spike.slab.prior.base {BoomSpikeSlab}

Base class for spike and slab priors

Description

A base class for SpikeSlabPrior and SpikeSlabPriorBase to ensure that elements common to both classes are handled consistently. Users will not normally interact with this function.

Usage

SpikeSlabPriorBase(number.of.variables,
                   expected.r2 = .5,
                   prior.df = .01,
                   expected.model.size = 1,
                   optional.coefficient.estimate = NULL,
                   mean.y,
                   sdy,
                   prior.inclusion.probabilities = NULL,
                   sigma.upper.limit = Inf)

Arguments

number.of.variables

The number of columns in x.

expected.r2

The expected R-square for the regression. The spike and slab prior requires an inverse gamma prior on the residual variance of the regression. The prior can be parameterized in terms of a guess at the residual variance, and a "degrees of freedom" representing the number of observations that the guess should weigh. The guess at sigma^2 is set to (1-expected.r2) * var(y) .

prior.df

A positive scalar representing the prior 'degrees of freedom' for estimating the residual variance. This can be thought of as the amount of weight (expressed as an observation count) given to the expected.r2 argument.

expected.model.size

A positive number less than ncol(x), representing a guess at the number of significant predictor p variables. Used to compute a default value of prior.inclusion.probabilities if the latter is NULL.

optional.coefficient.estimate

If desired, an estimate of the regression coefficients can be supplied. In most cases this will be a difficult parameter to specify. If omitted then a prior mean of zero will be used for all coordinates except the intercept, which will be set to mean.y.

mean.y

The mean of the response vector. Used to create a default value of optional.coefficient.estimate when the latter is NULL.

sdy

The standard deviation of the response vector. Used along with expected.r2 to create a prior estimate of the residual variance.

prior.inclusion.probabilities

A vector giving the prior probability of inclusion for each coefficient.

sigma.upper.limit

The largest acceptable value for the residual standard deviation. A non-positive number is interpreted as Inf.

Value

Returns an object of class SpikeSlabPriorBase, which is a list with the following elements.

• prior.inclusion.probabilities: A vector giving the prior probability of inclusion for each coefficient.

• mu: A vector giving the prior mean of each coefficient conditional on inclusion.

• sigma.guess: A prior estimate of the residual standard deviation.

• prior.df: The number of observations worth of weight to be given to sigma.guess.

Author(s)

Steven L. Scott

References

George and McCulloch (1997), "Approaches to Bayesian Variable Selection", Statistica Sinica, 7, 339 – 373.

https://www3.stat.sinica.edu.tw/statistica/oldpdf/A7n26.pdf