Statistical Methods for ICT Applications


STATICA's research interests centre around issues of applying Bayesian methods of statistical inference to a wide variety of applications, motivated by the "data explosion" of the last few decades.

Below are brief descriptions of the research projects that are currently being undertaken by STATICA researchers.

Source separation for multi-spectral images:

STATICA post-doctoral researcher Ji Won Yoon is working with Simon Wilson and colleagues in information science, Drs. Ercan Kuruo─člu
and Emanuele Salerno of CNR Pisa, on statistical methods for source separation.  It is motivated by the problem of source separation for the cosmic microwave background (CMB).  This is a very exciting time for the study of this phenomenon that is believed to be a relic of the early state of the Universe.  A new satellite, Planck, was launched this year that will observe CMB in unprecedented detail and is already starting to produce data.  The statistical problem here is that CMB is not the only source of microwaves in the sky, and so we must "separate" out the contribution of CMB from all of these other sources.  Our particular interest in this is how to quantify the uncertainty in our reconstruction of the CMB that arises because of this complication.  The project was given initial funcding by the now-concluded EU-funded project MUSCLE.

Estimating the number of species of different taxa:

Simon Wilson is working with STATICA post-doctoral researcher Brett Houlding and Dr. Mark Costello of the Leigh Marine Laboratory, University of Auckland on estimating the total numbers of marine species of different taxa.  Currently this is based on data from the dates of first reporting of different species, starting with the initial work of Linnaeus.  This question is important in discussion of species extinction rates and biodiversity.  We form part of a global team, including researchers in Canada, France, the United States and Australia, that is evaluating the many different methods of estimating species numbers.

Implementing Bayesian inverse regression using variational Bayes:

An important aspect of STATICA research, that cuts across much of its work, is fast approximations to posterior distributions that arise in the implementation of Bayesian statistical methods.  One approach is the method of variational Bayes, a functional approximation.  Work with graduate student Richa Vatsa is trying to improve the accuracy of variational Bayes when it is used in inverse regression problems.  The motivating example here is in reconstructing ancient climates from so-called proxy data, such as pollen deposited in lake sediment.  A regression model relates the amount of different species that are deposited into lakes as a function of climate.  This is fitted using modern data on both pollen adundances and the climate where it is deposited.  On observing ancient pollen, we invert this regression model to infer climate.  Good climate reconstructions depend on good modelling of the relationships and (most importantly) dependencies between different pollen types and climate; this leads to a very complicated inference procedure that VB offers some advantages to solving.  This project was initially funded by Science Foundation Ireland under its Research Frontiers Programme.

Fast Bayesian updating for dynamic models with Laplace approximations

Another important set of statistical problems involve dynamic data that is arriving in time, perhaps quite quickly, such as video or audio streams, and some analysis is needed in ''real time''. One approach is to dynamically update estimates and predictions as new data arrive. STATICA postgraduate Arnab Bhattacharya is looking at new ways to do Bayesian inference dynamically through Laplace approximations, and their recent extensions due to Rue et al. This project was initially funded by Science Foundation Ireland under the Centre for Telecommunications Value-Chain Research.