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# Estimate of the mean number of events per period *l*

...

We discuss two approaches: Bayesian and classical statistics

#### 1. Bayesian inference

Assuming an uninformed prior *p*(* l)* = 1/

*and the Poisson likelihood function for observing*

*l**events in period*

*a**t*:

The proportional statement is acceptable because we can ignore terms that don't involve * l*, and we then get the posterior distribution:

which by comparison with a Gamma density function is a Gamma(0,1/*t*,* a*) distribution. The Gamma distribution can also be used to describe our uncertainty about

*if we start off with an informed opinion and then observe*

*l**events in time*

*a**t*. If we can reasonably describe our prior belief with a Gamma(0,

*b*,

*a*) distribution, the posterior is given by a Gamma(0,

*b*/ (1 +

*b*

*t*),

*a*+

*) distribution.*

*a*...

Various classic statistics approaches to estimating *l* are discussed here.

#### 3. Comparison of classical and Bayesian methods

A comparison of the different approaches to estimating *l* are discussed here.