Surya T. Tokdar
Dimension adaptability of Gaussian process models with variable selection and projection.
Tue, 12/06/2011 - 15:01 — SomNambulAuthors: Surya T. Tokdar
Subjects: Statistics
AbstractIt is now known that an extended Gaussian process model equipped with
rescaling can adapt to different smoothness levels of a function valued
parameter in many nonparametric Bayesian analyses, offering a posterior
convergence rate that is optimal (up to logarithmic factors) for the smoothness
class the true function belongs to. This optimal rate also depends on the
dimension of the function's domain and one could potentially obtain a faster
rate of convergence by casting the analysis in a lower dimensional subspace
that does not amount to any loss of information about the true function.Semiparametric inference in mixture models with predictive recursion marginal likelihood.
Mon, 06/20/2011 - 15:01 — SomNambulAuthors: Surya T. Tokdar, Ryan Martin
Subjects: Methodology
AbstractPredictive recursion is an accurate and computationally efficient algorithm
for nonparametric estimation of mixing densities in mixture models. In
semiparametric mixture models, however, the algorithm fails to account for any
uncertainty in the additional unknown structural parameter. As an alternative
to existing profile likelihood methods, we treat predictive recursion as a
filter approximation to fitting a fully Bayes model, whereby an approximate
marginal likelihood of the structural parameter emerges and can be used for
inference.Consistency of a recursive estimate of mixing distributions.
Tue, 08/25/2009 - 22:41 — SomNambulAuthors: Surya T. Tokdar, Ryan Martin, Jayanta K. Ghosh
Subjects: gr. Statistics
AbstractMixture models have received considerable attention recently and Newton
[Sankhy\={a} Ser. A 64 (2002) 306--322] proposed a fast recursive algorithm for
estimating a mixing distribution. We prove almost sure consistency of this
recursive estimate in the weak topology under mild conditions on the family of
densities being mixed. This recursive estimate depends on the data ordering and
a permutation-invariant modification is proposed, which is an average of the
original over permutations of the data sequence.
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