16,014 research outputs found
Approximate Integrated Likelihood via ABC methods
We propose a novel use of a recent new computational tool for Bayesian
inference, namely the Approximate Bayesian Computation (ABC) methodology. ABC
is a way to handle models for which the likelihood function may be intractable
or even unavailable and/or too costly to evaluate; in particular, we consider
the problem of eliminating the nuisance parameters from a complex statistical
model in order to produce a likelihood function depending on the quantity of
interest only. Given a proper prior for the entire vector parameter, we propose
to approximate the integrated likelihood by the ratio of kernel estimators of
the marginal posterior and prior for the quantity of interest. We present
several examples.Comment: 28 pages, 8 figure
A note on marginal posterior simulation via higher-order tail area approximations
We explore the use of higher-order tail area approximations for Bayesian
simulation. These approximations give rise to an alternative simulation scheme
to MCMC for Bayesian computation of marginal posterior distributions for a
scalar parameter of interest, in the presence of nuisance parameters. Its
advantage over MCMC methods is that samples are drawn independently with lower
computational time and the implementation requires only standard maximum
likelihood routines. The method is illustrated by a genetic linkage model, a
normal regression with censored data and a logistic regression model
Beyond first-order asymptotics for Cox regression
To go beyond standard first-order asymptotics for Cox regression, we develop
parametric bootstrap and second-order methods. In general, computation of
-values beyond first order requires more model specification than is
required for the likelihood function. It is problematic to specify a censoring
mechanism to be taken very seriously in detail, and it appears that
conditioning on censoring is not a viable alternative to that. We circumvent
this matter by employing a reference censoring model, matching the extent and
timing of observed censoring. Our primary proposal is a parametric bootstrap
method utilizing this reference censoring model to simulate inferential
repetitions of the experiment. It is shown that the most important part of
improvement on first-order methods - that pertaining to fitting nuisance
parameters - is insensitive to the assumed censoring model. This is supported
by numerical comparisons of our proposal to parametric bootstrap methods based
on usual random censoring models, which are far more unattractive to implement.
As an alternative to our primary proposal, we provide a second-order method
requiring less computing effort while providing more insight into the nature of
improvement on first-order methods. However, the parametric bootstrap method is
more transparent, and hence is our primary proposal. Indications are that
first-order partial likelihood methods are usually adequate in practice, so we
are not advocating routine use of the proposed methods. It is however useful to
see how best to check on first-order approximations, or improve on them, when
this is expressly desired.Comment: Published at http://dx.doi.org/10.3150/13-BEJ572 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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