I am interested in
composite hypothesis testing where one can not easily estimate the nuisance
parameter of a particular hypothesis even when the data size becomes large. A
typical situation occurs in detecting weak sinusoidal type of signal buried by
heavy noise floor (SNR<-20dB) with random phase reversal due to the flip of
spin alignment in magnetic resonance force microscopy. Another application is
to detect weak echoes from target return through the processing of multiple
radar scans. Traditional track-before-detect method relies on the assumption that
the target, if exists, undergoes a certain deterministic motion which can be
extracted out through some kind of “smart” measurement alignment with a proper
account for the possible clutter originated measurements. However, a target can
be evasive which makes its motion highly unpredictable and the generalized
likelihood ratio test won’t work in this case simply due to the unreliable
estimate of target motion parameters.
Traditionally,
hypothesis testing is treated within a parametric setting of the data
generation assumption, e.g., the likelihood function of each hypothesis can be
fully specified given the possibly unknown nuisance parameter. As the data size
grows and the advances of statistical learning theory become more and more
accessible to the engineers, the need to handle signal detection problem in a
nonparametric or even semi-parametric setting draws much of the attention to me
(and I believe to lots of researchers in this field). I have been working on
model selection problems for determining the order of linear regression models
when the noise distribution is unknown. I see a strong connection to the
inherent difficulty of making a composite hypothesis simple when little can be
said about the nuisance parameter. Besides, even the performance evaluation of algorithms
operating on multiple composite hypothesis testing is a nontrivial issue. I
would like to build a semi-parametric framework to treat those nuisance
parameters separately, i.e., either estimable or non-estimable, for weak signal
detection problems where the generalized likelihood test fails to yield good
performance.
Sadly, I have not
made much progress so far but I already spotted the non-optimal behaviors of some
popularly used approaches in hypothesis testing and model selection. I hope that
people will gradually switch their focus to the formulation of the hypothesis
testing itself from trying to develop a so called optimal test procedure under
certain restrictive assumptions. My research has been supported in part by
DARPA MOSAIC, NSF/LEQSF-PFund.
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People working in
Signal Detection area
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