credsubs.level {credsubs}

Compute the maximum credible levels at which conclusions may be drawn

Description

For each covariate point, credsubs.level computes the maximum credible level at which a conclusion may be drawn at each point, and what that conclusion is.

Usage

credsubs.level(
  params,
  design = NULL,
  FUN = function(x, params) {     params %*% t(x) },
  threshold = 0,
  method = c("asymptotic", "quantile"),
  step.down = TRUE,
  sides = c("both", "exclusive", "inclusive"),
  est.FUN = mean,
  var.FUN = sd,
  point.estimate = NULL,
  track = numeric(0),
  verbose = FALSE,
  z.store = c("ram", "recompute", "disk")
)

Arguments

params

A numeric matrix whose rows are draws from the posterior distribution of either the regression surface or the parameter vector.

design

(Optional) A numeric matrix whose rows are covariate points over which the band is to be constructed.

FUN

(Optional) a function of the form function(x, params) that takes a row of design and the entire params matrix and returns a vector of the same length of x representing the regression surface.

threshold

Numeric; the value of FUN above which a covariate is included in the target subset.

method

Either "asymptotic" (default) or "quantile"; see details.

step.down

Logical (default TRUE); should the step-down procedure be used?

sides

One of "both" (default), "exclusive", or "inclusive". Which bounds should be constructed?

est.FUN

The function used to produce estimates of the regression surface. Default is mean.

var.FUN

The function used to quantify the variability of the regression surface posterior. Default is sd.

point.estimate

If not null, replaces the mean and sets the reference around which the standard error is computed. Useful for bootstrapping methods. Treated as a row of the params matrix.

track

A numeric vector of indices indicating which rows (default none) of the design matrix should have the sample of the corresponding FUN(x, params) returned.

verbose

Logical (default FALSE); print progress?

z.store

How should certain intermediate computations be handled? See details.

Details

If design is NULL (default), it is taken to be the identity matrix of dimension ncol(params), so that the rows of params are treated as draws from the posterior FUN(x, params).

The 'asymptotic' method assumes that the marginal posteriors of the FUN(x, params) are asymptotically normal and is usually significantly faster and less memory-intensive than the 'quantile' method, which makes no such assumption.

By default (z.store = "ram"), the maximum credible level computation stores a potentially very large amount of intermediate computation results in memory. If not enough memory is available, z.store = "disk" uses the ff package to store the intermediate results on disk, which can still be fairly quick if the storage is fast (e.g. a local SSD). Alternatively, z.store = "recompute" discards the intermediate results and recomputes whenever needed. This uses minimal memory, but is usually the slowest option.

Value

An object of class credsubs.level, which contains:

level

A numeric vector indicating the maximum credible level at which a conclusion may be drawn at each covariate point.

sign

A numeric vector indicating the which credible subsets of which each covariate point is a member at the credible level indicated by level. Exclusive and inclusive: 1, inclusive only: 0, neither: -1.

threshold

As provided.

method

As provided.

step.down

As provided.

sides

As provided.

est

Posterior estimate of the regression surface.

est.FUN

As provided.

var

Summary of posterior variability of the regression surface.

var.FUN

As provided.

trace

The posterior samples of the regression surface indicated by the track argument.

Examples

### Sample from regression surface posterior
reg.surf.sample <- matrix(rnorm(1000, mean=1:10), ncol=2, byrow=TRUE)
credsubs.level(reg.surf.sample)

### Parametric case
design <- cbind(1, 1:10)
params <- matrix(rnorm(200, mean=1:2), ncol=2, byrow=TRUE)
credsubs(params, design)

### With custom function
params.sd <- cbind(1 / rgamma(100, 1), params)
FUN.sd <- function(x, params) { params[, -1] %*% t(x) / params[, 1] }
credsubs(params.sd, design, FUN.sd, threshold=1)