I am looking into Bayesian learning for the first time ever and am just wondering why we look to have a conjugate prior to carry out our estimation with.
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4$\begingroup$ you don't have to, its for computational ease. $\endgroup$– bdeonovicFeb 12, 2017 at 14:42
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1$\begingroup$ This question may be useful: stats.stackexchange.com/questions/155059/… $\endgroup$– Christoph HanckFeb 12, 2017 at 16:56
1 Answer
You do not have to have a conjugate prior and indeed, you should not have a conjugate prior unless it fits your prior knowledge. Many conjugate prior distributions are good approximations of actual knowledge. Some can be problematic, like the inverse Wishart, when used in a way that is not representative of information or as a diffuse prior.
Conjugate priors permit fast Bayesian updating, which can be valuable in high dimension problems.
Conjugacy only exists for a fraction of likelihood functions. You cannot always use one.