Tree-Structured Stick Breaking Processes for Hierarchical Data

Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeable. One can view our model as providing infinite mixtures where the components have a dependency structure corresponding to an evolutionary diffusion down a tree. By using a stick-breaking approach, we can apply Markov chain Monte Carlo methods based on slice sampling to perform Bayesian inference and simulate from the posterior distribution on trees. We apply our method to hierarchical clustering of images and topic modeling of text data.

Nonparametric Bayesian Density Modeling with Gaussian Processes

We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution defined by a density that is a transformation of a function drawn from a Gaussian process prior. Our formulation allows us to infer an unknown density from data using Markov chain Monte Carlo, which gives samples from the posterior distribution over density functions and from the predictive distribution on data space. We describe two such MCMC methods. Both methods also allow inference of the hyperparameters of the Gaussian process.

Campylobacter jejuni colonization and transmission in broiler chickens: a modelling perspective.

Campylobacter jejuni is one of the most common causes of acute enteritis in the developed world. The consumption of contaminated poultry, where C. jejuni is believed to be a commensal organism, is a major risk factor. However, the dynamics of this colonization process in commercially reared chickens is still poorly understood. Quantification of these dynamics of infection at an individual level is vital to understand transmission within populations and formulate new control strategies. There are multiple potential routes of introduction of C. jejuni into a commercial flock. Introduction is followed by a rapid increase in environmental levels of C. jejuni and the level of colonization of individual broilers. Recent experimental and epidemiological evidence suggest that the celerity of this process could be masking a complex pattern of colonization and extinction of bacterial strains within individual hosts. Despite the rapidity of colonization, experimental transmission studies exhibit a highly variable and unexplained delay time in the initial stages of the process. We review past models of transmission of C. jejuni in broilers and consider simple modifications, motivated by the plausible biological mechanisms of clearance and latency, which could account for this delay. We show how simple mathematical models can be used to guide the focus of experimental studies by providing testable predictions based on our hypotheses. We conclude by suggesting that competition experiments could be used to further understand the dynamics and mechanisms underlying the colonization process. The population models for such competition processes have been extensively studied in other ecological and evolutionary contexts. However, C. jejuni can potentially adapt phenotypically through phase variation in gene expression, leading to unification of ecological and evolutionary time-scales. For a theoretician, the colonization dynamics of C. jejuni offer an experimental system to explore these 'phylodynamics', the synthesis of population dynamics and evolutionary biology.

Innovation processes within the healthcare industry: Determining critical success factors aligned to product strategies

The impact of differing product strategies on product innovation processes pursued by healthcare firms is discussed. The critical success factors aligned to product strategies are presented. A definite split between pioneering product strategies and late entrant product strategies is also recognised.

Tractable nonparametric bayesian inference in poisson processes with Gaussian process intensities

The inhomogeneous Poisson process is a point process that has varying intensity across its domain (usually time or space). For nonparametric Bayesian modeling, the Gaussian process is a useful way to place a prior distribution on this intensity. The combination of a Poisson process and GP is known as a Gaussian Cox process, or doubly-stochastic Poisson process. Likelihood-based inference in these models requires an intractable integral over an infinite-dimensional random function. In this paper we present the first approach to Gaussian Cox processes in which it is possible to perform inference without introducing approximations or finitedimensional proxy distributions. We call our method the Sigmoidal Gaussian Cox Process, which uses a generative model for Poisson data to enable tractable inference via Markov chain Monte Carlo. We compare our methods to competing methods on synthetic data and apply it to several real-world data sets. Copyright 2009.

Tractable nonparametric Bayesian inference in Poisson processes with Gaussian process intensities

The inhomogeneous Poisson process is a point process that has varying intensity across its domain (usually time or space). For nonparametric Bayesian modeling, the Gaussian process is a useful way to place a prior distribution on this intensity. The combination of a Poisson process and GP is known as a Gaussian Cox process, or doubly-stochastic Poisson process. Likelihood-based inference in these models requires an intractable integral over an infinite-dimensional random function. In this paper we present the first approach to Gaussian Cox processes in which it is possible to perform inference without introducing approximations or finite-dimensional proxy distributions. We call our method the Sigmoidal Gaussian Cox Process, which uses a generative model for Poisson data to enable tractable inference via Markov chain Monte Carlo. We compare our methods to competing methods on synthetic data and apply it to several real-world data sets.

Bayesian learning of noisy Markov decision processes

This work addresses the problem of estimating the optimal value function in a Markov Decision Process from observed state-action pairs. We adopt a Bayesian approach to inference, which allows both the model to be estimated and predictions about actions to be made in a unified framework, providing a principled approach to mimicry of a controller on the basis of observed data. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from theposterior distribution over the optimal value function. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller.