23,422 research outputs found
Continual Reassessment and Related Dose-Finding Designs
During the last twenty years there have been considerable methodological
developments in the design and analysis of Phase 1, Phase 2 and Phase 1/2
dose-finding studies. Many of these developments are related to the continual
reassessment method (CRM), first introduced by O'Quigley, Pepe and Fisher
(\citeyearQPF1990). CRM models have proven themselves to be of practical use
and, in this discussion, we investigate the basic approach, some connections to
other methods, some generalizations, as well as further applications of the
model. We obtain some new results which can provide guidance in practice.Comment: Published in at http://dx.doi.org/10.1214/10-STS332 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Reliable ABC model choice via random forests
Approximate Bayesian computation (ABC) methods provide an elaborate approach
to Bayesian inference on complex models, including model choice. Both
theoretical arguments and simulation experiments indicate, however, that model
posterior probabilities may be poorly evaluated by standard ABC techniques. We
propose a novel approach based on a machine learning tool named random forests
to conduct selection among the highly complex models covered by ABC algorithms.
We thus modify the way Bayesian model selection is both understood and
operated, in that we rephrase the inferential goal as a classification problem,
first predicting the model that best fits the data with random forests and
postponing the approximation of the posterior probability of the predicted MAP
for a second stage also relying on random forests. Compared with earlier
implementations of ABC model choice, the ABC random forest approach offers
several potential improvements: (i) it often has a larger discriminative power
among the competing models, (ii) it is more robust against the number and
choice of statistics summarizing the data, (iii) the computing effort is
drastically reduced (with a gain in computation efficiency of at least fifty),
and (iv) it includes an approximation of the posterior probability of the
selected model. The call to random forests will undoubtedly extend the range of
size of datasets and complexity of models that ABC can handle. We illustrate
the power of this novel methodology by analyzing controlled experiments as well
as genuine population genetics datasets. The proposed methodologies are
implemented in the R package abcrf available on the CRAN.Comment: 39 pages, 15 figures, 6 table
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