Dynamic density estimation with diffusive Dirichlet mixtures

We introduce a new class of nonparametric prior distributions on the space of continuously varying densities, induced by Dirichlet process mixtures which diffuse in time. These select time-indexed random functions without jumps, whose sections are continuous or discrete distributions depending on the choice of kernel. The construction exploits the widely used stick-breaking representation of the Dirichlet process and induces the time dependence by replacing the stick-breaking components with one-dimensional Wright-Fisher diffusions. These features combine appealing properties of the model, inherited from the Wright-Fisher diffusions and the Dirichlet mixture structure, with great flexibility and tractability for posterior computation. The construction can be easily extended to multi-parameter GEM marginal states, which include, for example, the Pitman--Yor process. A full inferential strategy is detailed and illustrated on simulated and real data.Comment: Published at http://dx.doi.org/10.3150/14-BEJ681 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

On a Construction of Markov Models in Continuous Time

This paper studies a novel idea for constructing continuous-time stationary Markov models. The approach undertaken is based on a latent representation of the corresponding transition probabilities that conveys to appealing ways to study and simulate the dynamics of the constructed processes. Some well-known models are shown to fall within this construction shedding some light on both theoretical and applied properties. As an illustration of the capabilities of our proposal a simple estimation problem is posed.Gibbs sampler; Markov process; Stationary process

Hindgut specification and cell-adhesion functions of Sphox11/13b in the endoderm of the sea urchin embryo

Sphox11/13b is one of the two hox genes of Strongylocentrotus purpuratus expressed in the embryo. Its dynamic pattern of expression begins during gastrulation, when the transcripts are transiently located in a ring of cells at the edge of the blastopore. After gastrulation, expression is restricted to the anus–hindgut region at the boundary between the ectoderm and the endoderm. The phenotype that results when translation of Sphox11/13b mRNA is knocked down by treatment with morpholino antisense oligonucleotides (MASO) suggests that this gene may be indirectly involved in cell adhesion functions as well as in the proper differentiation of the midgut–hindgut and midgut–foregut sphincters. The MASO experiments also reveal that Sphox11/13b negatively regulates several downstream endomesoderm genes. For some of these genes, Sphox11/13b function is required to restrict expression to the midgut by preventing ectopic expression in the hindgut. The evolutionary conservation of these functions indicates the general roles of posterior Hox genes in regulating cell-adhesion, as well as in spatial control of gene regulatory network subcircuits in the regionalizing gut

A Bayesian Nonparametric Method for Prediction in EST Analysis

In this work we propose a Bayesian nonparametric approach for tackling statistical problems related to EST surveys. In particular, we provide estimates for: a) the coverage, defined as the proportion of unique genes in the library represented in the given sample of reads; b) the number of new unique genes to be observed in a future sample; c) the discovery rate of new genes as a function of the future sample size. The Bayesian nonparametric model we adopt conveys, in a statistically rigorous way, the available information into prediction. Our proposal has appealing properties over frequentist nonparametric methods, which become unstable when prediction is required for large future samples. EST libraries studied in Susko and Roger (2004), with frequentist methods, are analyzed in detail.

Spatial expression of Hox cluster genes in the ontogeny of a sea urchin

The Hox cluster of the sea urchin Strongylocentrous purpuratus contains ten genes in a 500 kb span of the genome. Only two of these genes are expressed during embryogenesis, while all of eight genes tested are expressed during development of the adult body plan in the larval stage. We report the spatial expression during larval development of the five 'posterior' genes of the cluster: SpHox7, SpHox8, SpHox9/10, SpHox11/13a and SpHox11/13b. The five genes exhibit a dynamic, largely mesodermal program of expression. Only SpHox7 displays extensive expression within the pentameral rudiment itself. A spatially sequential and colinear arrangement of expression domains is found in the somatocoels, the paired posterior mesodermal structures that will become the adult perivisceral coeloms. No such sequential expression pattern is observed in endodermal, epidermal or neural tissues of either the larva or the presumptive juvenile sea urchin. The spatial expression patterns of the Hox genes illuminate the evolutionary process by which the pentameral echinoderm body plan emerged from a bilateral ancestor

Exchangeable Claims Sizes in a Compound Poisson Type Proces

When dealing with risk models the typical assumption of independence among claim size distributions is not always satisfied. Here we consider the case when the claim sizes are exchangeable and study the implications when constructing aggregated claims through compound Poisson type processes. In par- ticular, exchangeability is achieved through conditional independence and using parametric and nonparametric measures for the conditioning distribution. A full Bayesian analysis of the proposed model is carried out to illustrate.Bayes nonparametrics, compound Poisson process, exchangeable claim process, exchangeable sequence, risk model.

Geometric Stick-Breaking Processes for Continuous-Time Nonparametric Modeling

This paper is concerned with the construction of a continuous parameter sequence of random probability measures and its application for modeling random phenomena evolving in continuous time. At each time point we have a random probability measure which is generated by a Bayesian nonparametric hierarchical model, and the dependence structure is induced through a Wright-Fisher diffusion with mutation. The sequence is shown to be a stationary and reversible diffusion taking values on the space of probability measures. A simple estimation procedure for discretely observed data is presented and illustrated with simulated and real data sets.Bayesian non-parametric inference, continuous time dependent random measure, Markov process, measure-valued process, stationary process, stick-breaking process