# ciBA: Bayesian method of CI estimation with different or same... In proportion: Inference on Single Binomial Proportion and Bayesian Computations

## Description

Bayesian method of CI estimation with different or same parameteric values for Beta prior distribution

## Usage

 `1` ```ciBA(n, alp, a, b) ```

## Arguments

 `n` - Number of trials `alp` - Alpha value (significance level required) `a` - Shape parameter 1 for prior Beta distribution in Bayesian model. Can also be a vector of length n+1 priors. `b` - Shape parameter 2 for prior Beta distribution in Bayesian model. Can also be a vector of length n+1 priors.

## Details

Highest Probability Density (HPD) and two tailed intervals are provided for all xi = 0, 1, 2 ..n based on the conjugate prior β(ai, bi) (i = 1, 2..n+1) for the probability of success `p` of the binomial distribution so that the posterior is β(xi + ai, n - xi + bi).

## Value

A dataframe with

 `x ` - Number of successes (positive samples) `pomean ` - Posterior mean `LBAQ ` - Lower limits of Quantile based intervals `UBAQ ` - Upper limits of Quantile based intervals `LBAH ` - Lower limits of HPD intervals `UBAH ` - Upper limits of HPD intervals

## 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

`prop.test and binom.test` for equivalent base Stats R functionality, `binom.confint` provides similar functionality for 11 methods, `wald2ci` which provides multiple functions for CI calculation , `binom.blaker.limits` which calculates Blaker CI which is not covered here and `propCI` which provides similar functionality.
Other Basic methods of CI estimation: `PlotciAS`, `PlotciAllg`, `PlotciAll`, `PlotciBA`, `PlotciEX`, `PlotciLR`, `PlotciLT`, `PlotciSC`, `PlotciTW`, `PlotciWD`, `ciAS`, `ciAll`, `ciEX`, `ciLR`, `ciLT`, `ciSC`, `ciTW`, `ciWD`
 ```1 2 3 4``` ```n=5; alp=0.05; a=0.5;b=0.5; ciBA(n,alp,a,b) n=5; alp=0.05; a=c(0.5,2,1,1,2,0.5);b=c(0.5,2,1,1,2,0.5) ciBA(n,alp,a,b) ```