ABSTRACT

Choice of prior distributions is very important as it can be the case that the prior distributions of parameters can affect the posterior significantly. The balance between prior and posterior evidence is related to the dominance of the likelihood and is a sample size issue. For example, with large samples the likelihood usually dominates the prior distributions. This effectively means that current data are given priority in their weight of evidence. Prior distributions that dominate the likelihood are informative, but have less influence as simple size increases. Hence, with additional data, the data speak more. Of course when parameters are not identified within a likelihood then additional data are unlikely to change the importance of informative priors in identification. Propriety of posterior distributions is important as only under propriety can the absolute statements about probability of posterior parameter values be made.