Contour maps and contour map quality measures using Monte Carlo samples

contourmap.mc is used for calculating contour maps and quality measures for contour maps based on Monte Carlo samples of a model.

Usage

contourmap.mc(
  samples,
  n.levels,
  ind,
  levels,
  type = c("standard", "equalarea", "P0-optimal", "P1-optimal", "P2-optimal"),
  compute = list(F = TRUE, measures = NULL),
  alpha,
  verbose = FALSE
)

Arguments

samples

Matrix with model Monte Carlo samples. Each column contains a sample of the model.

n.levels

Number of levels in contour map.

ind

Indices of the nodes that should be analyzed (optional).

levels

Levels to use in contour map.

type

Type of contour map. One of:

'standard'

Equidistant levels between smallest and largest value of the posterior mean (default).

'pretty'

Equally spaced 'round' values which cover the range of the values in the posterior mean.

'equalarea'

Levels such that different spatial regions are approximately equal in size.

'P0-optimal'

Levels chosen to maximize the P0 measure.

'P1-optimal'

Levels chosen to maximize the P1 measure.

'P2-optimal'

Levels chosen to maximize the P2 measure.

compute

A list with quality indices to compute

'F':

TRUE/FALSE indicating whether the contour map function should be computed (default TRUE).

'measures':

A list with the quality measures to compute ("P0", "P1", "P2") or corresponding bounds based only on the marginal probabilities ("P0-bound", "P1-bound", "P2-bound").

alpha

Maximal error probability in contour map function (default=0.1).

verbose

Set to TRUE for verbose mode (optional).

Value

contourmap returns an object of class "excurobj" with the following elements

u

Contour levels used in the contour map.

n.levels

The number of contours used.

u.e

The values associated with the level sets G_k.

G

A vector which shows which of the level sets G_k each node belongs to.

map

Representation of the contour map with map[i]=u.e[k] if i is in G_k.

F

The contour map function (if computed).

M

Contour avoiding sets (if F is computed). \(M=-1\) for all non-significant nodes and \(M=k\) for nodes that belong to \(M_k\).

P0/P1/P2

Calculated quality measures (if computed).

P0bound/P1bound/P2bound

Calculated upper bounds quality measures (if computed).

meta

A list containing various information about the calculation.

Details

The contour map is computed for the empirical mean of the samples. See contourmap() and contourmap.inla() for further details.

References

Bolin, D. and Lindgren, F. (2017) Quantifying the uncertainty of contour maps, Journal of Computational and Graphical Statistics, 26:3, 513-524.

Bolin, D. and Lindgren, F. (2018), Calculating Probabilistic Excursion Sets and Related Quantities Using excursions, Journal of Statistical Software, 86(5), 1–20.

See also

contourmap(), contourmap.inla(), contourmap.colors()

Author

David Bolin davidbolin@gmail.com

Examples

n <- 100
Q <- Matrix(toeplitz(c(1, -0.5, rep(0, n - 2))))
mu <- seq(-5, 5, length = n)
## Sample the model 100 times (increase for better estimate)
X <- mu + solve(chol(Q), matrix(rnorm(n = n * 100), nrow = n, ncol = 100))

lp <- contourmap.mc(X, n.levels = 2, compute = list(F = FALSE, measures = c("P1", "P2")))

# plot contourmap
plot(lp$map)

# display quality measures
c(lp$P1, lp$P2)
#> [1] 0.18 0.00