rlDirectEval: Fitting restricted likelihood location-scale model using...

In jrlewi/brlm: Bayesian Restricted Likelihood Methods

Description

Deprecated - use rl_direct Full model:

μ~N(η, τ^2), σ^2~IG(α, β), y_1, …, y_n~N(μ, σ^2)

For the restricted likelihood, conditioning is done on a pair of location and scale statistics T(y)=(l(y), s(y)) with the property that l(σ y+μ)=σ l(y)+μ and s(σ y+μ)=σ s(y). Current implementation allows for these to be a pair of M-estimators as implemented in rlm

Usage

rlDirectEval(
  y,
  psi,
  ...,
  scale.est = "Huber",
  k2 = 1.345,
  eta,
  tau,
  alpha,
  beta,
  mu_lims,
  sigma2_lims,
  length_mu,
  length_sigma2,
  smooth = 1,
  N,
  maxit = 1000
)

Arguments

y	vector of data
psi	the psi function used to define the location estimator. It is a function (possibly given by name) that is described in rlm. Tuning constants are passed via ...
...	additional arguments to be passed to psi
scale.est, k2	specification of the scale estimator (issued by name- either 'MAD', 'Huber', or 'proposal 2') and the tuning constant for the Huber proposal 2 scale estimation. See these parameters in rlm for more information.
eta, tau	prior mean and standard deviation for mu
alpha, beta	prior shape and scale for sigma^2
mu_lims, sigma2_lims	vectors of length 2 defining the limits for the numerical integration necessary to find the normalizing constant in Bayes' Theorem
length_mu, length_sigma2	length of the grid in each parameter to do the numerical integration (standard Riemann sum)
smooth	scalar or vector of length 2 that will scale the initial bandwidth computed by hpi.
N	number of samples of the statistics to use for the kernel density estimation
maxit	the limit on the number of IWLS iterations. Same as in rlm

Details

Direct evaluation uses kernel density estimation with a Gaussian kernel to estimate the restricted likelihood. N specifies the number of samples of the statistics to generate for the kernel density estimate. hpi is used to specify the initial bandwidths independently for the location and the scale. These can be multiplied by smooth to 'oversmooth' or 'undersmooth' the estimate. Oversmoothing may result in more stable estimates.

A simple Riemann sum is used to determine the normalizing constant. Parameters for this numerical integration are specified by mu_lims,sigma2_lims, length_mu, and length_sigma2.

Value

A list of length 4: the joint posterior, the two marginals, and the bandwidths used for the kernel density estimate

Author(s)

John R. Lewis [e-mail]

Examples

library(MASS)
set.seed(1) # for reproducibility,
 # length_mu, length_sigma2, N should be larger in reality -
 # they are small so the example runs quickly
y<-data(newcomb)
fit<-rlDirectEval(y=newcomb, psi=psi.bisquare, scale.est='Huber',
   eta=23.6, tau=2.04, alpha=5, beta=10, mu_lims=c(20,32),
   sigma2_lims=c(0.001,100), length_mu=20, length_sigma2=20,
   smooth=1,N=100)
names(fit)
plot(fit$muPost[,1],fit$muPost[,2], type='l', col=4)
plot(fit$sigma2Post[,1],fit$sigma2Post[,2], type='l')

jrlewi/brlm documentation built on March 17, 2021, 1:10 a.m.