Searcharxiv⌕ Search

arXiv subjects

Joyee Ghosh

Publications and source records attributed to Joyee Ghosh.

16 recordsLinked to original sources
arXiv2026

Posterior Mode-Guided Dimension Reduction for Bayesian Model Averaging in Heavy-Tailed Linear Regression

For large model spaces in linear regression with spike-and-slab priors, the potential entrapment of Markov chain Monte Carlo (MCMC)-based methods poses significant challenges in posterior computation. Existing maximum a posteriori (MAP)-based methods provide more computationally viable alternatives, but fail to perform tail heaviness estimation and uncertainty quantification. To address these problems, we propose a method that blends MAP estimation with MCMC-based stochastic search algorithms within an error framework comprising a combination of the hyperbolic and Student-t distributions. The hyperbolic distribution has the light-tailed normal and heavy-tailed Laplace distributions as limiting cases, but is thinner-tailed than the Student-t family. Including the Student-t distribution in the error density enables better adaptation to heavier tails. Amalgamating the two error densities thus ensures a model with more flexible tail behavior when faced with unknown tail thickness in the data, compared to MAP estimators with fixed levels of tail heaviness that assume the errors have a normal or Laplace distribution. Under this proposed error model, the current work develops a two-step expectation conditional maximization (ECM)-guided MCMC algorithm. First, we conduct an ECM-based posterior maximization to guide variable selection. We then execute a Gibbs sampler on the resulting ECM-guided model space for tail heaviness estimation and uncertainty quantification. Through simulation studies and benchmark real datasets, our proposed method is shown to exhibit several advantages in variable selection and uncertainty quantification over state-of-the-art MAP-based methods. To implement our proposed method, we developed the R package FlexBayesReg, available at https://github.com/shamriddha1998/FlexBayesReg.

stat.ME↗
arXiv2025

On the Choice of Model Space Priors and Multiplicity Control in Bayesian Variable Selection: An Application to Streaming Logistic Regression

Bayesian variable selection (BVS) depends critically on the specification of a prior distribution over the model space, particularly for controlling sparsity and multiplicity. This paper examines the practical consequences of different model space priors for BVS in logistic regression, with an emphasis on streaming data settings. We review some popular and well-known Beta--Binomial priors alongside the recently proposed matryoshka doll (MD) prior. We introduce a simple approximation to the MD prior that yields independent inclusion indicators and is convenient for scalable inference. Using BIC-based approximations to marginal likelihoods, we compare the effect of different model space priors on posterior inclusion probabilities and coefficient estimation at intermediate and final stages of the data stream via simulation studies. Overall, the results indicate that no single model space prior uniformly dominates across scenarios, and that the recently proposed MD prior provides a useful additional option that occupies an intermediate position between commonly used Beta--Binomial priors with differing degrees of sparsity.

stat.ME↗
arXiv2025

Bayesian Variable Selection in Multivariate Regression Under Collinearity in the Design Matrix

We consider the problem of variable selection in Bayesian multivariate linear regression models, involving multiple response and predictor variables, under multivariate normal errors. In the absence of a known covariance structure, specifying a model with a non-diagonal covariance matrix is appealing. Modeling dependency in the random errors through a non-diagonal covariance matrix is generally expected to lead to improved estimation of the regression coefficients. In this article, we highlight an interesting exception: modeling the dependency in errors can significantly worsen both estimation and prediction. We demonstrate that Bayesian multi-outcome regression models using several popular variable selection priors can suffer from poor estimation properties in low-information settings--such as scenarios with weak signals, high correlation among predictors and responses, and small sample sizes. In such cases, the simultaneous estimation of all unknown parameters in the model becomes difficult when using a non-diagonal covariance matrix. Through simulation studies and a dataset with measurements from NIR spectroscopy, we illustrate that a two-step procedure--estimating the mean and the covariance matrix separately--can provide more accurate estimates in such cases. Thus, a potential solution to avoid the problem altogether is to routinely perform an additional analysis with a diagonal covariance matrix, even if the errors are expected to be correlated.

stat.ME↗
arXiv2025

An Online Algorithm for Bayesian Variable Selection in Logistic Regression Models With Streaming Data

In several modern applications, data are generated continuously over time, such as data generated from smartwatches. We assume data are collected and analyzed sequentially, in batches. Since traditional or offline methods can be extremely slow, Ghosh et al. (2025) proposed an online method for Bayesian model averaging (BMA). Inspired by the literature on renewable estimation, they developed an online Bayesian method for generalized linear models (GLMs) that reduces storage and computational demands dramatically compared to traditional methods for BMA. The method of Ghosh et al. (2025) works very well when the number of models is small. It can also work reasonably well in moderately large model spaces. For the latter case, the method relies on a screening stage to identify important models in the first several batches via offline methods. Thereafter, the model space remains fixed in all subsequent batches. In the post-screening stage, online updates are made to the model specific parameters, for models selected in the screening stage. For high-dimensional model spaces, the chance of missing important models in the screening stage is more likely. This necessitates the development of a method, which permits the model space to be updated as new batches of data arrive. In this article, we develop an online Bayesian model selection method for logistic regression, where the selected model can potentially change throughout the data collection process. We use simulation studies to show that our new method can outperform the method of Ghosh et al. (2025). Furthermore, we describe scenarios under which the gain from our new method is expected to be small. We revisit the traffic crash data analyzed by Ghosh et al. (2025) and illustrate that our new model selection method can have better performance for variable selection.

