arXiv subjects

Prasenjit Ghosh

Publications and source records attributed to Prasenjit Ghosh.

At least 19 recordsLinked to original sources

arXiv2026

Sharp Asymptotic Minimaxity of the Gavrilov-Benjamini-Sarkar Step-Down Testing Procedure in Sparse Gaussian Sequence Models

We investigate the sharp asymptotic minimaxity of the classical Gavrilov-Benjamini-Sarkar (GBS) step-down multiple testing procedure in sparse Gaussian sequence models. Abraham et al. (2024) recently established sharp asymptotic minimax benchmarks for sparse multiple testing under both the classical beta-min framework and more general heterogeneous signal-strength classes. Although several multiple testing procedures attain these benchmarks, corresponding results for the GBS procedure have remained unavailable. We prove that the GBS procedure is sharply asymptotically minimax under both normalized Hamming loss and the combined $\mathrm{FDP}+\mathrm{FNP}$ loss over the classical beta-min parameter classes. We further establish a sharp asymptotic upper bound for the normalized Hamming risk over the heterogeneous signal-strength classes and show that the GBS procedure attains the corresponding sharp asymptotic minimax benchmark under the combined $\mathrm{FDP}+\mathrm{FNP}$ loss. Our analysis is based on a shifted order-statistic inequality for the GBS critical values together with deterministic and empirical signal-crossing arguments for ordered alternative $p$-values. Unlike existing analyses of Benjamini-Hochberg procedures and empirical Bayes $\ell$-value methods, the proposed approach is intrinsic to the geometry of the GBS step-down procedure and avoids localization of a single implicit rejection threshold. Consequently, our results extend sharp asymptotic minimaxity theory to a genuinely step-down multiple testing procedure whose rejection rule depends on the entire ordered sequence of $p$-values.

math.ST↗

arXiv2026

Asymptotic Bayes Optimality Under Sparsity of the Gavrilov-Benjamini-Sarkar Step-Down Testing Procedure

In this article, we investigate the asymptotic Bayes optimality under sparsity (ABOS) of the Gavrilov-Benjamini-Sarkar (GBS) step-down multiple testing procedure of Gavrilov et al. (2009) in the sparse Gaussian sequence model. While the asymptotic optimality properties of the Benjamini-Hochberg procedure have been extensively studied, corresponding results for the GBS procedure remain unavailable despite its favorable finite-sample performance and widespread applicability. Within the spike-and-slab Bayesian formulation and the asymptotic decision-theoretic framework of Bogdan et al. (2011), we establish that the GBS procedure is ABOS over a broad class of sparse asymptotic regimes. Existing ABOS analyses of the Benjamini-Hochberg procedure rely on approximating the random rejection threshold by a suitable deterministic surrogate. In contrast, our approach analyzes the Bayes risk directly, separately controlling the false discovery and false nondiscovery components. The analysis combines two key ingredients: a new finite-sample inequality for shifted order statistics associated with the GBS critical constants and a signal-crossing argument for ordered alternative p-values that exploits the procedure's sequential step-down structure. Together, these tools yield the desired ABOS property without resorting to threshold-localization arguments. To the best of our knowledge, this is the first asymptotic decision-theoretic analysis of the GBS procedure and the first proof of its asymptotic Bayes optimality under sparsity.

