Choosing a polynomial

In Bayesian regression, we place a prior on the coefficients of the linear regression model that biases the model parameters to 0. The hyperparameters of the model control this prior and to what extent it biases the coefficients of the model to 0. In Bayesian ridge regression, the estimated parameters are the maximum a posteriori probability (MAP) estimates. While I haven't discussed it, there is, in fact, a prior distribution that we are imposing upon the coefficients of the model, and Bayesian ridge regression will estimate a posterior distribution. The coefficients that maximize this posterior distribution are referred to as the MAP estimates of the coefficients. We will choose a polunomial using the following steps: ...

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