gold_stat: Statistics from GOLD.
In reykp/BEDr: What the Package Does in One 'Title Case' Line

Description Usage Arguments Details Value Examples

Calculates a variety of statistics from the gold density estimate.

1	gold_stat(stat, gold_output, p = NA, burnin = NA)

`stat`	A value indicating choice of statistic (see details).
`gold_output`	The list returned by `gold` containing the density estimate results.
`p`	A list of quantiles if quantiles are requested (see details).
`burnin`	The desired burnin to discard from the results. If no values is entered, the default is half the number of iterations.

The form of the density is below:

f(x) =

exp(g(x)) / (\int_{0}^{1} exp(g(u)) du)

where g(x) is an unknown log density.

Given that g(x) is unknown, the normalizing constant is estimated using a weighted average and the set of unknown paramters that recieve a prior is g(x) at a finite set of points.

E[X] = \int_{0}^{1} x * exp(g(x)) / (\int_{0}^{1} exp(g(u)) du)

Var[X] = \int_{0}^{1} (x-x^2) * exp(g(x)) / (\int_{0}^{1} exp(g(u)) du)

The inverse CDF is specified below:

Options for stat

Several of the standard statistics are available through the function gold_stat.

"mean" or "m": The E[x] is calculated as in the deatils section for each iteration, and the average of this result is returned as the mean.
"var" or "v": The Var[x] is calculated as in the deatils section for each iteration, and the average of this result is returned as the variance.
"quant" or "q": Returns the quantiles specified in 'p' using the inverse CDF described in the details section.

Options for p

Default is NA is quantiles are not the desired statistics. If 'quant' is specified for stat, p is a single value or vector of values between 0 and 1.

gold_stat the statistic of choice and the credible intervals associated with it.

If 'mean' or 'm' is specified for stat:

`mean`	The E[X] from the details is calulated at each iteration and the mean of these is returned.
`cri`	The credible intervals for E[X] calculated using the 0.025th and 0.975th quantiles.

If 'var' or 'v' is specified for stat:

`variance`	The Var[X] from the details is calulated at each iteration and the mean of these is returned.
`cri`	The credible intervals for Var[X] calculated using the 0.025th and 0.975th quantiles.

If 'quant' or 'q' is specified for stat:

`quantiles`	The quantils specified in 'p' is calulated using the inverse CDF in the details at each iteration and the mean of these is returned.
`cri`	The credible intervals for the quantiles calculated using the 0.025th and 0.975th quantiles.

## --------------------------------------------------------------------------------
## Beta Distribution
## --------------------------------------------------------------------------------

# First run 'gold' on data sampled from a Beta(2, 6) distribution with 100 data points.
y <- rbeta(100, 2, 6)
gold_beta <- gold(y, s1 = 1, c1 = 1, s2 = 1, c2 = 0.8, MH_N = 20000)

#Get an estimate of the mean and its credible intervals
gold_stat(gold_beta, stat="mean")

#Get an estimate of the variance and its credible intervals
gold_stat(gold_beta, stat="var")

## --------------------------------------------------------------------------------
## Normal Distribution
## --------------------------------------------------------------------------------

# First run 'gold' on data sampled from a Normal(0, 1) distribution with 200 data points.
y <- rnorm(200, 0, 1)
gold_norm <- gold(y, s1 = 1, c1 = 1, s2 = 0.5, c2 = 0.8, MH_N = 20000)

#Get an estimate of the quantils and their credible intervals
gold_stat(gold_norm, stat="q", p=c(0.1, 0.5, 0.9))