math.ST↗

arXiv2026

Bayesian Model Pursuit and Near-Oracle Sparse Signal Discovery Under Dependence

Sparse signal discovery is a fundamental problem in large-scale inference, where the goal is to identify a small number of active signals hidden among a large collection of null effects. Despite the prevalence of dependence in modern applications, relatively little is known about how much dependence can be exploited for efficient sparse signal recovery from a Bayes-risk perspective. In this paper, we develop a Bayesian Step-Down (BSD) procedure for sparse signal discovery under arbitrary known covariance dependence. BSD adopts a posterior-guided model-pursuit strategy that sequentially accumulates evidence for competing sparse signal configurations while explicitly incorporating the data's covariance structure. To assess its effectiveness, we introduce a Bayes Oracle for a class of sparse one-factor dependence models and compare BSD with the Oracle, the recently proposed MRD-GBS procedure of Ghosh and Chakrabarti (2026), the original MRD procedure of Cohen et al. (2009), and the Benjamini-Hochberg method. Our simulation studies reveal a striking phenomenon: across a broad range of dimensions, sparsity levels, and dependence structures, BSD exhibits near-oracle behavior and is often virtually indistinguishable from the Bayes Oracle in terms of Bayes risk and support recovery performance. Remarkably, a similarly close agreement is observed between BSD and MRD-GBS despite their fundamentally different Bayesian and frequentist foundations. These findings provide new insight into the attainable Bayes-risk frontier for sparse signal discovery under dependence and suggest that BSD may serve as a useful benchmark when exact Oracle calculations are unavailable. Finally, we show that BSD admits a residual representation, thereby yielding admissibility under arbitrary covariance dependence and substantial computational simplifications.

stat.ME↗

arXiv2026

Covariance-Adaptive Residualization and Stagewise Calibration for Dependent Multiple Testing

In this paper, we study simultaneous hypothesis testing for multivariate Gaussian means under arbitrary covariance dependence. Building upon the Maximum Residual Down (MRD) procedure of Cohen et al. (2009), we investigate a systematic stagewise calibration strategy based on the generalized step-down critical constants of Gavrilov et al. (2009). The proposed methodology retains the covariance-adaptive residualization mechanism of MRD while replacing the original model-dependent threshold specification with a simple and principled calibration rule. Since the resulting procedure belongs to the class of monotone residual-based step-down procedures studied by Ghosh and Chakrabarti (2026), its admissibility follows directly from their general theory. We also derive alternative representations of the MRD residual statistics that express all active residuals through a single active precision matrix, substantially reducing computational complexity while revealing a direct connection between covariance-adaptive residualization and active precision-matrix geometry. Extensive simulation studies under a broad range of dependence structures demonstrate that the proposed methodology frequently achieves substantially lower normalized misclassification risk than several widely used marginal testing procedures. Under several structured dependence models, it also exhibits remarkably strong signal-recovery behavior, simultaneously attaining false discovery rates close to the nominal level, extremely small false non-discovery rates, powers approaching one, and average numbers of rejections close to the expected number of true signals. These findings suggest that covariance-adaptive residualization and stagewise calibration play complementary roles in exploiting dependence information for large-scale multiple testing under arbitrary covariance structures.

stat.ME↗

arXiv2026

Impact of Disorder Dynamics and Multi-Domain Kinetics on the Sliding Ferroelectricity of CVD-Grown 3R-WSe2 Bilayers

Sliding ferroelectricity in van der Waals (vdW) layered systems has emerged as a promising route toward non-volatile nanoscale devices, where interlayer displacement in non-centrosymmetric bilayers generates an out-of-plane polarization. In particular, 3R-stacked bilayer transition metal dichalcogenides (TMDs) grown via chemical vapor deposition (CVD) have been shown to host such polarization due to broken inversion symmetry. However, a detailed investigation of the 2D ferroelectric (FE) properties of CVD-grown 2D films, particularly the role of intrinsic disorder, such as structural defects and domain structure, remains poorly understood. Here, we investigate the FE switching characteristics of CVD-grown 3R-stacked WSe2 using a graphene-based ferroelectric field-effect transistor (graphene-FE-FET) architecture, where graphene serves as a highly sensitive probe of induced charge modulation due to polarization switching of FEs. We show that the growth-induced structural disorder significantly impacts polarization switching, while multi-domain kinetics governs the evolution of the FE response. These findings provide important insights into the design and optimization of FE devices based on vdW materials.

