Improper Prior

uniform prior represents the belief that there is no most likely value for \theta and that all values are equally likely

improper priors, which are not proper densities because the integral of f open bracket theta close bracket does not exist.

$$U(a,\infty)$$

$$U(-\infty,\infty)$$

$$U(\infty, b)$$

other improper priors

$$N(a,\infty)$$

$$Gamma(0,0)$$

$$Beta(0,0)$$

can be thought of as a strong prior because as a->0 and b->0, the f(x) forms a strong peak at 0 and 1, indicating belief that the variable can only take those values.