# probPOS: Bayesian posterior Probabilities In proportion: Inference on Single Binomial Proportion and Bayesian Computations

## Description

Bayesian posterior Probabilities

## Usage

 `1` ```probPOS(n, a, b, th) ```

## Arguments

 `n` - Number of trials `a` - Prior Parameters `b` - Prior Parameters `th` - Theta value seeking Pr(Theta/X < th)

## Details

Computes probability of the event p < p0 (p0 is specified in [0, 1]) based on posterior distribution of Beta-Binomial model with given parameters for prior Beta distribution for all x = 0, 1, 2......n where `n` is the number of trials

## Value

A dataframe with

 `x` Number of successes `PosProb` Posterior probability

## References

[1] 2002 Gelman A, Carlin JB, Stern HS and Dunson DB Bayesian Data Analysis, Chapman & Hall/CRC [2] 2006 Ghosh M, Delampady M and Samanta T. An introduction to Bayesian analysis: Theory and Methods. Springer, New York

Other Miscellaneous functions for Bayesian method: `empericalBAx`, `empericalBA`, `probPOSx`, `probPREx`, `probPRE`

## Examples

 ```1 2``` ```n=5; a=0.5; b=0.5; th=0.5; probPOS(n,a,b,th) ```

### Example output

```  x     PosProb
1 0 0.993127696
2 1 0.912287200
3 2 0.669765259
4 3 0.330234727
5 4 0.087712909
6 5 0.006872303
```

proportion documentation built on May 29, 2017, 10:31 a.m.