cond-mat.mtrl-sci↗

arXiv2026

Admissibility of Adaptive Monotone Step-Down Multiple Testing Procedures Under Arbitrary Covariance Dependence

In this paper, we consider the problem of simultaneous testing of multivariate normal means under arbitrary covariance dependence. Specifically, let $\boldsymbol{X}\sim N_n(\boldsymbol{\theta},\boldsymbol{\Sigma})$, where $\boldsymbol{\theta}\in\mathbb{R}^n$ is unknown and $\boldsymbol{\Sigma}$ is a known positive definite covariance matrix. The objective is to test $H_{0i}:\theta_i=0$ against $H_{Ai}:\theta_i\neq 0$, simultaneously for $i=1,\ldots,n$. We establish a general admissibility theorem for a broad class of monotone residual-based step-down multiple testing procedures which iteratively rank the active hypotheses using statistics obtained through locally adaptive strictly increasing transformations of suitably standardized residual statistics arising from conditional normal distributions. Our main result shows that every such procedure is admissible with respect to a vector-valued loss function whose components are the usual individual $0$--$1$ testing losses. The proof relies on a delicate geometric analysis of the induced acceptance regions together with structural invariance properties of the adaptive stagewise rejection indices. The theorem substantially extends the admissibility theory developed for the maximum residual down procedure of Cohen et al. (2009) and reveals that admissibility under dependence is fundamentally driven by the monotone ordering structure induced by the residual statistics rather than by the precise functional form of the testing rule itself.

math.ST↗

arXiv2025

On Quantification of Borrowing of Information in Hierarchical Bayesian Models

In this work, we offer a thorough analytical investigation into the role of shared hyperparameters in a hierarchical Bayesian model, examining their impact on information borrowing and posterior inference. Our approach is rooted in a non-asymptotic framework, where observations are drawn from a mixed-effects model, and a Gaussian distribution is assumed for the true effect generator. We consider a nested hierarchical prior distribution model to capture these effects and use the posterior means for Bayesian estimation. To quantify the effect of information borrowing, we propose an integrated risk measure relative to the true data-generating distribution. Our analysis reveals that the Bayes estimator for the model with a deeper hierarchy performs better, provided that the unknown random effects are correlated through a compound symmetric structure. Our work also identifies necessary and sufficient conditions for this model to outperform the one nested within it. We further obtain sufficient conditions when the correlation is perturbed. Our study suggests that the model with a deeper hierarchy tends to outperform the nested model unless the true data-generating distribution favors sufficiently independent groups. These findings have significant implications for Bayesian modeling, and we believe they will be of interest to researchers across a wide range of fields.

stat.ME↗

arXiv2025

Fuzzy atomic system and fuzzy K-frame in fuzzy Hilbert space

Atomic system in fuzzy Hilbert space is introduced and the existence of the fuzzy atomic systems for a strongly fuzzy bounded linear operator is studied. The notion of a K-frame in fuzzy Hilbert space is presented and some of their characterizations are given. We will see that fuzzy frame operator of a fuzzy K-frame in fuzzy Hilbert space is invertible under some sufficient condition and validates this by giving some examples. Fuzzy K-frame property in fuzzy Hilbert space preserve by a strongly fuzzy bounded linear operator is established. We will describe stability condition of fuzzy K-frame in fuzzy Hilbert space under some perturbations. We construct new types of fuzzy K-frame using fuzzy K-frame in fuzzy Hilbert space. Further, it is seen that scalar combinations and product of two fuzzy K-frames is also a fuzzy K-frame in fuzzy Hilbert space

math.GM↗

arXiv2025

Sharp Asymptotic Minimaxity for Multiple Testing Using One-Group Shrinkage Priors

