# Bnormal: Bayesian modelling of a normal (Gaussian) distribution In wiqid: Quick and Dirty Estimates for Wildlife Populations

## Description

Bayesian estimation of centre (μ) and scale (σ) of a normal distribution based on a sample. `Bnormal` uses a gamma prior on the precision, τ = 1/σ^2, while `Bnormal2` applies a gamma prior to σ.

## Usage

 ```1 2 3 4 5 6``` ```Bnormal(y, priors=NULL, chains=3, sample=10000, burnin=100) Bnormal2(y, priors=NULL, chains=3, sample=3e4, burnin=0, thin=1, adapt=1000, doPriorsOnly=FALSE, parallel=NULL, seed=NULL) ```

## Arguments

 `y` a vector (length > 1) with observed sample values; missing values not allowed. `priors` an optional list with elements specifying the priors for the centre and scale; see Details. `doPriorsOnly` if TRUE, `Bnormal2` returns MCMC chains representing the prior distributions, not the posterior distributions for your data set. `chains` the number of MCMC chains to run. `sample` the number of MCMC observations per chain to be returned. `thin` thinning rate. If set to n > 1, n steps of the MCMC chain are calculated for each one returned. This is useful if autocorrelation is high. `burnin` number of steps to discard as burn-in at the beginning of each chain. `adapt` number of steps for adaptation. `seed` a positive integer (or NULL): the seed for the random number generator, used to obtain reproducible samples if required. `parallel` if NULL or TRUE and > 3 cores are available, the MCMC chains are run in parallel. (If TRUE and < 4 cores are available, a warning is given.)

## Details

The function generates vectors of random draws from the posterior distributions of the population centre (μ) and scale (σ). `Bnormal` uses a Gibbs sampler implemented in R, while `Bnormal2` uses JAGS (Plummer 2003).

Priors for all parameters can be specified by including elements in the `priors` list. For both functions, μ has a normal prior, with mean `muMean` and standard deviation `muSD`. For `Bnormal`, a gamma prior is used for the precision, τ = 1\σ^2, with parameters specified by `tauShape` and `tauRate`. For `Bnormal2`, a gamma prior is placed on σ, with parameters specified by mode, `sigmaMode`, and SD, `sigmaSD`.

When `priors = NULL` (the default), `Bnormal` uses improper flat priors for both μ and τ, while `Bnormal2` uses a broad normal prior (muMean = mean(y), muSD = sd(y)*5) for μ and a uniform prior on (sd(y) / 1000, sd(y) * 1000) for σ.

## Value

Returns an object of class `Bwiqid`, which is a data frame with a column for each parameter in the model.

There are `print` and `plot` methods for class `Bwiqid`, as well as diagnostic plots.

## Author(s)

Mike Meredith, `Bnormal` based on code by Brian Neelon, `Bnormal2` adapted from code by John Kruschke.

## References

Kruschke, J K. 2013. Bayesian estimation supersedes the t test. Journal of Experimental Psychology: General 142(2):573-603. doi: 10.1037/a0029146

Plummer, Martyn (2003). JAGS: A Program for Analysis of Bayesian Graphical Models Using Gibbs Sampling, Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003), March 20-22, Vienna, Austria. ISSN 1609-395X

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```# Generate a sample from a normal distribution, maybe the head-body length of a # carnivore in mm: HB <- rnorm(10, 900, 15) Bnormal(HB) # with improper flat priors for mu and tau Bnormal(HB, priors=list(muMean=1000, muSD=200)) Bnormal(HB, priors=list(muMean=1, muSD=0.2)) # a silly prior produces a warning. Bnormal2(HB) # with broad normal prior for mu, uniform for sigma Bnormal2(HB, priors=list(muMean=1000, muSD=200, sigmaMode=20, sigmaSD=10)) ```

wiqid documentation built on Sept. 10, 2017, 9:02 a.m.