Bayesian statistics and parameter estimation

We propose a mathematical relation, which maps the predictors x to the responses that involves a set of adjustable model parameters 0 e 9t, whose values we wish to estimate from the measured response data. Let us say that we have a set of N experiments, in which for experiment k=, 2. N, is the row vector of predictor variables and the row vector of measured response data isyf f For each experiment, we have a model prediction of the response 

The basic regression problem is given a proposed model how do we choose 

9 such that the model predictions agree most closely to die observations Of 

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