In this section are iid observations from the Binomial distribution with density:

In the parameterization above represent the probability of an exitus while is the number of repetitions of the experiment and hence, the maximum value for .

## Case 1: p unknown, n known Edit

Case 1: Recommended prior |
---|

### Formal endorsements Edit

This Beta distribution was first proposed by ^{[1]} and is the reference as well as the Jeffreys prior for .

### Posterior propriety Edit

The posterior distribution associated with this prior is always proper given that the prior it is so. In particular, the (marginal) posterior is

### Other properties Edit

add if any.

### Alternatives Edit

^{[2]} propose an improper prior also known as the Haldane prior.

This is a limiting case of a when

## Case 2: Prior for n Edit

Case 2: Recommended prior |
---|

### Formal endorsements Edit

This prior is the reference prior discussed by ^{[3]}.

### Posterior propriety Edit

add

## ReferencesEdit

- ↑ Bernardo, J. and Smith, A. (1994), Bayesian Theory, John Wiley and Sons, London.
- ↑ Novick, W.R. and Hall, W.J. (1965), A Bayesian indifference procedure.
*Journal of American Statistical Association*, 60, 1104-1117. - ↑ Alba, E.D. and Mendoza, M. (1995), A discrete model for Bayesian forecasting with stable seasonal patterns.
*Advances in Econometrics*,11.