuss the results of our test on simulated data.

A Bayesian approach to the ecosystem inverse problem

This study investigates a probabilistic approach for the inverse problem associated with blending time-dependent ecosystem models and observations. The goal is to combine prior information, in the form of ecological dynamics and substantive knowledge about uncertain parameters, with available measurements. Posterior estimates of both the time-varying ecological state variables and the model parameters are obtained, along with their uncertainty. Ecological models of interacting populations are considered in the context of a nonlinear, non-Gaussian state space model. This comprises a nonlinear stochastic difference equation for the ecological dynamics, and an observation equation which relates the model state to the measurements. Complex error processes are readily incorporated. The posterior probability density function provides a complete solution to the inverse problem. Bayes’ theorem allows one to obtain this posterior density through synthesis of the prior information and the observations. To illustrate this Bayesian inverse method, these ideas are applied to a simple ecosystem box model concerned with predicting the seasonal co-evolution of a population of grazing shellfish and its two food sources: plankton and detritus. Observations of shellfish biomass over time are available. Lognormal system noise was incorporated into the ecosystem equations at all time steps. Ingestion and respiration parameters for shellfish growth are considered as uncertain quantities described by beta distributions. Stochastic simulation was carried out and provided predictions of the model state with uncertainty estimates. The Bayesian inverse method was then used to assimilate the additional information contained in the observations. Posterior probability density functions for the parameters and time-varying ecological state were computed using Markov Chain Monte Carlo methods. The ecological dynamics spread the measurement information to all state variables and parameters, even those not directly observed. Probabilistic state estimates are refined in comparison to those from the stochastic simulation. It is concluded that this Bayesian approach appears promising as a framework for ecosystem inverse problems, but requires careful control of the dimensionality for practical applications.

Using Markov chain Monte Carlo methods for estimating parameters with gravitational radiation data

We present a Bayesian approach to the problem of determining parameters for coalescing binary systems observed with laser interferometric detectors. By applying a Markov Chain Monte Carlo (MCMC) algorithm, specifically the Gibbs sampler, we demonstrate the potential that MCMC techniques may hold for the computation of posterior distributions of parameters of the binary system that created the gravity radiation signal. We describe the use of the Gibbs sampler method, and present examples whereby signals are detected and analyzed from within noisy data.

Applied Bayesian Data Analysis Using State-Space Models

This paper reviews the Bayesian approach to parameter estimation in nonlinear nonnormal state-space models with posterior computations performed by Gibbs sampling. Fitting of nonlinear nonnormal state-space models is an important task in various scientific disciplines. The ease with which the Bayesian approach can now be implemented via BUGS, a recently developed, user-friendly, and freely available software package, should have a major impact on applied research. This is illustrated using examples from three different areas of currently active research: econonometrics, fisheries, and physics.