8,653 research outputs found
Fast MCMC sampling for Markov jump processes and extensions
Markov jump processes (or continuous-time Markov chains) are a simple and
important class of continuous-time dynamical systems. In this paper, we tackle
the problem of simulating from the posterior distribution over paths in these
models, given partial and noisy observations. Our approach is an auxiliary
variable Gibbs sampler, and is based on the idea of uniformization. This sets
up a Markov chain over paths by alternately sampling a finite set of virtual
jump times given the current path and then sampling a new path given the set of
extant and virtual jump times using a standard hidden Markov model forward
filtering-backward sampling algorithm. Our method is exact and does not involve
approximations like time-discretization. We demonstrate how our sampler extends
naturally to MJP-based models like Markov-modulated Poisson processes and
continuous-time Bayesian networks and show significant computational benefits
over state-of-the-art MCMC samplers for these models.Comment: Accepted at the Journal of Machine Learning Research (JMLR
Horseshoe-based Bayesian nonparametric estimation of effective population size trajectories
Phylodynamics is an area of population genetics that uses genetic sequence
data to estimate past population dynamics. Modern state-of-the-art Bayesian
nonparametric methods for recovering population size trajectories of unknown
form use either change-point models or Gaussian process priors. Change-point
models suffer from computational issues when the number of change-points is
unknown and needs to be estimated. Gaussian process-based methods lack local
adaptivity and cannot accurately recover trajectories that exhibit features
such as abrupt changes in trend or varying levels of smoothness. We propose a
novel, locally-adaptive approach to Bayesian nonparametric phylodynamic
inference that has the flexibility to accommodate a large class of functional
behaviors. Local adaptivity results from modeling the log-transformed effective
population size a priori as a horseshoe Markov random field, a recently
proposed statistical model that blends together the best properties of the
change-point and Gaussian process modeling paradigms. We use simulated data to
assess model performance, and find that our proposed method results in reduced
bias and increased precision when compared to contemporary methods. We also use
our models to reconstruct past changes in genetic diversity of human hepatitis
C virus in Egypt and to estimate population size changes of ancient and modern
steppe bison. These analyses show that our new method captures features of the
population size trajectories that were missed by the state-of-the-art methods.Comment: 36 pages, including supplementary informatio
Parameter estimation in pair hidden Markov models
This paper deals with parameter estimation in pair hidden Markov models
(pair-HMMs). We first provide a rigorous formalism for these models and discuss
possible definitions of likelihoods. The model being biologically motivated,
some restrictions with respect to the full parameter space naturally occur.
Existence of two different Information divergence rates is established and
divergence property (namely positivity at values different from the true one)
is shown under additional assumptions. This yields consistency for the
parameter in parametrization schemes for which the divergence property holds.
Simulations illustrate different cases which are not covered by our results.Comment: corrected typo
- …