A more substantial discussion of my current research interests can be
found in the Research page. This page
gives you a brief idea of what students are currently working on, what recent
students have done their thesis on, sponsored projects and so on.
-
Joint Model Evaluation and Inference in Difficult Problems:
Our goal is to find out how to evaluate
different statistical models used for fitting spatio-temporal dependent data, while
simultaneously ensuring that any statistical inference and prediction made are
consistent. We are studying a variety of methods, mainly involving
resampling
techniques and Bayesian methods.
The application contexts for these methods are varied, involving
(i) remote sensing and earth sciences,
(ii) socio-economic-political sciences,
(iii) neuroscience and imaging.
Depending on the context, computational algorithms and focus of the study changes.
A related currently funded project is titled:
On conditional statistical procedures for simultaneous model
selection, inference and prediction in complex climate systems.
In this project, methodology for studying climate data as functions of time and space
will be developed. Many of such data series are oscillatory in nature but
not strictly periodic, and vary in intensities at different points in time and in
different parts of the globe. A thorough study of these irregular oscillatory patterns is
of primary importance for planning of infrastructural needs, planning of
sustainable development and management of the planet's food, water and energy resources,
for decision making and addressing human, ecological and environmental
concerns, for better understanding of the physical process of climate systems and
to have more accurate predictive systems. The mutual dependence of these oscillatory
patterns and other climate variables will be studied.
The primary statistical challenges in modeling
these irregular, multi-scale and multi-dimensional, spatio-temporal processes will be
addressed using a functional data approach. Computational techniques and theoretical
machinery will be developed for simultaneous model selection
and inference in functional data, and in non-parametric and semi-parametric models
involving such data. Computation-based procedures will be developed for testing
goodness of fit of models for functional spatio-temporal data,
and for verifying technical assumptions about the nature of spatial or temporal dependency
patterns. Bayesian and resampling-based inferential procedures will be
developed, and used in multiple datasets.
-
Studying the Geometry of High-Dimensional Data:
In this project, we consider various ways of eliciting structures and patterns
in data, while using as
minimal assumptions as possible. For example, we do not
necessarily assume Gaussian distributions, or sparsity. Instead, we use
high-dimensional quantiles and other quantities that have interesting
robustness as well as efficiency properties. We develop related statistical
methodology, algorithms, theory and software ( MATS ).
The application domains for this
line of study are as in the previous case.
-
Inference in small area statistics, and in complex surveys:
Complex surveys are often used in understanding features of finite populations, and
can associate unequal probabilities to the population elements to elicit properties of
interest. Voluntary participation and the possibility of the potential response being
tied to the actual probability of responding, thus resulting in non-ignorable
non-responses, makes analysis of survey data hard.
Respondents often share common characteristics, like being members of the same
household, which result in unobservable features that make parts of the observed data
dependent on each other. Small area problems have a further limitation: the directly
observed data contains only a limited amount of information that is usually inadequate to
make sensible inferences or predictions. Consequently, the modeling for small area data
has to borrow strength from indirect information.
In our work on these topics, we use
resampling
techniques and Bayesian methods.
for consistent
estimation and inference, and prediction with high levels of accuracy. We are developing
a framework that accommodates both classical (design-based) survey properties
and modern, model-based, inferential techniques. We are broadening the scope of
scope of applicability of these methods to new domains in climate science, food security,
neuroscience, transportation and networks, while also working on the traditional
application domain of survey sampling data.