Minimum Energy Information Fusion in Sensor Networks

In this paper we consider how to organize the sharing of information in a distributed network of sensors and data processors so as to provide explanations for sensor readings with minimal expenditure of energy. We point out that the Minimum Description Length principle provides an approach to information fusion that is more naturally suited to energy minimization than traditional Bayesian approaches. In addition we show that for networks consisting of a large number of identical sensors Kohonen self-organization provides an exact solution to the problem of combining the sensor outputs into minimal description length explanations.Comment: postscript, 8 pages. Paper 65 in Proceedings of The 2nd International Conference on Information Fusio

Coastline Kriging: A Bayesian Approach

Statistical interpolation of chemical concentrations at new locations is an important step in assessing a worker's exposure level. When measurements are available from coastlines, as is the case in coastal clean-up operations in oil spills, one may need a mechanism to carry out spatial interpolation at new locations along the coast. In this paper we present a simple model for analyzing spatial data that is observed over a coastline. We demonstrate four different models using two different representations of the coast using curves. The four models were demonstrated on simulated data and one of them was also demonstrated on a dataset from the GuLF STUDY. Our contribution here is to offer practicing hygienists and exposure assessors with a simple and easy method to implement Bayesian hierarchical models for analyzing and interpolating coastal chemical concentrations

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

A Bayesian approach to the semi-analytic model of galaxy formation: methodology

We believe that a wide range of physical processes conspire to shape the observed galaxy population but we remain unsure of their detailed interactions. The semi-analytic model (SAM) of galaxy formation uses multi-dimensional parameterisations of the physical processes of galaxy formation and provides a tool to constrain these underlying physical interactions. Because of the high dimensionality, the parametric problem of galaxy formation may be profitably tackled with a Bayesian-inference based approach, which allows one to constrain theory with data in a statistically rigorous way. In this paper we develop a SAM in the framework of Bayesian inference. We show that, with a parallel implementation of an advanced Markov-Chain Monte-Carlo algorithm, it is now possible to rigorously sample the posterior distribution of the high-dimensional parameter space of typical SAMs. As an example, we characterise galaxy formation in the current $\Lambda$CDM cosmology using the stellar mass function of galaxies as an observational constraint. We find that the posterior probability distribution is both topologically complex and degenerate in some important model parameters, suggesting that thorough explorations of the parameter space are needed to understand the models. We also demonstrate that because of the model degeneracy, adopting a narrow prior strongly restricts the model. Therefore, the inferences based on SAMs are conditional to the model adopted. Using synthetic data to mimic systematic errors in the stellar mass function, we demonstrate that an accurate observational error model is essential to meaningful inference.Comment: revised version to match published article published in MNRA

Error Bands for Impulse Responses

We examine the theory and behavior in practice of Bayesian and bootstrap methods for generating error bands on impulse responses in dynamic linear models. The Bayesian intervals have a firmer theoretical foundation in small samples, are easier to compute, and are about as good in small samples by classical criteria as are the best bootstrap intervals. Bootstrap intervals based directly on the simulated small-sample distribution of an estimator, without bias correction, perform very badly. We show that a method that has been used to extend to the overidentified case standard algorithms for Bayesian intervals in reduced form models is incorrect, and we show how to obtain correct Bayesian intervals for this case.