sim2D_RandSet_HPPP {sim2Dpredictr}

Generate a Random Set Using a Poisson Process and Random Radii About Events

Description

A random set is generated by using a Poisson process in 2D space to choose 'event' locations, about which a circle of random radius is 'drawn'. The union of the circles defines ultimately defines the set.

Usage

sim2D_RandSet_HPPP(
  N,
  xlim = c(0, 1),
  ylim = c(0, 1),
  radius.bounds = c(0.02, 0.1),
  lambda = 50,
  lambda.sd = 10,
  lambda.bound = NULL,
  prior = "gamma",
  random.lambda = FALSE,
  sub.area = FALSE,
  min.sa = c(0.1, 0.1),
  max.sa = c(0.3, 0.3),
  radius.bounds.min.sa = c(0.02, 0.05),
  radius.bounds.max.sa = c(0.08, 0.15),
  print.subj.sa = FALSE,
  print.lambda = FALSE,
  print.iter = FALSE
)

Arguments

N

A scalar value determining the number of images to create.

xlim, ylim

These are the 2D image limits. Defaults for both are c(0, 1). It is not recommended to alter these arguments unless changing the limits has a specific practical utility.

radius.bounds

A 2-element vector whose first and second entries determine the minimum and maximum radius sizes, respectively; these will be the bounds of the uniform distribution used to draw the radii. If sub.area = TRUE, then use radius.bounds.min.sa and radius.bounds.max.sa.

lambda

A scalar value specifying the mean/intensity value of the Poisson process. If random.lambda = FALSE then this is the parameter used to generate the binary image for each subject. If random.lambda = TRUE, then this is the mean parameter in the distribution used to draw subject-specific lambda.

lambda.sd

Only utilized when random.lambda = TRUE, and specifies the standard deviation in the distribution used to draw subject-specific lambda.

lambda.bound

Only utilized when random.lambda = TRUE, and allows the user to specify a lower and upper bound for the subject-specific lambda; if the randomly selected value is outside of this range, then another draw is taken. This continues until a value is selected within the specified bounds. If no bounds are desired then specify lambda.bound = NULL.

prior

Only utilized when random.lambda = TRUE, and specifies the distribution from which to draw the subject-specific lambda. Options are c("gaussian", "gamma").

random.lambda

random.lambda = TRUE allows the lambda (mean/intensity) parameter in the Poisson process to vary randomly by subject.

sub.area

When sub.area = TRUE, a random sub-section of the image is chosen, within which the Poisson process is used to generate the binary image.

min.sa, max.sa

Only utilized when sub.area = TRUE, and determines the width and height of the minimum and maximum sub-areas; e.g., if min.sa = c(0.1, 0.1), then the smallest possible random sub-area is a 0.1 x 0.1 square.

radius.bounds.min.sa, radius.bounds.max.sa

Only utilized when sub.area = TRUE, and specifies radius.bounds for the minimum and maximum sub-areas, respectively. This information is used to adaptively alter the bounds in between the minimum and maximum sub-areas.

print.subj.sa, print.lambda, print.iter

These arguments are either TRUE or FALSE, and define print options for checking that the function is working as the user intends. print.subj.sa = TRUE prints the x-and y-limits for each subject's sub-area. print.lambda = TRUE prints each subject's mean and realized events; the means will be the same unless random.lambda = TRUE, but the number of realized events will always vary. print.iter = TRUE is only used when random.lambda = TRUE and is.null(lambda.bound) = FALSE, and shows iterations for re-drawing when the randomly selected intensity is outside the specified bounds.

Value

A dataframe with columns for subject ID, x-coordinates, y-coordinates, and associated radii.

References

Cressie N, Wikle CK (2011). Statistics for Spatio-Temporal Data, Wiley Series in Probability and Statistics. John Wiley & Sons, Hoboken, NJ.