The prior should reflect knowledge of the distribution of the parameters because it influences the MAP estimate. If a prior is not known with certainty, we need to make a choice, often from several reasonable options. In general, it is good practice to justify the prior and check for robustness by testing whether alternatives lead to the same conclusion.

There are several types of priors:

• Objective priors maximize the impact of the data on the posterior. If the parameter distribution is unknown, we can select an uninformative prior like a uniform distribution, also called a flat prior, over a relevant range of parameter values.
• In contrast, subjective priors aim to incorporate information that's external to the model into the estimate.
• An empirical prior combines Bayesian and frequentist methods and uses historical data to eliminate subjectivity, such as by estimating various moments to fit a standard distribution.

In the context of a machine learning model, the prior can be viewed as a regularizer because it limits the values that the posterior can assume. Parameters that have zero prior probability, for example, are not part of the posterior distribution. Generally, more good data allows for stronger conclusions and reduces the influence of the prior.