Research
Interests:
Functional
data analysis and Bayesian nonparametric statistics; computer model
validation; spatial statistics; spatio-temporal models; Bayesian
Hierarchical modeling, Multiple testing; data mining.
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Publications
/ work in progress:
- Bayarri, M. J., Berger, J. O.,
Cafeo, J., Garcia-Donato, G., Liu, F., Palomo, Parthasarathy, R.J.,
Paulo, R., Sacks, J., Walsh, D. (2006) Computer
Model Validation with Functional Output. Annals of Statistics. To appear.
- G.
Garcia-Donato, F. Liu, and J. Palomo. (2004). Documentation for SAVE-2
methodology and software. Niss Tech.
Rep.
- F. Liu,
M. J. Bayarri, J. Berger, R. Paulo, J. Sacks. (2006). A Bayesian Analysis of the Thermal
Challenge Problem. Manuscript.
- F. Liu,
L. Zhang, M. West (2006). Bayesian
Dynamic Model for Complex Computer Systems. Manuscript.
- F. Liu,
M. J. Bayarri, J. Berger. (2006). Modularization of the Bayesian
Analysis for Random Effect Models. Work
in progress.
- F. Liu,
M. J. Bayarri, J. Berger.(2006). A Multi-scale Bayesian Functional Data
Analysis. Work in progress.
- F. Liu,
J. Berger. (2006). Bayesian Reconstruction of nonlinear dynamic
systems. Work in progress.
- F. Liu,
F. Liang, W. Jang. (2006). A Bayesian method for partially-paired high
dimensional data, with application to unpaired micro-array data. Work in progress.
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Current
Research:
My thesis, Bayesian
Functional Data Analysis for Computer Model
Validation, has developed
the Bayesian space-time models for four types of functional data,
arsing in the context of computer model validation. These methods
utilize approaches such as Bayesian nonparametric statistics, Bayesian
dynamic linear modeling, and Wavelet analysis. Besides the issues of
functional data, these methods take into account other issues such as
building emulators for expensive computer models, measuring discrepancy
between the computer model output and the reality, and solving the
statistical inverse problem for the unknown inputs associated with the
field experiments. The methods are,
- Gaussian
Stochastic Process -- The test bed case study for this model is: the
Thermal Computer Model Challenge Problem. Talk slide on this
methodology is here.
- Wavelet
analysis with Gaussian Stochastic Process method -- The test bed case
study is a real commercial simulator (confidential). Talk slide on this
methodology is here
and a concise version here.
- Wavelet
PCA with Gaussian Stochastic Process method -- This is an on-going
research, extending the Wavelet method to eigen-basis representation.
- multivariate
Dynamic Linear Model (DLM) -- This method utilize the Bayesian dynamic
linear model techniques to build emulators for the simulators. I
am trying to apply this method to CMAQ
-- an air quality model used by EPA. Slide on this methodology is here.
I also collaborated with Professor Liang and
Professor Jang
on Bayesian
analysis of partially paired data in high dimensional space. Our
method extends Professor Berger's
work on Bayesian Multiple Testing to
cases with partially paired data. We compare this method with the FDR
adjustment approach
by Professor Benjamini
and Professor Hochberg.
This
model has been applied to a cDNA micro-array data set. The work was
presented at the Case Studies in
Bayesian Statistics, 2005 (slide).
Here is a later version
presented at SAMSI, 2006.
I am currently participating the SAMSI
program on
Development, Assessment and Utilization of Complex Computer Models.
There
are many interesting research topics and collabration opportunities. Of
my particular interest are the
methodology working group (I am in charge of this
webpage :-) ),
the Air Quanlity working group, and the
Terrestrial
working group. |
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