Michael Stewart's Research
- Research Areas
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Current theoretical work:
- Mixture models When sampling student heights we tend
to see a bimodal distribution, since male heights form one population quite different
from female heights. If we ignore the labels, we see a sample from a mixture. However
it is also possible to get a sample from a single smooth population whose histogram
has a bump in it. Distinguishing these two cases is a delicate statistical problem
which does not fall into the class of well-understood, so-called "regular" statistical problems.
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- Log-concave densities Many standard, popular statistical distributions have density
functions whose logarithm is a concave function. Continuous examples are the normal and gamma,
discrete examples are binomial, Poisson and negative binomial. The class of log-concave densities
is thus a broader semiparametric (or nonparametric, depending on your point of view) alternative
class of distributions, suitable for modelling data from many areas where a smooth shape is
expected but a parametric family such as the normal or gamma is too restrictive.
In particular it is possible to estimate a log-concave density by maximum likelihood, however
new computationally intensive methods are required to perform the necessary computations and
new analytical tools are needed to develop the necessary theory.
- Cross-disciplinary applied work:
- Ecology Various analyses pertaining mostly to diversity
of archaea appearing in soils in the context of cotton production.
- Medical genetics Resampling based analyses relating to markers associated with breast cancer.
- Health Economics Applying portfolio theory
to the study of possible synergistic/interactive effects of several simultaneous health interventions.
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Member of the Mathematical Statistics research group.
- Publications
- Technical Reports
- PhD thesis
Asymptotic methods for tests of homogeneity in
finite mixture models.
