Implementation of the Bayesian inference for the two independent Poisson samples model, using the semi-conjugate family of prior distributions.

**Bayesian inference on the ratio of two Poisson rates.**

Suppose you have two counts of events and, assuming each count follows a Poisson distribution with an unknown incidence rate, you are interested in the ratio of the two rates (or *relative risk*). The `brr`

package allows to perform the Bayesian analysis of the relative risk using the natural semi-conjugate family of prior distributions, with a default non-informative prior (see references).

You can install:

- the latest released version from CRAN with

`install.packages("brr")`

- the latest development version from
`github`

using the`devtools`

package:

`devtools::install_github('stla/brr', build_vignettes=TRUE)`

Create a `brr`

object with the `Brr`

function to set the prior parameters `a`

, `b`

, `c`

, `d`

, the two Poisson counts `x`

and `y`

and the samples sizes (times at risk) `S`

and `T`

in the two groups. Simply do not set the prior parameters to use the non-informative prior:

`model <- Brr(x=2, S=17877, y=9, T=16674)`

Plot the posterior distribution of the rate ratio `phi`

:

`plot(model, dpost(phi))`

Get credibility intervals about `phi`

:

`confint(model)`

Get the posterior probability that `phi>1`

:

`ppost(model, "phi", 1, lower.tail=FALSE)`

Update the `brr`

object to include new sample sizes and get a summary of the posterior predictive distribution of `x`

:

`model <- model(Snew=10000, Tnew=10000)spost(model, "x", output="pandoc")`

Look at the vignettes:

`browseVignettes(package = "brr")`

Please report at https://github.com/stla/brr/issues

S. Laurent, C. Legrand: *A Bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials.* ESAIM, Probability & Statistics 16 (2012), 375--398.

S. Laurent: *Some Poisson mixtures distributions with a hyperscale parameter.* Brazilian Journal of Probability and Statistics 26 (2012), 265--278.

S. Laurent: *Intrinsic Bayesian inference on a Poisson rate and on the ratio of two Poisson rates.* Journal of Statistical Planning and Inference 142 (2012), 2656--2671.