Conjugate priors noninformative priors

The gamma density as a prior for the Poisson parameter or the beta density as the prior for the binomial parameter are called conjugate priors. The meaning is this: we begin with a density (say the gamma), collect data (from a Poisson process), and update using Bayes's theorem to end with a posterior that is also the same type of density, but with changed parameters. We say that the density is ''closed'' during updating. When computation was very difficult to do, conjugate priors played a key and important role in Bayesian analysis because they allowed operational implementation of the Bayesian approach. Modern computational methods allow us to operationalize Bayesian approaches without resort to conjugate priors. Another common prior used in Bayesian analysis is called the non-informative prior. The rough idea with these is that one chooses the prior so that the location but not the shape of the posterior is changed by the data; this is not the same as choosing a uniform prior. A simple illustration of these differences is provided by Mangel and Beder (1985). For more general details, I suggest any of Martz and Waller (1982), Leonard and Hsu (1999), or Congdon (2001).

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