The envelope model is a new paradigm to address estimation and prediction in multivariate analysis. Using sufficient dimension reduction techniques, it has the potential achieve substantial efficiency gains compared standard models. This was first introduced by [Statist. Sinica 20 (2010) 927–960] for linear regression, since been adapted many other contexts. However, Bayesian approach analyzing models not yet investigated literature. In this paper, we develop comprehensive framework...

In recent years, a large variety of continuous shrinkage priors have been developed for Bayesian analysis the standard linear regression model in high dimensional settings. We consider two such priors, Dirichlet-Laplace prior (developed Bhattacharya et al. (2013)), and Normal-Gamma (Griffin Brown, 2010)). For both Gibbs sampling Markov chains to generate approximate samples from corresponding posterior distributions. show by using drift minorization based that aforementioned models are...

Abstract Background Prediction and classification algorithms are commonly used in clinical research for identifying patients susceptible to conditions such as diabetes, colon cancer, Alzheimer’s disease. Developing accurate prediction methods benefits personalized medicine. Building an excellent predictive model involves selecting the features that most significantly associated with outcome. These can include several biological demographic characteristics, genomic biomarkers health history....

We introduce a new family of probability distributions that we call the Modified-Half-Normal distributions. It is supported on positive part real line with its density proportional to function x↦xα−1 exp (−βx2+γx)I(x>0),α>0,β>0,γ∈R. explore number properties including showing fact normalizing constant and moments distribution can be represented in terms Fox-Wright function. demonstrate relevance by connection Bayesian statistical methods appearing from multiple areas research such as Binary...

The data augmentation (DA) approach to approximate sampling from an intractable probability density fX is based on the construction of a joint density, fX, Y, whose conditional densities, fX|Y and fY|X, can be straightforwardly sampled. However, many applications DA algorithm do not fall in this “single-block” setup. In these applications, X partitioned into two components, = (U, V), such way that it easy sample fU|V, fV|U, Y. We refer alternative version DA, which effectively three-variable...

This study made an attempt to forecast and best fitted trend of Public Distribution System in India by using Box Jenkins methodology univariate Auto Regressive Integrated Moving Average (ARIMA) model. For empirical analysis a set rice, wheat total food grains for procurement, off take stocks PDS were considered with available annual data from 1972–2013 forecasted values estimated 2017. The validity the model verified based on minimum value AIC (Akaike Information Criterion), SBC (Schwarz's...

Directional data emerges in a wide array of applications, ranging from atmospheric sciences to medical imaging. Modeling such data, however, poses unique challenges by virtue their being constrained non-Euclidean spaces like manifolds. Here, we present unified Bayesian framework for inference on the Stiefel manifold using Matrix Langevin distribution. Specifically, propose novel family conjugate priors and establish number theoretical properties relevant statistical inference. Conjugacy...

Recent advances in neuroimaging technologies have provided opportunities to acquire brain images of different modalities for studying human organization from both functional and structural perspectives. Analysis derived various involves some common goals such as dimension reduction, denoising, feature extraction. However, since these vastly data characteristics, the current analysis is usually performed using distinct analytical tools that are only suitable a specific imaging modality. In...

The Horseshoe is a widely used and popular continuous shrinkage prior for high-dimensional Bayesian linear regression. Recently, regularized versions of the have also been introduced in literature. Various Gibbs sampling Markov chains developed literature to generate approximate samples from corresponding intractable posterior densities. Establishing geometric ergodicity these provides crucial technical justification accuracy asymptotic standard errors chain based estimates quantities. In...

Abstract The main aim of this paper is to study the arithmetic Bohr radius for holomorphic functions defined on a Reinhardt domain in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>ℂ</m:mi> <m:mi>n</m:mi> </m:msup> </m:math> {\mathbb{C}^{n}} with positive real part. present investigation motivated by work Lev Aizenberg [Proc. Amer. Math. Soc. 128 (2000), 2611–2619]. A part our includes connection between classical and unit ball Minkowski space <m:msubsup> <m:mi...

