plot_outputs function

Graphical output describing the posterior distributions

A graphical representation of the posterior distributions in terms of histograms and trace plots.

plot_outputs(Output)

Arguments

• Output: list, output of the main function estintp().

Returns

Series of plots providing a graphical representation of the posterior distributions in terms of histograms and trace plots.

Details

If the covariate list z_beta was non-empty, the estimated intensity function of the parent process is plotted. Then, the estimated surface representing the location dependent mean number of points in a cluster is plotted, and similarly, the estimated surface representing the location dependent scale of clusters is plotted.

After that, histograms of the sample posterior distributions of the individual parameters are plotted, together with the histograms of p-values giving significance of the individual covariates in z_beta with respect to the population of parent points.

Then, the trace plots for individual model parameters are plotted, with highlighted sample median (full red line) and sample 2.5% and 97.5% quantiles (dashed red lines), and similarly for the p-values giving significance of the individual covariates in z_beta with respect to the population of parent points.

Additionally, the following graphs are also plotted:

• trace plot for the log-likelihood of the model,
• trace plot for the number of parent points,
• trace plot for the probability of accepting proposed updates of $(alpha, alpha_1, …, alpha_l)$, ****
• trace plot for the fraction of accepted updates of $alpha, alpha_1, …, alpha_l$ in the last 1000 iterations,
• trace plot for the probability of accepting proposed updates of $omega, omega_1, …, omega_m$, ****
• trace plot for the fraction of accepted updates of $omega, omega_1, …, omega_m$ in the last 1000 iterations,
• trace plot for the fraction of accepted updates of parent points in the last 1000 iterations.

Examples

library(spatstat)
# Prepare the dataset:
X = trees_N4
x_left = x_left_N4
x_right = x_right_N4
y_bottom = y_bottom_N4
y_top = y_top_N4

z_beta = list(refor = cov_refor, slope = cov_slope)
z_alpha = list(tmi = cov_tmi, tdensity = cov_tdensity)
z_omega = list(slope = cov_slope, reserv = cov_reserv)

# Determine the union of rectangles:
W = owin(c(x_left[1], x_right[1]), c(y_bottom[1], y_top[1]))
if (length(x_left) >= 2) {
  for (i in 2:length(x_left)) {
    W2 = owin(c(x_left[i], x_right[i]), c(y_bottom[i], y_top[i]))
    W = union.owin(W, W2)
  }
}

# Dilated observation window:
W_dil = dilation.owin(W, 100)

# Default parameters for prior distributions:
control = list(NStep = 100, BurnIn = 20, SamplingFreq = 5)

# MCMC estimation:
Output = estintp(X, control, x_left, x_right, y_bottom, y_top, W_dil,
                 z_beta, z_alpha, z_omega, verbose = FALSE)

# Text output + series of figures:
print_outputs(Output)
plot_outputs(Output)