Bernoulli.heredity

Independent Bernoulli prior on models that with constraints for
model hierarchy induced by interactions

Package for Bayesian Variable Selection and Model Averaging
in linear models and generalized linear models using stochastic or
deterministic sampling without replacement from posterior
distributions. Prior distributions on coefficients are
from Zellner's g-prior or mixtures of g-priors
corresponding to the Zellner-Siow Cauchy Priors or the
mixture of g-priors from Liang et al (2008)
<DOI:10.1198/016214507000001337>
for linear models or mixtures of g-priors from Li and Clyde
(2019) <DOI:10.1080/01621459.2018.1469992> in generalized linear models.
Other model selection criteria include AIC, BIC and Empirical Bayes
estimates of g. Sampling probabilities may be updated based on the sampled
models using sampling w/out replacement or an efficient MCMC algorithm which
samples models using a tree structure of the model space
as an efficient hash table. See Clyde, Ghosh and Littman (2010)
<DOI:10.1198/jcgs.2010.09049> for details on the sampling algorithms.
Uniform priors over all models or beta-binomial prior distributions on
model size are allowed, and for large p truncated priors on the model
space may be used to enforce sampling models that are full rank.
The user may force variables to always be included in addition to imposing
constraints that higher order interactions are included only if their
parents are included in the model.
This material is based upon work supported by the National Science
Foundation under Division of Mathematical Sciences grant 1106891.
Any opinions, findings, and
conclusions or recommendations expressed in this material are those of
the author(s) and do not necessarily reflect the views of the
National Science Foundation.

Merlise Clyde

Bayesian Variable Selection and Model Averaging using Bayesian
Adaptive Sampling

Michael Littman

Joyee Ghosh

Yingbo Li

Betsy Bersson

Don van de Bergh

Quanli Wang

Bernoulli.heredity function

<dl><dt>pi</dt>
<dd>Bernoulli probability that term is included</dd>
<dt>parents</dt>
<dd>matrix of terms and parents with indicators of which terms
are parents for each term</dd></dl>

Arguments

Independent Bernoulli prior on models that with constraints for
model hierarchy induced by interactions — Bernoulli.heredity

<dl>

<dt>pi</dt>
<dd>Bernoulli probability that term is included</dd>


<dt>parents</dt>
<dd>matrix of terms and parents with indicators of which terms
are parents for each term</dd>

</dl>

Bernoulli.heredity: Independent Bernoulli prior on models that with constraints for model hierarchy induced by interactions

Description

Usage

Arguments

See Also