365 research outputs found
Shape restricted regression with random Bernstein polynomials
Shape restricted regressions, including isotonic regression and concave
regression as special cases, are studied using priors on Bernstein polynomials
and Markov chain Monte Carlo methods. These priors have large supports, select
only smooth functions, can easily incorporate geometric information into the
prior, and can be generated without computational difficulty. Algorithms
generating priors and posteriors are proposed, and simulation studies are
conducted to illustrate the performance of this approach. Comparisons with the
density-regression method of Dette et al. (2006) are included.Comment: Published at http://dx.doi.org/10.1214/074921707000000157 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
A semi-parametric model for circular data based on mixtures of beta distributions
This paper introduces a new, semi-parametric model for circular data, based on mixtures of
shifted, scaled, beta (SSB) densities. This model is more general than the Bernstein polynomial
density model which is well known to provide good approximations to any density with finite
support and it is shown that, as for the Bernstein polynomial model, the trigonometric moments of
the SSB mixture model can all be derived.
Two methods of fitting the SSB mixture model are considered. Firstly, a classical, maximum
likelihood approach for fitting mixtures of a given number of SSB components is introduced. The
Bayesian information criterion is then used for model selection. Secondly, a Bayesian approach
using Gibbs sampling is considered. In this case, the number of mixture components is selected
via an appropriate deviance information criterion.
Both approaches are illustrated with real data sets and the results are compared with those
obtained using Bernstein polynomials and mixtures of von Mises distributions
Profiling time course expression of virus genes---an illustration of Bayesian inference under shape restrictions
There have been several studies of the genome-wide temporal transcriptional
program of viruses, based on microarray experiments, which are generally useful
in the construction of gene regulation network. It seems that biological
interpretations in these studies are directly based on the normalized data and
some crude statistics, which provide rough estimates of limited features of the
profile and may incur biases. This paper introduces a hierarchical Bayesian
shape restricted regression method for making inference on the time course
expression of virus genes. Estimates of many salient features of the expression
profile like onset time, inflection point, maximum value, time to maximum
value, area under curve, etc. can be obtained immediately by this method.
Applying this method to a baculovirus microarray time course expression data
set, we indicate that many biological questions can be formulated
quantitatively and we are able to offer insights into the baculovirus biology.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS258 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A semi-parametric model for circular data based on mixtures of beta distributions
This paper introduces a new, semi-parametric model for circular data, based on mixtures of shifted, scaled, beta (SSB) densities. This model is more general than the Bernstein polynomial density model which is well known to provide good approximations to any density with finite support and it is shown that, as for the Bernstein polynomial model, the trigonometric moments of the SSB mixture model can all be derived. Two methods of fitting the SSB mixture model are considered. Firstly, a classical, maximum likelihood approach for fitting mixtures of a given number of SSB components is introduced. The Bayesian information criterion is then used for model selection. Secondly, a Bayesian approach using Gibbs sampling is considered. In this case, the number of mixture components is selected via an appropriate deviance information criterion. Both approaches are illustrated with real data sets and the results are compared with those obtained using Bernstein polynomials and mixtures of von Mises distributions.Circular data, Shifted, scaled, beta distribution; Mixture models, Bernstein polynomials
Circular Bernstein polynomial distributions
This paper introduces a new non-parametric approach to the modeling of circular data, based on the use of Bernstein polynomial densities which generalizes the standard Bernstein polynomial model to account for the specific characteristics of circular data. It is shown that the trigonometric moments of the proposed circular Bernstein polynomial distribution can all be derived in closed form. We comment on how to fit the Bernstein polynomial density approximation to a sample of data and illustrate our approach with a real data example.Circular data, Non-parametric modeling, Bernstein polynomials
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