This paper investigates asymptotic minimaxity properties of Bayesian multiple testing rules in the sparse Gaussian sequence model using a broad class of global-local scale mixtures of normals as priors for the means. Minimaxity is studied under standard misclassification loss and the composite loss given by the sum of the false discovery proportion (FDP) and false non-discovery proportion (FNP). When the sparsity level is known, we show that by suitably choosing the global shrinkage parameter based on the sparsity level, our proposed testing rule achieves the exact minimax risk asymptotically for both losses under the ''beta-min'' separation condition. When the sparsity level is unknown, both empirical Bayes and fully Bayesian adaptations of the same rule are shown to achieve exact minimax risk asymptotically under suitable assumptions on sparsity. Our results reveal that minimaxity is attained for ''horseshoe-type'' priors that are broad enough to include the horseshoe, Strawderman-Berger, standard double Pareto, and certain inverse-gamma priors, among others. For non-''horseshoe-type'' priors, minimaxity fails to hold for either loss function. To the best of our knowledge, these are the first results of their kind for multiple hypothesis testing based on global-local shrinkage priors.

math.ST↗

arXiv2025

Skyrmionic Transport and First Order Phase Transitions in Twisted Bilayer Graphene Quantum Hall Ferromagnet

Large-angle twisted bilayer graphene (TBLG) realizes a multicomponent quantum Hall (QH) platform of spin, valley and layer pseudospins with strong Coulomb interaction-driven symmetry broken phases. Here, we investigate the low energy Landau-level spectrum of layer-decoupled TBLG and identify skyrmion-textured charged excitations and a field-induced insulating transition to an intervalley coherent state at zero-filling factor. Symmetric potential difference perpendicular to TBLG demonstrated layer coherent population of ground states with uniform energy barriers, while the charge imbalance in the layers at finite displacement field led to multidomain nucleation and a pronounced hysteresis in the exchange-dominated transport regime suggesting first order phase transitions between different QH ferromagnetic ground states.

cond-mat.mes-hall↗

arXiv2024

Constructions of bi-g-fusion frame in Hilbert space

The concept of a bi-g-fusion frame for a Hilbert space, which is a generalizations of a controlled g-fusion frame, is introduced and an example is given. Finally, bi-g-fusion frame in tensor product of Hilbert spaces is considered.

math.FA↗

arXiv2024

Continuous K-biframes in Hilbert spaces and their tensor products

A generalization of continuous biframe in a Hilbert space is introduced and a few examples are discussed. Some characterizations and algebraic properties of this biframe are given. Here we also construct various types of continuous K-biframes with the help of a bounded linear operator. Relationship between continuous K-biframe and quotient operator is established. Finally, we define continuous K-biframe for the tensor products of Hilbert spaces and give an example.

math.FA↗

arXiv2023

Tensile strain induced brightening of momentum forbidden dark exciton in WS$_2$

Transition-metal dichalcogenides (TMDs) host tightly bound quasi-particles called excitons. Based on spin and momentum selection rules, these excitons can be either optically bright or dark. In tungsten-based TMDs, momentum-forbidden dark exciton is the energy ground state and therefore it strongly affect the emission properties. In this work, we brighten the momentum forbidden dark exciton by placing WS$_2$ on top of nanotextured substrates which put the WS$_2$ layer under tensile strain, modifying electronic bandstructure. This enables phonon assisted scattering of exciton between momentum valleys, thereby brightening momentum forbidden dark excitons. Our results will pave the way to design ultrasensitive strain sensing devices based on TMDs.

cond-mat.mes-hall↗

arXiv2023

A study on Best Approximation and Banach Algebra in n-normed linear space

The idea of best approximation in linear n-normed space is presented and some examples showing various possibilities of best approximations in linear n-normed space is given. Also, we study strictly convex n-norm and enquire about the uniqueness of best approximations in n-normed linear space. Furthermore, best approximations in n-Hilbert space is discussed. Moreover, the notion of a Banach algebra in n-Banach space is presented and some examples are discussed. A set-theoretic property of invertible and non-invertible elements in a n-Banach algebra is explained and then topological divisor of zero in n-Banach algebra is defined. Finally, we introduce the notion of a complex homeomorphism in a n-Banach algebra and derive Gleason, Kahane, Zelazko type theorem with the help of complex b-homeomorphism in the case of n-Banach algebra.

