marginal: Functions which operates on marginals

In inbo/INLA: Full Bayesian Analysis of Latent Gaussian Models using Integrated Nested Laplace Approximations

Description

Density, distribution function, quantile function, random generation, hpd-interval, interpolation, expectations, mode and transformations of marginals obtained by inla or inla.hyperpar(). These functions computes the density (inla.dmarginal), the distribution function (inla.pmarginal), the quantile function (inla.qmarginal), random generation (inla.rmarginal), spline smoothing (inla.smarginal), computes expected values (inla.emarginal), computes the mode (inla.mmarginal), transforms the marginal (inla.tmarginal), and provide summary statistics (inla.zmarginal).

Usage

 inla.dmarginal(x, marginal, log = FALSE)
 inla.pmarginal(q, marginal, normalize = TRUE, len = 2048L)
 inla.qmarginal(p, marginal, len = 2048L)
 inla.rmarginal(n, marginal)
 inla.hpdmarginal(p, marginal, len = 2048L)
 inla.smarginal(marginal, log = FALSE, extrapolate = 0.0, keep.type = FALSE, factor=15L)
 inla.emarginal(fun, marginal, ...)
 inla.mmarginal(marginal)
 inla.tmarginal(fun, marginal, n=2048L, h.diff = .Machine$double.eps^(1/3),
                method = c("quantile", "linear")) 
 inla.zmarginal(marginal, silent = FALSE)
 

Arguments

marginal	A marginal object from either inla or inla.hyperpar(), which is either list(x=c(), y=c()) with density values y at locations x, or a matrix(,n,2) for which the density values are the second column and the locations in the first column. Theinla.hpdmarginal()-function assumes a unimodal density.
fun	A (vectorised) function like function(x) exp(x) to compute the expectation against, or which define the transformation new = fun(old)
x	Evaluation points
q	Quantiles
p	Probabilities
n	The number of observations. If length(n) > 1, the length is taken to be the number required.
h.diff	The step-length for the numerical differeniation inside inla.tmarginal
...	Further arguments to be passed to function which expectation is to be computed.
log	Return density or interpolated density in log-scale?
normalize	Renormalise the density after interpolation?
len	Number of locations used to interpolate the distribution function.
keep.type	If FALSE then return a list(x=, y=), otherwise if TRUE, then return a matrix if the input is a matrix
extrapolate	How much to extrapolate on each side when computing the interpolation. In fraction of the range.
factor	The number of points after interpolation is factor times the original number of points; which is argument n in spline
method	Which method should be used to layout points for where the transformation is computed.
silent	Output the result visually (TRUE) or just through the call.

Value

inla.smarginal returns list=c(x=c(), y=c()) of interpolated values do extrapolation using the factor given, and the remaining function returns what they say they should do.

Author(s)

Havard Rue [e-mail]

See Also

inla, inla.hyperpar

Examples

 ## a simple linear regression example
 n = 10
 x = rnorm(n)
 sd = 0.1
 y = 1+x + rnorm(n,sd=sd)
 res = inla(y ~ 1 + x, data = data.frame(x,y),
            control.family=list(initial = log(1/sd^2),fixed=TRUE))
 
 ## chose a marginal and compare the with the results computed by the
 ## inla-program
 r = res$summary.fixed["x",]
 m = res$marginals.fixed$x

 ## compute the 95% HPD interval
 inla.hpdmarginal(0.95, m)

 x = seq(-6, 6, len = 1000)
 y = dnorm(x)
 inla.hpdmarginal(0.95, list(x=x, y=y))

 ## compute the the density for exp(r), version 1
 r.exp = inla.tmarginal(exp, m)
 ## or version 2
 r.exp = inla.tmarginal(function(x) exp(x), m)
 
 ## to plot the marginal, we use the inla.smarginal, which interpolates (in
 ## log-scale). Compare with some samples.
 plot(inla.smarginal(m), type="l")
 s = inla.rmarginal(1000, m)
 hist(inla.rmarginal(1000, m), add=TRUE, prob=TRUE)
 lines(density(s), lty=2)
 
 m1 = inla.emarginal(function(x) x^1, m)
 m2 = inla.emarginal(function(x) x^2, m)
 stdev = sqrt(m2 - m1^2)
 q = inla.qmarginal(c(0.025,0.975), m)
 
 ## inla-program results
 print(r)
 
 ## inla.marginal-results (they shouldn't be perfect!)
 print(c(mean=m1, sd=stdev, "0.025quant" = q[1], "0.975quant" = q[2]))
 ## using the buildt-in function
 inla.zmarginal(m)
 

inbo/INLA documentation built on Dec. 6, 2019, 9:51 a.m.