Select from the following statements the true ones for uniform priors. Here, we define the maximum a posteriori estimator to be the value that maximizes the posterior distribution. (In this question, we also allow improper priors.)

Question

They can be defined only on parameter sets \Theta with a finite number of possible values.

They necessarily integrate to 1 over all continuous and discrete parameter sets

They reflect an equal belief in each possible value of the parameter.

The maximum a posteriori estimator and maximum likelihood estimator are the same when using such a prior distribution.

Answer 1

They reflect an equal belief in each possible value of the parameter.

The maximum a posteriori estimator and maximum likelihood estimator are the same when using such a prior distribution.