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Bayesian Data Analysis for Data Mining
 In Handbook of Data Mining
, 2002
"... Introduction The Bayesian approach to data analysis computes conditional probability distribu tions of quantities of interest (such as future observables) given the observed data. Bayesian analyses usually begin with a .full probability model  a joint probability dis tribution for all the observ ..."
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Introduction The Bayesian approach to data analysis computes conditional probability distribu tions of quantities of interest (such as future observables) given the observed data. Bayesian analyses usually begin with a .full probability model  a joint probability dis tribution for all the observable and unobservable quantities under study  and then use Bayes' theorem (Bayes, 1763) to compute the requisite conditional probability distributions (called poster'Joy distributions). The theorem itself is innocuous enough. In its simplest form, if Q denotes a quantity of interest and D denotes data, the theorem states: P(ql D) P(;lq) X P(q)/P(). This theorem prescribes the basis for statistical learning in the probabilistic frame work. With p(Q) regarded as a probabilistic statement of prior knowledge about Q before obtaining the data D, p(QI D) becomes a revised probabilistic statement of our knowledge about Q in the light of the data (Bernardo and Smith, 1994, p.2). The marginal lik