# findbetamupsi: The findbetamupsi function In PriorGen: Generates Prior Distributions for Proportions

## Description

A function to estimate (a) the parameters of a Beta distribution for the expected mean of a proportion - usually the prevalence of disease/infection for the units in an area/region and (b) the parameters of a Gamma distribution expressing our prior beleif about the variability of the prevalence estimates across the units of the area/region under consideration.

## Usage

 ```1 2 3``` ```findbetamupsi(themean, percentile=0.95, lower.v=T, percentile.value, psi.percentile=0.90, percentile.median, percentile95value) ```

## Arguments

 `themean` specify your prior beleif about the mean. It takes a value between 0 and 1. `percentile` specify the level of confidence that the true value of the mean is greater or lower than the percentile.value. It takes a value between 0 and 1 and the default is 0.95. `lower.v` logical, if TRUE the specified percentile.value is the upper limit for the mean at the specified confidence level (percentile). If FALSE the specified percentile.value is the lower limit for the mean at the specified confedence level (percentile).The default is TRUE. `percentile.value` specify the upper or lower limit for the mean at the specified level of confidence (percentile). It takes a value between 0 and 1. `psi.percentile` specify the level of confidence that a certain fraction of the units under study has a prevalence less than the percentile.median. It takes a value between 0 and 1 and the default is 0.90. `percentile.median` specify the median value that corresponds to the defined psi.percentile. It takes a value between 0 and 1 and has to be higher than both themean and the percentile. `percentile95value` specify the value that the percentile.median does not exceed with 95% confidence. It takes a value between 0 and 1 and has to be higher than the percentile.median.

## References

Branscum, A. J., Gardner, I. A., & Johnson, W. O. (2004): Bayesian modeling of animal– and herd–level prevalences. Preventive Veterinary Medicine, 66, 101–112.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```##Example 1 ##The mean prevalence of a disease/infection for the units within an area/region ##is thought to be 0.20 and we are 99% confident that it is not more than 0.40. ##Within this area, we are also confident that 90% of all units have a prevalence ##less or equal to 0.50 and we are 95% certain that it does not exceed 0.60 findbetamupsi(themean=0.20, percentile=0.99, lower.v=TRUE, percentile.value=0.30, psi.percentile=0.90, percentile.median=0.50, percentile95value=0.60) ##The output is: ## "The desired Beta distribution that satisfies the specified conditions ##about the mean of the prevalence 'mu' is: Beta( 20.27 81.07 )" ## "The desired Gamma distribution that satisfies the specified conditions ##about the variability 'psi' of the prevalence is: Gamma( 8.97 2.79 )" ## "The plot gives the specified prior beleif on the prevalence distribution." ## "Descriptive statistics for this distrubiton are:" ## Min. 1st Qu. Median Mean 3rd Qu. Max. ##0.00000 0.03589 0.13164 0.20156 0.30799 0.99971 ```

PriorGen documentation built on May 1, 2019, 9:17 p.m.