Ralph S. Silva

Copula, marginal distributions and model selection: a Bayesian note

Copula functions and marginal distributions are combined to produce multivariate distributions. We show advantages of estimating all parameters of these models using the Bayesian approach, which can be done with standard Markov chain Monte Carlo algorithms. Deviance-based model selection criteria are also discussed when applied to copula models since they are invariant under monotone increasing transformations of the marginals. We focus on the deviance information criterion. The joint estimation takes into account all dependence structure of the parameters’ posterior distributions in our chosen model selection criteria. Two Monte Carlo studies are conducted to show that model identification improves when the model parameters are jointly estimated. We study the Bayesian estimation of all unknown quantities at once considering bivariate copula functions and three known marginal distributions.

Bayesian ratemaking procedure of crop insurance contracts with skewed distribution

Over the years, crop insurance programs became the focus of agricultural policy in the USA, Spain, Mexico, and more recently in Brazil. Given the increasing interest in insurance, accurate calculation of the premium rate is of great importance. We address the crop-yield distribution issue and its implications in pricing an insurance contract considering the dynamic structure of the data and incorporating the spatial correlation in the Hierarchical Bayesian framework. Results show that empirical (insurers) rates are higher in low risk areas and lower in high risk areas. Such methodological improvement is primarily important in situations of limited data.

Modeling volatility using state space models with heavy tailed distributions

This article deals with a non-Gaussian state space model (NGSSM) which is attractive because the likelihood can be analytically computed. The paper focuses on stochastic volatility models in the NGSSM, where the observation equation is modeled with heavy tailed distributions such as Log-gamma, Log-normal and Weibull. Parameter point estimation can be accomplished either using Bayesian or classical procedures and a simulation study shows that both methods lead to satisfactory results. In a real data application, the proposed stochastic volatility models in the NGSSM are compared with the traditional autoregressive conditionally heteroscedastic, its exponential version, and stochastic volatility models using South and North American stock price indexes.