This optimization problem depends on the stochastic process only
through its covariance structure. For processes with a product type
covariance structure, i.e., for $Cov(Y(s),Y(t))=u(s) v(t)$, $s < t$, a
set of necessary and sufficient conditions for a design to be exactly
optimal will be presented. Explicit calculations of optimal designs
for any given $n$ for Brownian Motion, Brownian Bridge and
Ornstein-Uhlenbeck process will illustrate the simplicity and
usefulness of these conditions. Starting from the set of exact
optimality conditions for a fixed $n$, an asymptotic result yielding
the density whose percentile points furnish a set of asymptotically
optimal design points (in some suitable sense) will be described.
Results on the problem when one tries to estimate the integral of
$Y(t)$ instead of the path will be discussed briefly. The integral
estimation problem is related to certain regression design problems
with correlated errors.

For a more general covariance structure, satisfying natural regularity
conditions, some interesting asymptotic results will be presented. It
will be shown that for processes with no quadratic mean derivative, a
much simpler estimator is asymptotically equivalent to the BLUE. This
will lead to an intuitively appealing argument in establishing the
asymptotic behaviour of the BLUE and also in deriving an analytical
expression for the asymptotically optimal design density.

I will omit technical details and focus on explaining the principal
ideas.Seminar page

Aimed at solving this problem, this thesis introduces two new
criteria: the generalized minimum aberration and the minimum moment
aberration, which are extensions of the minimum aberration and minimum
$G_2$-aberration. These new criteria work for symmetrical and
asymmetrical designs, regular and nonregular designs, orthogonal and
nonorthogonal designs, nonsaturated and supersaturated designs. They
are equivalent for symmetrical designs and in a weak sense for
asymmetrical designs.

The theory developed for these new criteria covers many existing
theoretical results as special cases. In particular, a general
complementary design theory is developed for asymmetrical designs and
some general optimality results for mixed-level supersaturated
designs.

As an application, a two-step approach is proposed for finding optimal
designs and some 16-, 27- and 36-run optimal designs are tabulated.
As another application, an algorithm is developed for constructing
mixed-level orthogonal and nearly orthogonal arrays, which can
efficiently construct a variety of small-run arrays with good
statistical properties.Seminar page

In this talk I describe two non-parametric approaches, one for
comparing and another for characterizing, distributions of a gene
region (sequence pair) heterogeneity measure between groups with
similar phenotype. For comparing distributions, hypotheses are
constructed for testing differential between-group heterogeneity and
within-group homogeneity. Group comparisons are made based on either
developed asymptotics (extending U-statistic theory to a correlated
multivariate two-sample setting) or permutation tests. For
characterizing gene region heterogeneity, a method is constructed for
identifying potentially important locations and their mutation
patterns. The relative importance of locations is evaluated through
estimation of their contribution to observed gene region differences;
mutation patterns are discerned through location descriptive
statistics. As motivation for the methods, I examine the problem of
altered HIV drug susceptibility and illustrate their use in testing
and characterizing protease region differences associated with a
phenotypic treatment response.Seminar page

In this talk, I will present some interesting results obtained from
statistical analysis of complete mitochondrial genomes of coelacanth,
lungfish and several mammals, birds, amphibia, reptiles and ray-finned
fish based on {\bf distributions of DNA words}. I will demonstrate
the use of a software called {\bf SWORDS}, which has been developed at
Indian Statistical Institute for statistical analysis of large DNA
sequences based on distributions of DNA words. This software has been
specifically designed for handling very large DNA sequences (for
instance, the size of a full mitochondrial genome of any vertebrate
lies between 15,000 and 18,000 base pairs) to compare them for
phylogenetic analysis.Seminar
page