# Trisha Maitra

## Publications Authored By Trisha Maitra

In this article we derive the almost sure convergence theory of Bayes factor in the general set-up that includes even dependent data and misspecified models, as a simple application of a result of Shalizi (2009) to a well-known identity satisfied by the Bayes factor. Read More

Delattre et al. (2013) considered n independent stochastic differential equations (SDEs), where in each case the drift term is modeled by a random effect times a known function free of parameters. The distribution of the random effects are assumed to depend upon unknown parameters which are to be learned about. Read More

Delattre et al. (2013) considered a system of stochastic differential equations (SDEs) in a random effects set-up. Under the independent and identical (iid) situation, and assuming normal distribution of the random effects, they established weak consistency and asymptotic normality of the maximum likelihood estimators (MLEs) of the population parameters of the random effects. Read More

In this article we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our asymptotic theory to random effects models based on systems of state space SDEs, covering both independent and identical and independent but non-identical collections of state space SDEs. We also address asymptotic inference in the case of multidimensional linear random effects, and in situations where the data are available in discretized forms. Read More

Research on asymptotic model selection in the context of stochastic differential equations (SDEs) is almost non-existent in the literature. In particular, when a collection of SDEs is considered, the problem of asymptotic model selection has not been hitherto investigated. Indeed, even though the diffusion coefficients may be considered known, questions on appropriate choice of the drift functions constitute a non-trivial model selection problem. Read More

The problem of model selection in the context of a system of stochastic differential equations (SDEs) has not been touched upon in the literature. Indeed, properties of Bayes factors have not been studied even in single SDE based model comparison problems. In this article, we first develop an asymptotic theory of Bayes factors when two SDEs are compared, assuming the time domain expands. Read More

Delattre et al. (2013) considered n independent stochastic differential equations (SDEs), where in each case the drift term is associated with a random effect, the distribution of which depends upon unknown parameters. Assuming the independent and identical (iid) situation the authors provide independent proofs of weak consistency and asymptotic normality of the maximum likelihood estimators (MLEs) of the hyper-parameters of their random effects parameters. Read More

Delattre et al. (2013) investigated asymptotic properties of the maximum likelihood estimator of the population parameters of the random effects associated with n independent stochastic differential equations (SDEs) assuming that the SDEs are independent and identical (iid). In this article, we consider the Bayesian approach to learning about the population parameters, and prove consistency and asymptotic normality of the corresponding posterior distribution in the iid set-up as well as when the SDEs are independent but non-identical. Read More