In the preview: By John Lu
   1. Data assimilation and Bayesian design for physical/complex/high-
dimensional space-time process.   
                
    Data assimilation and model-based Bayesian design have been proposed as a 
general approach to solving complex design and dynamic control issues for 
building future factory plants, which are built in to satisfy environmental law, 
automated data measurements and process control, to minimize costs and to 
maximize economic benefits.  The problems will require optimization of 
multipurpose design goals over conflicting conditions, including economic and 
environmental factors, for large scale systems, which may be complex and 
nonlinear, automated in a reasonable computation time. Similar problems occur in 
other areas such as virtual measurements, material sciences, and Internet 
traffic control. Common to these diverse problems is the need to model and 
measure dynamic and  high-dimensional processes, where only meager observations 
are available, and where incorporation of physical models as well as prior 
information  is necessary. Bayesian approach offers the most natural and 
flexible solution to such problems. The advantage is to build a robust design 
strategy so as to take into account various uncertainty factors in inputs, 
models, and noisy environments.  The key is to develop realistically fast 
computational algorithms for solving complex and nonlinear large scale problems. 

    Data assimilation has been studied for a long time in geosciences, 
especially in atmospheric and oceanic sciences. The challenges of producing 
timely weather forecasts using data assimilation and numerical forecast model 
code have forced meteorologists to develop various computational tools for 
dealing large scale data assimilation and real-time implementation. The most 
recent techniques of targeted observation and ensemble forecasting are 
particularly noteworthy: the former is an economical way of dynamically 
collecting most critical data to improve intermediate-range forecast, and the 
latter is an efficient sampling method for high-dimensional nonlinear systems 
and for producing some kind of uncertainty measures for nonlinear forecast and 
may be potentially useful for operational probability weather forecast. 

   Our goals in relation to the Bayesian project are to formulate and identify 
the data assimilation and Bayesian design problems in the context of metrology 
problems and to leverage the knowledge of data assimilation and Bayesian design 
gained in geoscience problems (e.g. Berliner, Lu, Snyder). We will use and 
develop realistic physical/dynamic/stochastic models in each context and 
identify and find a  Bayesian solution. The milestone for this subproject is to 
develop realistic data assimilation and Bayesian design computational algorithms 
which can be applied to real-world dynamic systems and potentially useful in 
real-time environments. We vision that the strategy of sequential processing and 
updating algorithms, greedy search algorithms, hierarchical and hidden process 
models, spatial and dynamic modeling, and problem-based simplifications and 
approximations will play important roles. 

2. Bayesian analysis and consensus guidance for measurement curves and images 
from interlaboratory studies 

    (motivated by a consensus curve problem by James Yen, Bob Zerr)
  A general conceptual setup is that, we assume that measurements from each 
laboratory consist of laboratory specific bias and measurement errors, common 
functional curve, effects due to experiment conditions and time, potential 
interaction effects, and individual measurement errors. Then we propose a 
Bayesian formulation where block-based Gibbs sampling will allow us to separate 
the laboratory effects from modeling the common curves, and the MCMC samples 
also allow us to construct the uncertainty of the reconstructed curve as well as 
of laboratory effects. The functional data analysis framework allows irregular 
sampling points of input variable and different data format (such as missing 
data) from each laboratory.

   Milestone: Concensus and computational algorithms for nonparametric 
regression and Bayesian solution of functional data analysis 
 
 b. Analysis of image maps 
    Advances in instrumentation enable high throughput measurements such as 
images. Analyzing and assessing data quality from image maps such as from DNA 
chips or FMRIs presents challenging issues for future metrology. 
We vision that functional data analysis should provide some useful lessons for 
image analysis, and we will work on the image analysis problems in context of  
some real applications.

3. Statistical design and standardization of microarray experiments and data 
anlysis. 
   
    There's an explosion of research activity in microarray technologies in last 
few years, and they are probably well justified, since these technologies are 
associated with greatly improved productivity in gene mapping and allow 
simultaneous measurements of thousands of genes at different experimental 
conditions at the same time. The number of runs  and the number of genes that  
can be accommodated in one experiment will increase rapidly in future. This 
movement presents golden and huge opportunity for statistical and metrological 
research such as finding signals in the huge mountains of noisy data and 
standardizing or calibrating various array measuring devices. Statistical issues 
include data cleaning, normalization issues, image analysis,  modeling and 
analysis of variations due to different factors, main effects as well as 
interactions, and  experimental design. Statistical experimental design, 
originally developed in agricultural experiments (Fisher, Cochran, Cox, Bose), 
then in chemistry (Box, Youden, Cameron, Mandel) will be extremely relevant. 
Many methods,  such as comparison experiment, calibration and replications, 
factorial design, and balanced or partial balanced incomplete block designs 
directly applicable (Kerr and Churchill 2000). Another, more fundamental issue 
is to improve the data quality and information content through adding reference 
spots and calibration experiments. Bayesian analysis is used in analyzing the 
hierarchical models of gene expression models where prior information is 
generated from calibration experiments (Tseng, Oh, Rohlin, Liao, Wong 2001). Our 
goals are to investigate the crucial standardization and experimental design 
issues in microarray experimentation by keeping pace with the rapid advances in 
bioinformatics and the budding interest from the statistics community, and to 
actively collaborate with scientists from NIST and other agencies or 
institutions. 

4. High-dimensional modeling: 

  a. Classification and prediction
Bioinformatics and data mining in IT has revived research on clustering and 
classification (pattern recognition), a traditional area multivariate analysis. 
Among the techniques studied, the classification and prediction method, proposed 
by V.N. Vapnik, which he called, support vector machines (SVMs), is especially a 
powerful and effective approach. It is based on statistical learning theory, so 
has good predictive properties, and avoids the usual ad hoc model selection 
step. By allowing constraints and penalization on the model coefficients, the 
technique solves a Bayesian classification problem, and is very close to the 
penalized likelihood method in situations when the data are noisy. Our goals 
include the following three parts: one is to futher understand and then develop 
software support for automated tuning of SVMs in both classification and 
prediction problems, and to develop some uncertainty measures and theory for SVM 
estimation and prediction using Bayesian method, and finally to apply the method 
to more complicated metrology problems, such as functional data analysis and 
image analysis. 
  
  b. Hierarchial and space-time models
The hidden Markov models (HMMs) are the most successful statistical and 
probabilistic models that have been proposed for DNA and protein sequence 
analysis. HMMs belong to the general class of Markov switching or hierarchical 
models, for which Bayesian method is the most effective approach. Hierarchical 
dynamic models have been used in many other contexts such as hydrology (e.g. Lu 
and Berliner 1999) and economics. Recently Internet traffic modeling presents 
new challenges of modeling heterogeneous and multiscale processes, potentially 
in continuous time or space-time. The aim is to come up with realistic and 
flexible models which can take into account the underlying physical process as 
well as multiscale and various subprocesses, so that the model can have good 
realism as well as predictive power. The application is to prediction and 
intelligent traffic monitoring and control.