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Bayesian inference is a method of statistical inference that relies on treating the model parameters as random variables and applying Bayes' theorem to deduce subjective probability statements about the parameters or hypotheses, conditional on the observed dataset.

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Which likelihood and prior corresponds to which loss and regularization?

In Bayesian linear regression having the objective $$\min_w \underbrace{\sum_{i=1}^N (w^Tx_i - y_i)^2}_{\text{log-likelihood}} + \underbrace{\lambda ~ w^Tw}_{\text{log prior distribution}}$$ can be seen …