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Search Results: 1 - 10 of 1894 matches for " Abhra Sarkar "
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Bayesian Nonparametric Modeling of Higher Order Markov Chains
Abhra Sarkar,David B. Dunson
Statistics , 2015,
Abstract: We consider the problem of flexible modeling of higher order Markov chains when an upper bound on the order of the chain is known but the true order and nature of the serial dependence are unknown. We propose Bayesian nonparametric methodology based on conditional tensor factorizations, which can characterize any transition probability with a specified maximal order. The methodology selects the important lags and captures higher order interactions among the lags, while also facilitating calculation of Bayes factors for a variety of hypotheses of interest. We design efficient Markov chain Monte Carlo algorithms for posterior computation, allowing for uncertainty in the set of important lags to be included and in the nature and order of the serial dependence. The methods are illustrated using simulation experiments and real world applications.
Nonparametric Bayesian Approaches to Non-homogeneous Hidden Markov Models
Abhra Sarkar,Anindya Bhadra,Bani K. Mallick
Statistics , 2012,
Abstract: In this article a flexible Bayesian non-parametric model is proposed for non-homogeneous hidden Markov models. The model is developed through the amalgamation of the ideas of hidden Markov models and predictor dependent stick-breaking processes. Computation is carried out using auxiliary variable representation of the model which enable us to perform exact MCMC sampling from the posterior. Furthermore, the model is extended to the situation when the predictors can simultaneously in influence the transition dynamics of the hidden states as well as the emission distribution. Estimates of few steps ahead conditional predictive distributions of the response have been used as performance diagnostics for these models. The proposed methodology is illustrated through simulation experiments as well as analysis of a real data set concerned with the prediction of rainfall induced malaria epidemics.
Bayesian Low Rank and Sparse Covariance Matrix Decomposition
Lin Zhang,Abhra Sarkar,Bani K. Mallick
Statistics , 2013,
Abstract: We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis and random effects models. We propose a Bayesian method of estimating the covariance matrices by representing the covariance model in the form of a factor model with unknown number of latent factors. We introduce binary indicators for factor selection and rank estimation for the low rank component combined with a Bayesian lasso method for the sparse component estimation. Simulation studies show that our method can recover the rank as well as the sparsity of the two components respectively. We further extend our method to a graphical factor model where the graphical model of the residuals as well as selecting the number of factors is of interest. We employ a hyper-inverse Wishart prior for modeling decomposable graphs of the residuals, and a Bayesian graphical lasso selection method for unrestricted graphs. We show through simulations that the extended models can recover both the number of latent factors and the graphical model of the residuals successfully when the sample size is sufficient relative to the dimension.
Bayesian Semiparametric Multivariate Density Deconvolution
Abhra Sarkar,Debdeep Pati,Bani K. Mallick,Raymond J. Carroll
Statistics , 2014,
Abstract: We consider the problem of multivariate density deconvolution when the interest lies in estimating the distribution of a vector valued random variable but precise measurements on the variable of interest are not available, observations being contaminated with additive measurement errors. The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error density is not known but replicated proxies are available for each unobserved value of the random vector. Additionally, we allow the variability of the measurement errors to depend on the associated unobserved value of the vector of interest through unknown relationships. Basic properties of finite mixture models, multivariate normal kernels and exchangeable priors are exploited in many novel ways to meet the modeling and computational challenges. Theoretical results that show the flexibility of the proposed methods are provided. We illustrate the efficiency of the proposed methods in recovering the true density of interest through simulation experiments. The methodology is applied to estimate the joint consumption pattern of different dietary components from contaminated 24 hour recalls.
Adaptive Posterior Convergence Rates in Bayesian Density Deconvolution with Supersmooth Errors
Abhra Sarkar,Debdeep Pati,Bani K. Mallick,Raymond J. Carroll
Statistics , 2013,
Abstract: Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty quantification and generalizability to more sophisticated models. This article is the first substantive effort to theoretically quantify the behavior of the posterior in this recent line of research. In particular, assuming a known supersmooth error density, a Dirichlet process mixture of Normals on the true density leads to a posterior convergence rate same as the minimax rate $(\log n)^{-\eta/\beta}$ adaptively over the smoothness $\eta$ of an appropriate H\"{o}lder space of densities, where $\beta$ is the degree of smoothness of the error distribution. Our main contribution is achieving adaptive minimax rates with respect to the $L_p$ norm for $2 \leq p \leq \infty$ under mild regularity conditions on the true density. En route, we develop tight concentration bounds for a class of kernel based deconvolution estimators which might be of independent interest.
