A natural question to ask is why should a person's personal prior about a parameter $\theta$ be restricted to be described by a conjugate prior?

Why not some other functional form that more sincerely describes the person's beliefs.

Why not some other functional form that more sincerely describes the person's beliefs?

To be argumentative, one could ask, why should the form of the likelihood function have *anything* to say about my

personal beliefs about $\theta$?

To be argumentative, one could ask, why should the form of the likelihood function have *anything* to say about my personal beliefs about $\theta$?

A dignified response to that question is, well, it shouldn't, but if you want to compute a posterior easily you'll just be happier if your prior is conjugate to your likelihood.

Otherwise, your posterior won't have a convenient analytical form and you'll be in the situation of wanting to

apply the Markov chain Monte Carlo techniques deployed in {doc}`this quantecon lecture <bayes_nonconj>`.

Otherwise, your posterior won't have a convenient analytical form and you'll be in the situation of wanting to apply the Markov chain Monte Carlo techniques deployed in {doc}`this quantecon lecture <bayes_nonconj>`.

We also apply these powerful methods to approximating Bayesian posteriors for non-conjugate priors in

{doc}`this quantecon lecture <ar1_bayes>` and {doc}`this quantecon lecture <ar1_turningpts>`