gold_plot: Plot PDF or CDF

In reykp/biRd: What the Package Does in One 'Title Case' Line

Description

Plots the posterior mean PDF or CDF based on the output from gold.

Usage

gold_plot(gold_output, type = "pdf", burnin = NA, cri = FALSE,
  data = FALSE, interact = FALSE)

Arguments

gold_output	The list returned by gold containing the density estimate results.
type	The type of desired graph (see details).
burnin	The desired burnin to discard from the results. If no values is entered, the default is half the number of iterations.
cri	An option to include credible intervals.
data	An option to include data in the graph (see details).
interact	An option to make the plots interactive.

Details

The form of the density whose paramters are estimated in gold 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.

F(x) =

\int_{0}^{x} exp(g(y)) / (\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. These weights are also used in the estimate of the integral in the numerator. Options for type

The input from gold can be used to plot a Bayesian estimate of the PDF or the CDF.

• "pdf": The density, f(x), is calculated at a grid overlayed with the data at each iteration to produce the results in the graph (DEFAULT).

• "cdf": The CDF, F(x), is calculated at a grid overlayed with the data at each iteration. The CDF at each grid point and data point is then averaged across the iterations to produce the results in the graph.

Options for cri

Credibal intervals can also be added to the plot of the PDF or CDF.

• "FALSE": No credible intervals lines are plotted (DEFAULT).

• "TRUE": Credible interval lines are plotted in red on the PDF or CDF. These are calculated by taking the 0.025th and 0.975th quantiles of the iterations from gold after burnin.

Options for data

Incoproates the data into the PDF and CDF.

• "FALSE": The data is not included (DEFAULT).

• "TRUE": If the PDF is plotted, a histogram is overlayed with the density estimate. If the CDF is plotted, the empirical CDF is overlayed with the gold CDF estimate.

Value

A plot of the PDF or CDF estimate.

Examples

## --------------------------------------------------------------------------------
## Uniform Distribution
## --------------------------------------------------------------------------------

# First run 'gold' on data sampled from a Uniform(0,1) distribution with 50 data points.
y <- runif(50)
gold_unif <- gold(y, s1 = 1, c1 = 1, s2 = 0.9, c2 = 0.8, MH_N = 20000)

#Plot the PDF with the data and credible intervals
gold_plot(gold_unif, type="pdf", data=TRUE)

#Plot the CDF with the credible intervals and the empirical CDF
gold_plot(gold_unif, type="cdf", cri=TRUE, data=TRUE)

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

# First run 'gold' on data sampled from a Beta(0.5,0.5) distribution with 300 data points.
y <- rbeta(300, 0.5, 0.5)
gold_arcsin <- gold(y, s1 = 2, c1 = 6, s2 = .2, c2 = 1.5, MH_N = 20000)
#Plot the PDF with the data
gold_plot(gold_arcsin, type="pdf", data=TRUE)

#Plot the CDF with the credible intervals
gold_plot(gold_arcsin, type="cdf", cri=TRUE)

## --------------------------------------------------------------------------------
## Bimodal Distribution
## --------------------------------------------------------------------------------

#Sample 150 random uniforms
U =runif(150)
y = rep(NA,150)
#Sampling from the mixture
for(i in 1:150){
  if(U[i]<.3){
   y[i] = rnorm(1,0,1)
  }else {
   y[i] = rnorm(1,4,1)
  }
}
# First run 'gold' on data sampled from a bimodal distribution with 150 data points.
gold_bimodal <- gold(y, s1 = 1, c1 = 5, s2 = .4, c2 = 3, MH_N = 20000)

#Plot the PDF
gold_plot(gold_bimodal)

#Plot the PDF with credible intervals and a histogram of the data
gold_plot(gold_bimodal, cri=TRUE, data=TRUE)

#Plot the CDF with the empirical CDF
gold_plot(gold_bimodal, type="cdf", data=TRUE)

reykp/biRd documentation built on May 17, 2019, 8:16 p.m.