Perfect Entanglement Transport in Quantum Spin Chain Systems  [PDF]
Sujit Sarkar
Journal of Quantum Information Science (JQIS) , 2011, DOI: 10.4236/jqis.2011.13014
Abstract: We propose a mechanism for perfect entanglement transport in anti-ferromagnetic (AFM) quantum spin chain systems with modulated exchange coupling and also for the modulation of on-site magnetic field. We use the principle of adiabatic quantum pumping process for entanglement transfer in the spin chain systems. We achieve the perfect entanglement transfer over an arbitrarily long distance and a better entanglement transport for longer AFM spin chain system than for the ferromagnetic one. We explain analytically and physically—why the entanglement hops in alternate sites. We find the condition for blocking of entanglement transport even in the perfect pumping situation. Our analytical solution interconnects quantum many body physics and quantum information science.
Multifractal analysis of the pore space of real and simulated sedimentary rocks
Abhra Giri,Sujata Tarafdar,Philippe Gouze,Tapati Dutta
Physics , 2013,
Abstract: It is well known that sedimentary rocks having same porosity can have very different pore size distribution. The pore distribution determines many characteristics of the rock among which, its transport property is often the most useful. Multifractal analysis is a powerful tool that is increasingly used to characterize the pore space. In this study we have done multifractal analysis of pore distribution on sedimentary rocks simulated using the Relaxed Bidisperse Ballistic Model (RBBDM). The RBBDM can generate a $3-D$ structure of sedimentary rocks of variable porosity by tuning the fraction $p$ of particles of two different sizes. We have also done multifractal analysis on two samples of real sedimentary rock to compare with the simulation studies. One sample, an oolitic limestone is of high porosity (40%)while the other is a reefal carbonate of low porosity around 7%. $2-D$ sections of X-ray micro-tomographs of the real rocks were stacked sequentially to reconstruct the real rock specimens. Both samples show a multifractal character, but we show that RBBDM gives a very realistic representation of a typical high porosity sedimentary rock.
Electrical Impedance Response of Gamma Irradiated Gelatin based Solid Polymer Electrolytes Analyzed Using a Generalized Calculus Formalism
Tania Basu,Abhra Giri,Sujata Tarafdar,Shantanu Das
Physics , 2015,
Abstract: The electrical impedance response of Gelatin based solid polymer electrolyte to gamma irradiation is investigated by impedance spectroscopy. An analysis based on Poisson-Nernst-Plank model, incorporating fractional time derivatives is carried out. A detailed derivation for anomalous impedance function is given.The model involves boundary conditions with convolution of the fractional time derivative of ion density and adsorption desorption relaxation kinetics. A fractional diffusion-drift equation is used to solve the bulk behavior of the mobile charges in the electrolyte. The complex adsorption-desorption process at the electrode-electrolyte interface produces an anomalous effect in the system. The model gives a very good fit for the observed impedance data for this biopolymer based solid electrolyte in wide range of frequencies. We have compared different parameters based upon this model for both irradiated and unirradiated samples.
Adsorptive Mass Transport of Dye on Rice Husk Ash  [PDF]
Debasish Sarkar, Amitava Bandyopadhyay
Journal of Water Resource and Protection (JWARP) , 2010, DOI: 10.4236/jwarp.2010.25049
Abstract: Experimentations have been carried out to characterize the adsorption of Methylene Blue (MB) and Congo Red (CR) dyes in the aqueous phase onto Rice Husk Ash (RHA). Theoretically analyses are also made for describing the sorption and diffusion processes. The effective pore diffusivities of the dye molecules studied in RHA are determined by a suitable global optimization technique. The depth of penetration, on the other hand, has been estimated for various initial concentrations of dyes. Theoretically predicted concentration pro-files are compared with the experimental values at different initial concentrations of these dyes. Such com-parative studies indicate that the predicted values are in excellent agreement with the experimental values.
Global Climate Change and Emerging Environmental and Strategic Security Issues for South Asia  [PDF]
Amarendra Nath Sarkar
Journal of Environmental Protection (JEP) , 2011, DOI: 10.4236/jep.2011.29135
Abstract: Global climate change-essentially an adverse consequence of global warming, is principally caused by progressive build-up and extensive spread of greenhouse gases (GHGs) across countries, regions or continents because of earth’s rotational movement. The potent sources of GHGs are fossil-fuels and biomass. With the increasing pace of globalization, industrialization and rapid change of life-style the demand and consumption of these feed-stocks to stimulate economic growth is steadily rising-both in the developing and developed economy. In the process, the emissions level is also rising phenomenally; and of late become quite alarming-more in the former than latter case, affecting thereby the environmental quality as also its security concerns globally. This paper highlights the major impacts of global warming and consequential climate change on the environmental quality and overall security aspects-including commercial, strategic and defense angles for the South-Asian region. The paper also discusses some relevant aspects linking the larger question of energy security with environmental security through the approach of sustainable energy development for envisioning a balanced economic development as well as growth perspective for South Asia. The significance of International cooperation in the mitigation and adaptation of climate change impacts with special reference to Asia- Pacific and South Asian region is also discussed at some length in the paper.
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