## Poisson sampling with a discrete prior

### Description

Evaluates and plots the posterior density for mu, the mean rate of occurance in a Poisson process and a discrete prior on mu

### Usage

```poisdp(y.obs, mu, mu.prior, ...)
```

### Arguments

 `y.obs` a random sample from a Poisson distribution. `mu` a vector of possibilities for the mean rate of occurance of an event over a finite period of space or time. `mu.prior` the associated prior probability mass. `...` additional arguments that are passed to `Bolstad.control`

### Value

A list will be returned with the following components:

 `likelihood` the scaled likelihood function for mu given y.obs `posterior` the posterior probability of mu given y.obs `mu` the vector of possible mu values used in the prior `mu.prior` the associated probability mass for the values in mu

`poisgamp` `poisgcp`

### Examples

```
## simplest call with an observation of 4 and a uniform prior on the
## values mu = 1,2,3
poisdp(4,1:3,c(1,1,1)/3)

##  Same as the previous example but a non-uniform discrete prior
mu = 1:3
mu.prior = c(0.3,0.4,0.3)
poisdp(4,mu=mu,mu.prior=mu.prior)

##  Same as the previous example but a non-uniform discrete prior
mu = seq(0.5,9.5,by=0.05)
mu.prior = runif(length(mu))
mu.prior = sort(mu.prior/sum(mu.prior))
poisdp(4,mu=mu,mu.prior=mu.prior)

## A random sample of 50 observations from a Poisson distribution with
## parameter mu = 3 and  non-uniform prior
y.obs = rpois(50,3)
mu = c(1:5)
mu.prior = c(0.1,0.1,0.05,0.25,0.5)
results = poisdp(y.obs, mu, mu.prior)

##  Same as the previous example but a non-uniform discrete prior
mu = seq(0.5,5.5,by=0.05)
mu.prior = runif(length(mu))
mu.prior = sort(mu.prior/sum(mu.prior))
y.obs = rpois(50,3)
poisdp(y.obs,mu=mu,mu.prior=mu.prior)

```