Nonparametric Dynamic State Space Modeling of Observed Circular Time Series with Circular Latent States: A Bayesian Perspective

Circular time series has received relatively little attention in statistics and modeling complex circular time series using the state space approach is non-existent in the literature. In this article we introduce a flexible Bayesian nonparametric approach to state space modeling of observed circular time series where even the latent states are circular random variables. Crucially, we assume that the forms of both observational and evolutionary functions, both of which are circular in nature, are unknown and time-varying. We model these unknown circular functions by appropriate wrapped Gaussian processes having desirable properties. We develop an effective Markov chain Monte Carlo strategy for implementing our Bayesian model, by judiciously combining Gibbs sampling and Metropolis-Hastings methods. Validation of our ideas with a simulation study and two real bivariate circular time series data sets, where we assume one of the variables to be unobserved, revealed very encouraging performance of our model and methods. We finally analyse a data consisting of directions of whale migration, considering the unobserved ocean current direction as the latent circular process of interest. The results that we obtain are encouraging, and the posterior predictive distribution of the observed process correctly predicts the observed whale movement.Comment: This significantly updated version will appear in Journal of Statistical Theory and Practic

A New Spatio-Temporal Model Exploiting Hamiltonian Equations

The solutions of Hamiltonian equations are known to describe the underlying phase space of the mechanical system. In Bayesian Statistics, the only place, where the properties of solutions to the Hamiltonian equations are successfully applied, is Hamiltonian Monte Carlo. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations, incorporating appropriate stochasticity via Gaussian processes. The resultant sptaio-temporal process, continuously varying with time, turns out to be nonparametric, nonstationary, nonseparable and no-Gaussian. Besides, the lagged correlations tend to zero as the spatio-temporal lag tends to infinity. We investigate the theoretical properties of the new spatio-temporal process, along with its continuity and smoothness properties. Considering the Bayesian paradigm, we derive methods for complete Bayesian inference using MCMC techniques. Applications of our new model and methods to two simulation experiments and two real data sets revealed encouraging performance

Resolving the confusion of the authorship attribution of a Bengali book

406-410The present paper aims to determine whether the Bengali book Londoner Naksa ebong France Bhraman (Wondrous Capers at London and Travelling in France) was written by the geologist Pramathanath Bose (P.N. Bose). To find it out, two well-established style markers often used in authorship attribution studies; namely, function words and punctuation marks, are used here. The result shows that possibly this book was penned by the geologist P.N. Bose. As a corollary, it may also be added that this approach may be used in future authorship attribution studies involving Bengali writings

Resolving the confusion of the authorship attribution of a Bengali book

The present paper aims to determine whether the Bengali book Londoner Naksa ebong France Bhraman (Wondrous Capers at London and Travelling in France) was written by the geologist Pramathanath Bose (P.N. Bose). To find it out, two well-established style markers often used in authorship attribution studies; namely, function words and punctuation marks, are used here. The result shows that possibly this book was penned by the geologist P.N. Bose. As a corollary, it may also be added that this approach may be used in future authorship attribution studies involving Bengali writings