math.FA↗

arXiv2023

Introduction to Continuous biframes in Hilbert spaces and their tensor products

We introduce the notion of a continuous biframe in a Hilbert space which is a generalization of discrete biframe in Hilbert space. Representation theorem for this type of generalized frame is verified and some characterizations of this biframe with the help of a invertible operator is given. Here we also introduce the concept of continuous biframe for the tensor products of Hilbert spaces and give an example. Further, we study dual continuous biframe and continuous biframe Bessel multiplier in Hilbert spaces and their tensor products.

math.FA↗

arXiv2023

Construction of continuous controlled K-g-fusion frames in Hilbert spaces

We present the notion of continuous controlled K-g-fusion frame in Hilbert space which is the generalization of discrete controlled K-g-fusion frame. We discuss some characterizations of continuous controlled K-g-fusion frame. Relationship between continuous controlled K-g-fusion frame and quotient operator is being studied. Finally, stability of continuous controlled g-fusion frame has been described.

math.FA↗

arXiv2023

An Approximate Bayesian Approach to Covariate-dependent Graphical Modeling

Gaussian graphical models typically assume a homogeneous structure across all subjects, which is often restrictive in applications. In this article, we propose a weighted pseudo-likelihood approach for graphical modeling which allows different subjects to have different graphical structures depending on extraneous covariates. The pseudo-likelihood approach replaces the joint distribution by a product of the conditional distributions of each variable. We cast the conditional distribution as a heteroscedastic regression problem, with covariate-dependent variance terms, to enable information borrowing directly from the data instead of a hierarchical framework. This allows independent graphical modeling for each subject, while retaining the benefits of a hierarchical Bayes model and being computationally tractable. An efficient embarrassingly parallel variational algorithm is developed to approximate the posterior and obtain estimates of the graphs. Using a fractional variational framework, we derive asymptotic risk bounds for the estimate in terms of a novel variant of the $α$-Rényi divergence. We theoretically demonstrate the advantages of information borrowing across covariates over independent modeling. We show the practical advantages of the approach through simulation studies and illustrate the dependence structure in protein expression levels on breast cancer patients using CNV information as covariates.

stat.ME↗

arXiv2023

Consistent Group selection using Global-local prior in High dimensional setup

We consider the problem of model selection when grouping structure is inherent within the regressors. Using a Bayesian approach, we model the mean vector by a one-group global-local shrinkage prior belonging to a broad class of such priors that includes the horseshoe prior. In the context of variable selection, this class of priors was studied by Tang et al. (2018). A modified form of the usual class of global-local shrinkage priors with polynomial tail on the group regression coefficients is proposed. The resulting threshold rule selects the active group if within a group, the ratio of the $L_2$ norm of the posterior mean of its group coefficient to that of the corresponding ordinary least square group estimate is greater than a half. In the theoretical part of this article, we have used the global shrinkage parameter either as a tuning one or an empirical Bayes estimate of it depending on the knowledge regarding the underlying sparsity of the model. When the proportion of active groups is known, using $\tau$ as a tuning parameter, we have proved that our method is oracle. In case this proportion is unknown, we propose an empirical Bayes estimate of $\tau$. Even if this empirical Bayes estimate is used, then also our half-thresholding rule captures the truly important groups and obtains optimal estimation rate of the group coefficients simultaneously. Though our theoretical works rely on a special form of the design matrix, for general design matrices also, our simulation results show that the half-thresholding rule yields results similar to that of Yang and Narisetty (2020). As a consequence of this, in a high dimensional sparse group selection problem, instead of using the so-called `gold standard' spike and slab prior, one can use the one-group global-local shrinkage priors with polynomial tail to obtain similar results.

math.ST↗