Plot samples from the output of Laplace's Demon
This may be used to plot, or save plots of, samples in an object of
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.
1 2 3 4
This required argument is an object of class
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
This required argument must receive the list of data that was
This logical argument indicates whether or not the user wants Laplace's Demon to save the plots as a .pdf file.
This argument accepts a vector of quoted strings to be matched for
selecting parameters for plotting. This argument defaults to
Additional arguments are unused.
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 (
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.
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### See the LaplacesDemon function for an example.
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