Statistical inference when both the model and/or data dimension is large

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The investigator is studying inference for data which is both high dimensional and complex.The main topics investigated are:I. Identifying graphical modelsII.Ascribing explanatory power to variablesIII.Frequentist behaviour of nonparametric Bayes proceduresIV.Particle filtersThe framework is non and semiparametric and the results will be asymptotic.But the qualitative insights gained have led to the discovery of new methods by the investigator and should do so again.A preeminent feature of 21st century data in almost all fields is their complexity compared to he number of replicates.Images can be viewed as vectors with dimensions in the thousands,climate models produce vectors giving predicted values at tens of thousands of locations ,genomes are 3 billion basepairs long.Accompanying this type of data is a dearth of models for their generation.What theory there is for such situations tells us that we should be unable to do anything without impossibly large numbers of replicates.Yet are coping,we believe because ,if we consider predictions the models are "sparse"(Most factors are irrelevant) or data are "sparse" (The factors which do matter are highly dependent and can in fact be represented much more compactly than is apparent.) The investigator is studying these underlying ideas and developing models which apply in contexts including climate modeling, genomics, and astronomy.