Inference using MCMC to a new conjugate prior to positive parameters, applied in environmental data

Choosing the prior distribution may have great impact on the result of the posterior distribution and, consequently, point and interval estimation of parameters and the respective predictive density. In situations where the parameters are positive, the gamma distribution is the most common as a conjugate prior to a wide family of parameters. Bourguignon presented the weighted Lindley (WL) distribution as an alternative conjugate prior to parameters conjugated from the gamma family. This work consists in presenting a general way to perform inference to this parameters in a p-parametric vector distribution. The method is illustrated with two cases where both the WL distribution and the gamma distribution are conjugated to these families. Estimation of posterior points is sampled using MCMC techniques. The results of the applications showed advantage on using the WL prior distribution, compared to results with the usual prior gamma distribution.