Bayesian Statistics Working Group
Department of Statistics, NC State University
Sujit K Ghosh
Professor
ghosh@stat.ncsu.edu
Bayesian methods are becoming increasingly popular in the academic and
practitioner communities because of the recent development of techniques like
Markov chain Monte Carlo (MCMC) simulation. The Bayesian paradigm is an attempt to utilize all available information in decision-making. Prior knowledge coming from experience, expert judgment, or previously collected data is used with current data to characterize the current state of knowledge. These methods allow the use of models of complex physical phenomena that were previously too difficult to estimate. Bayesian methods offer a means of more fully understanding issues that are central to many practical problems by allowing researchers to build integrated models of behavior that can be estimated with limited amounts of data. However, there is a reasonably wide gap between the background of the empirically trained scientists and the full weight of Bayesian statistical inference. Hence, one of the goals of vertical integration is to bridge the gap by offering elementary to advanced courses that emphasizes linkages between standard approaches and full probability modeling via Bayesian methods. As a part of this training researchers and students will become proficient in understanding how statistical methods can be informative in "real-world" data analysis settings. Among several possible challenging applications, the following two areas of research are noteworthy:
- (i) Environmental applications:
Most physical processes exhibit important spatial-temporal variability that needs to be characterized, in conjunction with dependencies on explanatory variables, and hierarchical Bayesian statistical modeling offers a natural framework and a very powerful means for representing complex global phenomena through a series of simple local structures. This type of research on Bayesian statistics for environmental data requires a good understanding of the processes involved in the particular problem, of the sources of data needed, a background in Bayesian statistics, and an interest in challenging multi-disciplinary problems. This implies active collaboration with non-statisticians, i.e. climatologists, ecologists and environmental scientists. VIGRE provides the ideal platform to generate strong interactions between faculty, postdocs,
undergraduate and graduate students at NCSU with atmospheric scientists from the Marine Earth Atmospheric Science Department (MEAS) at NCSU, from EPA (RTP, NC) and NOAA (Asheville, NC) for advance on science and research on Bayesian statistics for environmental data.
- (ii) Biomedical applications:
Bayesian networks with their associated methods have now been around in biomedical fields for more than a decade. They have become increasingly popular for representing and handling uncertain knowledge in biological phenomena. Almost simultaneously, the use of Bayesian methods in biology has increased in popularity. Moreover, interest in Bayesian methods is emerging within bioinformatics, e.g. for building models for protein structure prediction and the interpretation of microarray gene expression data. Bayesian models are used in medicine to assist in the diagnosis of disorders and to predict the natural course of disease or outcome after treatment (prognosis). More importantly, Bayesian model development is not only confined to extracting probabilistic information from datasets; graphical models like Bayesian networks can also be constructed with the help of biomedical domain experts or by consulting relevant biomedical literature and thus achieving the vertical integration of several biomedical areas of applications. In the context of medical decision making, Bayesian models can be easily integrated with decision theory to yield models for the selection of optimal treatments, or to develop models for health-care planning under uncertainty.
The fact that Bayesian models allow for the easy incorporation of knowledge of background populations, explains that they are also increasingly used in research on risk models of disease, associating risk with spatial distribution of populations, and hence integrating the above two broad areas of environmental and biomedical applications. By offering a forum for the exchange of ideas and problems, we hope VIGRE would promote good statistical practice and will stimulate new research that is relevant to the field of environmental and biomedical applications using Bayesian methods.
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