contourmap: Contour maps and contour map quality measures for latent...

In davidbolin/excursions: Excursion Sets and Contour Credibility Regions for Random Fields

Contour maps and contour map quality measures for latent Gaussian models

Description

contourmap is used for calculating contour maps and quality measures for contour maps for Gaussian models.

Usage

contourmap(
  mu,
  Q,
  vars,
  n.levels,
  ind,
  levels,
  type = c("standard", "pretty", "equalarea", "P0-optimal", "P1-optimal", "P2-optimal"),
  compute = list(F = TRUE, measures = NULL),
  use.marginals = TRUE,
  alpha,
  F.limit,
  n.iter = 10000,
  verbose = FALSE,
  max.threads = 0,
  seed = NULL
)

Arguments

mu	Expectation vector.
Q	Precision matrix.
vars	Precomputed marginal variances (optional).
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").
use.marginals	Only marginal distributions are used when finding P-optimal maps (default TRUE).
alpha	Maximal error probability in contour map function (default=1).
F.limit	The limit value for the computation of the F function. F is set to NA for all nodes where F<1-F.limit. Default is F.limit = alpha.
n.iter	Number or iterations in the MC sampler that is used for calculating the quantities in compute. The default value is 10000.
verbose	Set to TRUE for verbose mode (optional).
max.threads	Decides the number of threads the program can use. Set to 0 for using the maximum number of threads allowed by the system (default).
seed	Random seed (optional).

Details

The Gaussian model is specified using the mean mu and the precision matrix Q. The contour map is then computed for the mean, using either the contour levels specified in levels, or n.levels contours that are placed according to the argument type.

A number of quality measures can be computed based based on the specified contour map and the Gaussian distribution. What should be computed is specified using the compute argument. For details on these quanties, see the reference below.

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.

Author(s)

David Bolin [e-mail]

References

Bolin, D. and Lindgren, F. (2017) Quantifying the uncertainty of contour maps, Journal of Computational and Graphical Statistics, vol 26, no 3, pp 513-524.

Bolin, D. and Lindgren, F. (2018), Calculating Probabilistic Excursion Sets and Related Quantities Using excursions, Journal of Statistical Software, vol 86, no 1, pp 1-20.

See Also

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

Examples

n <- 10
Q <- Matrix(toeplitz(c(1, -0.5, rep(0, n - 2))))
mu <- seq(-5, 5, length = n)
lp <- contourmap(mu, Q,
  n.levels = 2,
  compute = list(F = FALSE, measures = c("P1", "P2")),
  max.threads = 1
)
# Plot the contourmap
plot(lp$map)
# Display the quality measures
cat(c(lp$P1, lp$P2))

davidbolin/excursions documentation built on April 12, 2025, 1 a.m.