Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations [20]. While it has several optimal properties, a major drawback of Bayesian inference is the lack of robustness against data contamination and model misspecification, which becomes pernicious in the use of objective priors. This paper presents the general formulation of a Bayes pseudo-posterior distribution yielding robust inference. Exponential convergence results related to the new pseudo-posterior and the corresponding Bayes estimators are established under the general parametric setup and illustrations are provided for the independent stationary as well as non-homogeneous models. Several additional details and properties of the procedure are described, including the estimation under fixed-design regression models.
Majority of the energy-aware routing protocols for wireless sensor networks focus on hierarchical routing mechanism which is having major drawback of rapid depletion of battery life of sensor nodes near the sink due to uneven distribution of packets. To mitigate the adverse effect of improper packet distribution policy flowing toward cluster head, we have introduced a novel packet distribution policy with constrained optimization problem foundation, so that powers at all nodes are uniformly dissipated. Our analysis shows, for a nonlinear network, this optimization strategy can be effectively employed for a 1D nonlinear network with three parallel paths consisting of five nodes. Additionally, we have incorporated our established source coding scheme known as dual-message compression with variable null symbol (DCVNS) followed by the concept of silent communication. This scheme reduces the duration of most energy-consuming active state of sensor node and also reduces receiver energy by reducing the length of the encoded message, which eventually reduces overall communication time. Simulation result on real-life sensor dataset with commercially available low-cost and low-power devices, e.g., CC1100 and Maxim 2820 shows our proposed approach outperforms in all aspects of transmission energy profile with the existing schemes.
The ordinary Bayes estimator based on the posterior density suffers from the potential problems of non-robustness under data contamination or outliers. In this paper, we consider the general set-up of independent but non-homogeneous (INH) observations and study a robustified pseudo-posterior based estimation for such parametric INH models. In particular, we focus on the R (α) -posterior developed by Ghosh and Basu (2016)[10] for IID data and later extended by Ghosh and Basu (2017)[11] for INH set-up, where its usefulness and desirable properties have been numerically illustrated. In this paper, we investigate the detailed theoretical properties of this robust pseudo Bayes R (α) -posterior and associated R (α) -Bayes estimate under the general INH set-up with applications to fixed-design regressions. We derive a Bernstein-von Mises types asymptotic normality results and Laplace type asymptotic expansion of the R (α) -posterior as well as the asymptotic distributions of the expected R (α) -posterior estimators. The required conditions and the asymptotic results are simplified for linear regressions with known or unknown error variance and logistic regression models with fixed covariates. The robustness of the R (α)posterior and associated estimators are theoretically examined through appropriate influence function analyses under general INH set-up; illustrations are provided for the case of linear regression. A high breakdown point result is derived for the expected R (α) -posterior estimators of the location parameter under a location-scale type model. Some interesting real life data examples illustrate possible applications.
The major problem of fitting a higher order Markov model is the exponentially growing number of parameters. The most popular approach is to use a Variable Length Markov Chain (VLMC), which determines relevant contexts (recent pasts) of variable orders and form a context tree. A more general approach is called Sparse Markov Model (SMM), where all possible histories of order m form a partition so that the transition probability vectors are identical for the histories belonging to a particular group. We develop an elegant method of fitting SMM using convex clustering, which involves regularization. The regularization parameter is selected using BIC criterion. Theoretical results demonstrate the model selection consistency of our method for large sample size. Extensive simulation studies under different set-up have been presented to measure the performance of our method. We apply this method to classify genome sequences, obtained from individuals affected by different viruses.
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