Plot samples from the output of Laplace's Demon

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Description

This may be used to plot, or save plots of, samples in an object of class demonoid or demonoid.hpc. Plots include a trace plot, density plot, autocorrelation or ACF plot, and if an adaptive algorithm was used, the absolute difference in the proposal variance, or the value of epsilon, across adaptations.

Usage

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## S3 method for class 'demonoid'
plot(x, BurnIn=0, Data, PDF=FALSE, Parms, ...)
## S3 method for class 'demonoid.hpc'
plot(x, BurnIn=0, Data, PDF=FALSE, Parms, ...)

Arguments

x

This required argument is an object of class demonoid or demonoid.hpc.

BurnIn

This argument requires zero or a positive integer that indicates the number of thinned samples to discard as burn-in for the purposes of plotting. For more information on burn-in, see burnin.

Data

This required argument must receive the list of data that was supplied to LaplacesDemon to create the object of class demonoid.

PDF

This logical argument indicates whether or not the user wants Laplace's Demon to save the plots as a .pdf file.

Parms

This argument accepts a vector of quoted strings to be matched for selecting parameters for plotting. This argument defaults to NULL and selects every parameter for plotting. Each quoted string is matched to one or more parameter names with the grep function. For example, if the user specifies Parms=c("eta", "tau"), and if the parameter names are beta[1], beta[2], eta[1], eta[2], and tau, then all parameters will be selected, because the string eta is within beta. Since grep is used, string matching uses regular expressions, so beware of meta-characters, though these are acceptable: ".", "[", and "]".

...

Additional arguments are unused.

Details

The plots are arranged in a 3 x 3 matrix. Each row represents a parameter, the deviance, or a monitored variable. The left column displays trace plots, the middle column displays kernel density plots, and the right column displays autocorrelation (ACF) plots.

Trace plots show the thinned history of the chain or Markov chain, with its value in the y-axis moving by thinned sample across the x-axis. A chain or Markov chain with good properties does not suggest a trend upward or downward as it progresses across the x-axis (it should appear stationary), and it should mix well, meaning it should appear as though random samples are being taken each time from the same target distribution. Visual inspection of a trace plot cannot verify convergence, but apparent non-stationarity or poor mixing can certainly suggest non-convergence. A red, smoothed line also appears to aid visual inspection.

Kernel density plots depict the marginal posterior distribution. Although there is no distributional assumption about this density, kernel density estimation uses Gaussian basis functions.

Autocorrelation plots show the autocorrelation or serial correlation between values of thinned samples at nearby thinned samples. Samples with autocorrelation do not violate any assumption, but are inefficient because they reduce the effective sample size (ESS), and indicate that the chain is not mixing well, since each value is influenced by values that are previous and nearby. The x-axis indicates lags with respect to thinned samples, and the y-axis represents autocorrelation. The ideal autocorrelation plot shows perfect correlation at zero lag, and quickly falls to zero autocorrelation for all other lags.

If an adaptive algorithm was used, then the distribution of absolute differences in the proposal variances, or the value of epsilon, is plotted across adaptations. The proposal variance, or epsilon, should change less as the adaptive algorithm approaches the target distributions. The absolute differences in the proposal variance plot should approach zero. This is called the condition of diminishing adaptation. If it is not approaching zero, then consider using a different adaptive MCMC algorithm. The following quantiles are plotted for absolute changes proposal variance: 0.025, 0.500, and 0.975.

Author(s)

Statisticat, LLC software@bayesian-inference.com

See Also

burnin, ESS, LaplacesDemon, and LaplacesDemon.hpc.

Examples

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### See the LaplacesDemon function for an example.

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