3,668 research outputs found
Bayesian semiparametric inference for multivariate doubly-interval-censored data
Based on a data set obtained in a dental longitudinal study, conducted in
Flanders (Belgium), the joint time to caries distribution of permanent first
molars was modeled as a function of covariates. This involves an analysis of
multivariate continuous doubly-interval-censored data since: (i) the emergence
time of a tooth and the time it experiences caries were recorded yearly, and
(ii) events on teeth of the same child are dependent. To model the joint
distribution of the emergence times and the times to caries, we propose a
dependent Bayesian semiparametric model. A major feature of the proposed
approach is that survival curves can be estimated without imposing assumptions
such as proportional hazards, additive hazards, proportional odds or
accelerated failure time.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS368 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Monte Carlo Co-Ordinate Ascent Variational Inference
In Variational Inference (VI), coordinate-ascent and gradient-based
approaches are two major types of algorithms for approximating
difficult-to-compute probability densities. In real-world implementations of
complex models, Monte Carlo methods are widely used to estimate expectations in
coordinate-ascent approaches and gradients in derivative-driven ones. We
discuss a Monte Carlo Co-ordinate Ascent VI (MC-CAVI) algorithm that makes use
of Markov chain Monte Carlo (MCMC) methods in the calculation of expectations
required within Co-ordinate Ascent VI (CAVI). We show that, under regularity
conditions, an MC-CAVI recursion will get arbitrarily close to a maximiser of
the evidence lower bound (ELBO) with any given high probability. In numerical
examples, the performance of MC-CAVI algorithm is compared with that of MCMC
and -- as a representative of derivative-based VI methods -- of Black Box VI
(BBVI). We discuss and demonstrate MC-CAVI's suitability for models with hard
constraints in simulated and real examples. We compare MC-CAVI's performance
with that of MCMC in an important complex model used in Nuclear Magnetic
Resonance (NMR) spectroscopy data analysis -- BBVI is nearly impossible to be
employed in this setting due to the hard constraints involved in the model
The TimeMachine for Inference on Stochastic Trees
The simulation of genealogical trees backwards in time, from observations up
to the most recent common ancestor (MRCA), is hindered by the fact that, while
approaching the root of the tree, coalescent events become rarer, with a
corresponding increase in computation time. The recently proposed "Time
Machine" tackles this issue by stopping the simulation of the tree before
reaching the MRCA and correcting for the induced bias. We present a
computationally efficient implementation of this approach that exploits
multithreading
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