In this paper, we study a more general version of multidimensional Bohr radii for the holomorphic functions defined on unit ball $\ell^n_q\,\,(1\leq q\leq \infty)$ spaces with values in arbitrary complex Banach spaces. More precisely, bounded linear operators between spaces, primarily motivated by work A. Defant, M. Maestre, and U. Schwarting [Adv. Math. 231 (2012), pp. 2837--2857]. We obtain exact asymptotic estimates radius both finite infinite dimensional As an application, find lower...

In this paper, we investigate the arithmetic Bohr radius of bounded linear operators between arbitrary complex Banach spaces. We establish close connection classical and operators. Further, study asymptotic estimates for identity operator on infinite dimensional Finally, obtain correct behavior radii sequence

It can be challenging to perform an integrative statistical analysis of multi-view high-dimensional data acquired from different experiments on each subject who participated in a joint study. Canonical Correlation Analysis (CCA) is procedure for identifying relationships between such sets. In that context, Structured Sparse CCA (ScSCCA) rapidly emerging methodological area aims robust modeling the interrelations modalities by assuming corresponding directional vectors sparse. Although it...

Observational data, such as electronic clinical records and claims can prove invaluable for evaluating the Average Treatment Effect (ATE) supporting decision-making, provided they are employed correctly. The Inverse Probability of Weighting (IPTW) method, based on propensity scores, has demonstrated remarkable efficacy in estimating ATE, assuming that assumptions exchangeability, consistency, positivity met. Directed Acyclic Graphs (DAGs) offer a practical approach to assess exchangeability...

Abstract Background Count data regression modeling has received much attention in several science fields which the Poisson, Negative binomial, and Zero-Inflated models are some of primary techniques. binomial is applied to count variables, usually when they over-dispersed. A Poisson distribution also utilized for counting where mean equal variance. This situation often unrealistic since counts will have a variance that not its mean. Modeling it as distributed leads ignoring under- or...

Directional data emerges in a wide array of applications, ranging from atmospheric sciences to medical imaging. Modeling such data, however, poses unique challenges by virtue their being constrained non-Euclidean spaces like manifolds. Here, we present unified Bayesian framework for inference on the Stiefel manifold using Matrix Langevin distribution. Specifically, propose novel family conjugate priors and establish number theoretical properties relevant statistical inference. %Importantly,...

This research article is meant to highlight the topic present ground water utilization scenario of West Bengal, India. Contribution irrigation structures for different minor censuses, potentiality, cropping pattern with development over time and extent use resources have included in study. Secondary data on pattern, censuses times has been assembled from Central Ground Water Board (CGWB) (Eastern Region), State investigation directorate (SWID) area crops official statistics published by...

In this paper, we study the complex symmetry of weighted composition-differentiation operator $D_{n, \psi, \phi}$ on Bergman spaces $\mathcal{A}^2_{\alpha}$ with respect to conjugation $C_{\mu, \eta}$ for $\mu, \eta \in \{z\in \mathbb{C}:|z|=1\}$. We obtain explicit conditions which is Hermitian and normal. also characterize symmetric derivative Hardy spaces.

The main aim of this paper is to study the $n$-dimensional Bohr radius for holomophic functions defined on Reinhardt domain in $\mathbb{C}^n$ with positive real part. present investigation motivated by work Lev Aizenberg [Proc. Amer. Math. Soc. 128 (2000), 2611--2619]. A part our includes a connection between classical and arithmetic unit ball Minkowski space $\ell^n_{q}\, , 1\leq q\leq \infty$. Further, we determine exact value terms arithmetric radius.

The main aim of this paper is to answer certain open questions related the exact values multidimensional Bohr radii by using concept arithmetic radius for vector-valued holomorphic functions defined in complete Reinhardt domains $\mathbb{C}^n$. More precisely, we study asymptotic estimates unit ball $\ell^n_q$ $(1\leq q\leq \infty)$ spaces with arbitrary complex Banach spaces. Many our results generalize obtained Defant, Maestre, and Prengel [Q. J. Math. 59, (2008), pp. 189--205].