# Bayesian point estimate of a random sample

I am new to statistics and some concepts are not clear to me. I have a random sample that is distributed as a Binomial with parameters $$k=2$$ and $$\theta$$ unknow. Using a Bayesian approach I must give a point estimate for $$\theta$$.

I understand that being binomial, a priori I must use a beta distribution, and there is a relationship between the expectation and the variance with the beta distribution. I intend to obtain the expectation and variance of my initial data and with them obtain shape1, shape2, (I am working in R).

to get my a priori beta distribution, but shape1 and shape2 come out negative, which tells me that I am doing something wrong. Can someone guide me? Or if I'm doing it wrong, how should I proceed?

• Are you doing MAP estimation?
– Dave
Commented Jun 12, 2021 at 3:10
• No, if so, I think the problem would be specific, right? Commented Jun 12, 2021 at 3:30
• By the way, you do not "have to" use a beta distribution. The main reason to do so would be that it's really easy to get the posterior (because it's a conjugate prior). In practice, people may choose any kind of prior for various reasons (e.g. a N(0, 2.5) prior on logit($\theta$)). Commented Jun 12, 2021 at 8:20