Estimation of a probability density function based on parametric statistical mod- els can be highly imprecise and misleading when data are sparse and irregular. In these cases a semiparametric or nonparametric model is preferable and can better capture the data structure. We propose a Bayesian hierarchical model for the estimation of the probability density function. We use a Polya tree (Lavine 1992, 1994) as a nonparametric prior for a random probability measure. The binary partition of the Polya tree is obtained through the quantiles of a Generalized Gamma density function whose parameters are themselves Gamma-distributed random variables. The estimation technique is based on a MCMC sampler using Metropolis-Hastings within Gibbs sampling. We then apply the presented model to the interevent times between strong earthquakes which have occurred between 1600 and 1992 in Italy.
Nonparametric Bayesian Estimation of Probability Density Function
SERI, RAFFAELLO;
2003-01-01
Abstract
Estimation of a probability density function based on parametric statistical mod- els can be highly imprecise and misleading when data are sparse and irregular. In these cases a semiparametric or nonparametric model is preferable and can better capture the data structure. We propose a Bayesian hierarchical model for the estimation of the probability density function. We use a Polya tree (Lavine 1992, 1994) as a nonparametric prior for a random probability measure. The binary partition of the Polya tree is obtained through the quantiles of a Generalized Gamma density function whose parameters are themselves Gamma-distributed random variables. The estimation technique is based on a MCMC sampler using Metropolis-Hastings within Gibbs sampling. We then apply the presented model to the interevent times between strong earthquakes which have occurred between 1600 and 1992 in Italy.
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