Poisson3_1D: 1-Dimensional NonHomogeneous Poisson example.

In inlabru: Bayesian Latent Gaussian Modelling using INLA and Extensions

1-Dimensional NonHomogeneous Poisson example.

Description

Point data and count data, together with intensity function and expected counts for a multimodal nonhomogeneous 1-dimensional Poisson process example. Counts are given for two different gridded data interval widths.

Usage

data(Poisson3_1D)

Format

The data contain the following R objects:

lambda3_1D

A function defining the intensity function of a nonhomogeneous Poisson process. Note that this function is only defined on the interval (0,55).

E_nc3a

The expected counts of gridded data for the wider bins (10 bins).

E_nc3b

The expected counts of gridded data for the wider bins (20 bins).

pts3

The locations of the observed points (a data frame with one column, named x).

countdata3a

A data frame with three columns, containing the count data for the 10-interval case:

countdata3b

A data frame with three columns, containing the count data for the 20-interval case:

x

The grid cell midpoint.

count

The number of detections in the cell.

exposure

The width of the cell.

Examples

if (require("ggplot2", quietly = TRUE)) {
  data(Poisson3_1D)
  # first the plots for the 10-bin case:
  p1a <- ggplot(countdata3a) +
    geom_point(data = countdata3a, aes(x = x, y = count), col = "blue") +
    ylim(0, max(countdata3a$count, E_nc3a)) +
    geom_point(
      data = countdata3a, aes(x = x), y = 0, shape = "+",
      col = "blue", cex = 4
    ) +
    geom_point(
      data = data.frame(x = countdata3a$x, y = E_nc3a),
      aes(x = x), y = E_nc3a, shape = "_", cex = 5
    ) +
    xlab(expression(bold(s))) +
    ylab("count")
  ss <- seq(0, 55, length.out = 200)
  lambda <- lambda3_1D(ss)
  p2a <- ggplot() +
    geom_line(
      data = data.frame(x = ss, y = lambda), aes(x = x, y = y),
      col = "blue"
    ) +
    ylim(0, max(lambda)) +
    geom_point(data = pts3, aes(x = x), y = 0.2, shape = "|", cex = 4) +
    xlab(expression(bold(s))) +
    ylab(expression(lambda(bold(s))))
  multiplot(p1a, p2a, cols = 1)

  # Then the plots for the 20-bin case:
  p1a <- ggplot(countdata3b) +
    geom_point(data = countdata3b, aes(x = x, y = count), col = "blue") +
    ylim(0, max(countdata3b$count, E_nc3b)) +
    geom_point(
      data = countdata3b, aes(x = x), y = 0, shape = "+",
      col = "blue", cex = 4
    ) +
    geom_point(
      data = data.frame(x = countdata3b$x, y = E_nc3b),
      aes(x = x), y = E_nc3b, shape = "_", cex = 5
    ) +
    xlab(expression(bold(s))) +
    ylab("count")
  ss <- seq(0, 55, length.out = 200)
  lambda <- lambda3_1D(ss)
  p2a <- ggplot() +
    geom_line(
      data = data.frame(x = ss, y = lambda), aes(x = x, y = y),
      col = "blue"
    ) +
    ylim(0, max(lambda)) +
    geom_point(data = pts3, aes(x = x), y = 0.2, shape = "|", cex = 4) +
    xlab(expression(bold(s))) +
    ylab(expression(lambda(bold(s))))
  multiplot(p1a, p2a, cols = 1)
}

inlabru documentation built on Aug. 9, 2025, 1:08 a.m.