Now, consider the case where our prior distribution is still extsf{Beta}(a, b). Suppose we are to change our conditional likelihood model from extsf{Ber}(p) to one of the options listed below, still maintaining the i.i.d. assumption for the observations. Which of these will necessarily result into the posterior distribution being a Beta distribution, regardless of the observations? Assume that we only define the likelihood over 0 \leq p \leq 1. (Choose all that apply.)

Question

Now, consider the case where our prior distribution is still 	extsf{Beta}(a, b). Suppose we are to change our conditional likelihood model from 	extsf{Ber}(p) to one of the options listed below, still maintaining the i.i.d. assumption for the observations. Which of these will necessarily result into the posterior distribution being a Beta distribution, regardless of the observations? Assume that we only define the likelihood over 0 \leq p \leq 1. (Choose all that apply.)

extsf{Geom}(p)

extsf{Poiss}(\frac{1}{p})

extsf{Unif}([0, p])

extsf{N}(0, p^2)

GPT 3.5 · Answer

The options that will necessarily result in the posterior distribution being a Beta distribution, regardless of the observations, are: 	extsf{Geom}(p) 	extsf{Unif}([0, p])