Functions which operates on marginals

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).

inla.smarginal(
  marginal,
  log = FALSE,
  extrapolate = 0,
  keep.type = FALSE,
  factor = 15L
)

inla.emarginal(fun, marginal, ...)

inla.dmarginal(x, marginal, log = FALSE)

inla.pmarginal(q, marginal, normalize = TRUE, len = 2048L)

inla.qmarginal(p, marginal, len = 2048L)

inla.hpdmarginal(p, marginal, len = 2048L)

inla.rmarginal(n, marginal)

inla.tmarginal(
  fun,
  marginal,
  n = 2048L,
  h.diff = .Machine[["double.eps"]]^(1/3),
  method = c("quantile", "linear")
)

inla.mmarginal(marginal)

inla.zmarginal(marginal, silent = FALSE)

inla.is.marginal(marginal)

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.

log

Return density or interpolated density in log-scale?

extrapolate

How much to extrapolate on each side when computing the interpolation. In fraction of the range.

keep.type

If FALSE then return a list(x=, y=), otherwise if TRUE, then return a matrix if the input is a matrix

factor

The number of points after interpolation is factor times the original number of points; which is argument n in spline

fun

A (vectorised) function like function(x) exp(x) to compute the expectation against, or which define the transformation new = fun(old)

...

Further arguments to be passed to function which expectation is to be computed.

x

Evaluation points

q

Quantiles

normalize

Renormalise the density after interpolation?

len

Number of locations used to interpolate the distribution function.

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

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

Havard Rue hrue@r-inla.org

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^2L),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)
#>                  low     high
#> level:0.95 0.9518712 1.074671

 x = seq(-6, 6, length.out = 1000)
 y = dnorm(x)
 inla.hpdmarginal(0.95, list(x=x, y=y))
#>                  low    high
#> level:0.95 -1.962892 1.95703

 ## 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, m)
 m2 = inla.emarginal(function(x) x^2L, m)
 stdev = sqrt(m2 - m1^2L)
 q = inla.qmarginal(c(0.025,0.975), m)

 ## inla-program results
 print(r)
#>       mean         sd 0.025quant 0.5quant 0.975quant     mode kld
#> x 1.013337 0.03133688  0.9519175 1.013337   1.074756 1.013337   0

 ## inla.marginal-results (they shouldn't be perfect!)
 print(c(mean=m1, sd=stdev, "0.025quant" = q[1], "0.975quant" = q[2L]))
#>       mean         sd 0.025quant 0.975quant 
#> 1.01333663 0.03132028 0.95187122 1.07467146 
 ## using the buildt-in function
 inla.zmarginal(m)
#> Mean            1.01334 
#> Stdev           0.0313203 
#> Quantile  0.025 0.951871 
#> Quantile  0.25  0.992139 
#> Quantile  0.5   1.01327 
#> Quantile  0.75  1.0344 
#> Quantile  0.975 1.07467