# conjugate prior: is ever the best choice?

I'm reading about the conjugate prior of classic probability distributions (e.g. beta distribution for binomial distribution); it's explained just as "algebric trick" to have easier calculation in computing $$Pr(x|\theta)=\frac{Pr(\theta|x)Pr(x)}{Pr(\theta)}$$ my questions are:

1. is conjugate prior the only possible choice for $Pr(\theta)$?
2. If not, conjugate is ever the best choice?
3. In parameter estimation methods (e.g. Maximum Likelihood Estimation), if I choice, for example, two different prior distribution $Pr^A(\theta)$ (e.g. the conjugate) and $Pr^B(\theta)$ (e.g. another distribution different from the conjugate) and compute MLE with both configurations, will I obtain the same solutions? If not, why? Parameter estimation methods should find best solution (e.g. MLE would maximize), so it should give me the best solution (i.e. the best value of $\theta$) independently from the shape of prior that I choice...Is right?
• Apr 16 '17 at 17:36