param function

Initialization of georamps Model Parameters

Function used in conjunction with ramps.control to specify the initial values and prior distributions used in calls to georamps.

param(init, prior = c("flat", "invgamma", "normal", "uniform", "user"), tuning,
         ...)

Arguments

• init: numerical vector of initial parameter values. NA elements will be replaced with random draws from the prior distribution when possible.
• prior: character string specifying the prior distribution. This must be one of "flat", "invgamma", "normal", "uniform", or "user", with default "flat", and may be abbreviated to a unique prefix.
• tuning: numerical tuning values the slice-simplex routine in the MCMC sampler.
• ...: hyperparameters of the specified prior distribution. See details below.

Details

The supported prior distributions and associated hyperparameters are:

• "flat": Flat prior with no hyperparameters.
• "invgamma": Inverse-gamma with hyperparameters shape > 0 and scale > 0 such that $f(x) = scale^shape / gamma(shape) * x^{-shape - 1} * exp(-scale / x)$.
• "normal": Normal with hyperparameters mean and variance such that $(2*pi)^(-n/2) * det(variance)^(-1/2) * exp(-1/2 * t(x - mean)$. The variance hyperparameter must be positive definite and may be supplied either as a vector (independence) or a matrix.
• "uniform": Uniform with hyperparameters min and max > min such that $f(x) = 1 / (max - min)$.
• "user": Use-defined function supplied as hyperparameter f which takes a single numeric vector of length and order equal to the associated model parameters and whose returns values are proportional to the prior distribution.

The number of model parameters to be initialized is determined by length(init). Missing values occurring in the supplied init vector will be replaced with draws from the prior distribution, for all but the "flat" specification.

Returns

A list of class 'param' containing the following components: - init: numerical vector of initial parameter values.

• prior: character string specifying the prior distribution.

• tuning: numerical vector of tuning values of length(init).

• ...: hyperparameters of the specified prior distribution.

Author(s)

Brian Smith brian-j-smith@uiowa.edu

See Also

georamps, ramps.control

Examples

## Initial values for a flat prior
param(rep(0, 2), "flat")

## Random generation of initial values for an inverse-gamma prior
param(rep(NA, 2), "invgamma", shape = 2.0, scale = 0.1)

## Independent normal priors
param(rep(0, 2), "normal", mean = c(0, 0), variance = c(100, 100))

## Correlated normal priors
npv <- rbind(c(100, 25), c(25, 100))
param(rep(0, 2), "normal", mean = c(0, 0), variance = npv)

## Uniform prior and MCMC tuning parameter specification
param(10, "uniform", min = 0, max = 100, tuning = 0.5)