estgtp {binspp} R Documentation

## Bayesian MCMC estimation of parameters of generalized Thomas process

### Description

Bayesian MCMC estimation of parameters of generalized Thomas process. The cluster size is allowed to have a variance that is greater or less than the expected value (cluster sizes are over or under dispersed).

### Usage

estgtp(
X,
kappa0 = exp(a_kappa + ((b_kappa^2)/2)),
omega0 = exp(a_omega + ((b_omega^2)/2)),
lambda0 = (l_lambda + u_lambda)/2,
theta0 = exp(a_theta + ((b_theta^2)/2)),
skappa,
somega,
dlambda,
stheta,
smove,
a_kappa,
b_kappa,
a_omega,
b_omega,
l_lambda,
u_lambda,
a_theta,
b_theta,
iter = 5e+05,
plot.step = 1000,
save.step = 1000,
filename
)


### Arguments

 X A point pattern dataset (object of class ppp) to which the model should be fitted. kappa0 Initial value for kappa, by default it will be set as expectation of prior for kappa. omega0 Initial value for omega, by default it will be set as expectation of prior for omega. lambda0 Initial value for lambda, by default it will be set as expectation of prior for lambda. theta0 Initial value for theta, by default it will be set as expectation of prior for theta. skappa variability of proposal for kappa: second parameter of log-normal distribution somega variability of proposal for omega: second parameter of log-normal distribution dlambda variability of proposal for lambda: half of range of uniform distribution stheta variability of proposal for theta: second parameter of log-normal distribution smove variability of proposal for moving center point: SD of normal distribution a_kappa First parameter of prior distribution for kappa, which is log-normal distribution. b_kappa Second parameter of prior distribution for kappa, which is log-normal distribution. a_omega First parameter of prior distribution for omega, which is log-normal distribution. b_omega Second parameter of prior distribution for omega, which is log-normal distribution. l_lambda First parameter of prior distribution for lambda, which is uniform distribution. u_lambda Second parameter of prior distribution for lambda, which is uniform distribution. a_theta First parameter of prior distribution for theta, which is log-normal distribution. b_theta Second parameter of prior distribution for theta, which is log-normal distribution. iter Number of iterations of MCMC. plot.step Step for the graph plotting. If the value is greater than iter parameter value, no plots will be visible. save.step Step for the parameters saving. The file must be specified or has to be set to larger than iter. filename The name of the output RDS file

### Value

The output is an estimated MCMC chain of parameters, centers and connections.

### Examples


library(spatstat)
kappa = 10
omega = .1
lambda= .5
theta = 10

X = rgtp(kappa, omega, lambda, theta, win = owin(c(0, 1), c(0, 1)))
plot(X$X) plot(X$C)

a_kappa = 4
b_kappa = 1
x <- seq(0, 100, length = 100)
hx <- dlnorm(x, a_kappa, b_kappa)
plot(x, hx, type = "l", lty = 1, xlab = "x value",
ylab = "Density", main = "Prior")

a_omega = -3
b_omega = 1
x <- seq(0, 1, length = 100)
hx <- dlnorm(x, a_omega, b_omega)
plot(x, hx, type = "l", lty = 1, xlab = "x value",
ylab = "Density", main = "Prior")

l_lambda = -1
u_lambda = 0.99
x <- seq(-1, 1, length = 100)

hx <- dunif(x, l_lambda, u_lambda)
plot(x, hx, type = "l", lty = 1, xlab = "x value",
ylab = "Density", main = "Prior")

a_theta = 4
b_theta = 1
x <- seq(0, 100, length = 100)
hx <- dlnorm(x, a_theta, b_theta)
plot(x, hx, type = "l", lty = 1, xlab = "x value",
ylab = "Density", main = "Prior")

est = estgtp(X\$X,
skappa = exp(a_kappa + ((b_kappa ^ 2) / 2)) / 100,
somega = exp(a_omega + ((b_omega ^ 2) / 2)) / 100,
dlambda = 0.01,
stheta = exp(a_theta + ((b_theta ^ 2) / 2)) / 100, smove = 0.1,
a_kappa = a_kappa, b_kappa = b_kappa,
a_omega = a_omega, b_omega = b_omega,
l_lambda = l_lambda, u_lambda = u_lambda,
a_theta = a_theta, b_theta = b_theta,
iter = 50, plot.step = 50, save.step = 1e9,
filename = "")



[Package binspp version 0.1.26 Index]