stat.ME↗
arXiv2024

Robust Bayesian Model Averaging for Linear Regression Models With Heavy-Tailed Errors

Our goal is to develop a Bayesian model averaging technique in linear regression models that accommodates heavier tailed error densities than the normal distribution. Motivated by the use of the Huber loss function in the presence of outliers, the Bayesian Huberized lasso with hyperbolic errors has been proposed and recently implemented in the literature (Park and Casella (2008); Kawakami and Hashimoto (2023)). Since the Huberized lasso cannot enforce regression coefficients to be exactly zero, we propose a fully Bayesian variable selection approach with spike and slab priors to address sparsity more effectively. The shapes of the hyperbolic and the Student-t density functions are different. Furthermore, the tails of a hyperbolic distribution are less heavy compared to those of a Cauchy distribution. Thus, we propose a flexible regression model with an error distribution encompassing both the hyperbolic and the Student-t family of distributions, along with an unknown tail heaviness parameter, that is estimated based on the data. It is known that the limiting form of both the hyperbolic and the Student-t distributions is a normal distribution. We develop an efficient Gibbs sampler with Metropolis Hastings steps for posterior computation. Through simulation studies and analyses of real datasets, we show that our method is competitive with various state-of-the-art methods.

stat.ME↗
arXiv2023

FSO-QKD protocols under free space losses and device imperfections: a comparative study

Quantum key distribution (QKD) is a technique to establish a secret key between two parties through a quantum channel. Several QKD protocols have been proposed and implemented over optical fibers or free space links. The main challenge of operating QKD protocols over a free space link is atmospheric losses. In this paper, we have studied and compared the performance of single and entangled photon based QKD protocols by evaluating the quantum bit error rate and secure key rate for terrestrial free-space quantum communication by considering different free-space losses, such as geometrical losses, atmospheric losses as well as device imperfections.

quant-ph↗
arXiv2019

Joint spectral amplitude analysis of SPDC photon pairs in a multimode ppLN ridge waveguide

In this paper, we study the possible parametric down conversion processes in a periodically poled customized Lithium Niobate (LiNbO3) ridge waveguide. Our analysis of spontaneous parametric down-conversion (SPDC), first, with a Gaussian pump beam mode and second, with an anti-symmetric Hermite-Gaussian HG (1,0) pump beam mode predict the possible down conversion processes in each case. From our JSA analysis, it is evident that the generated photons pairs in all these cases are negatively correlated and have orthogonal polarizations. In case of the former, degenerate photon pairs are emitted at 1550 nm with the highest efficiency in the fundamental waveguide mode. While, in case of the latter, non-degenerate photon pairs in different higher order spatial modes are generated. Such photons, thus, have multiple degrees of freedom, like polarization and spatial modes, which can be further harnessed towards hyper-entangled photons for quantum information applications.

physics.optics↗
arXiv2018

SPDC in ppLN ridge waveguide: an analysis for efficient twin photon generation at 1550 nm

We study modal characteristics of a customized ridge waveguide in Lithium Niobate designed to generate twin photons at telecom wavelength. A quantum analysis of SPDC predicts the possible down conversion processes and optimizes the input beam parameters for fundamental mode emission. Further, a Joint Spectral Amplitude (JSA) analysis ensures the generation of signal/idler at 1550 nm in the customized LN waveguide. A calculation of the parametric down conversion (PDC) signal power shows a dependence of L^(3/2) for a waveguide compared to a linear dependence in case of bulk crystal.

physics.optics↗
arXiv2017

On the Use of Cauchy Prior Distributions for Bayesian Logistic Regression

In logistic regression, separation occurs when a linear combination of the predictors can perfectly classify part or all of the observations in the sample, and as a result, finite maximum likelihood estimates of the regression coefficients do not exist. Gelman et al. (2008) recommended independent Cauchy distributions as default priors for the regression coefficients in logistic regression, even in the case of separation, and reported posterior modes in their analyses. As the mean does not exist for the Cauchy prior, a natural question is whether the posterior means of the regression coefficients exist under separation. We prove theorems that provide necessary and sufficient conditions for the existence of posterior means under independent Cauchy priors for the logit link and a general family of link functions, including the probit link. We also study the existence of posterior means under multivariate Cauchy priors. For full Bayesian inference, we develop a Gibbs sampler based on Polya-Gamma data augmentation to sample from the posterior distribution under independent Student-t priors including Cauchy priors, and provide a companion R package in the supplement. We demonstrate empirically that even when the posterior means of the regression coefficients exist under separation, the magnitude of the posterior samples for Cauchy priors may be unusually large, and the corresponding Gibbs sampler shows extremely slow mixing. While alternative algorithms such as the No-U-Turn Sampler in Stan can greatly improve mixing, in order to resolve the issue of extremely heavy tailed posteriors for Cauchy priors under separation, one would need to consider lighter tailed priors such as normal priors or Student-t priors with degrees of freedom larger than one.

stat.ME↗
arXiv2015

Measurement and shaping of biphoton spectral wavefunctions

In this work we present a simple method to reconstruct the complex spectral wavefunction of a biphoton, and hence gain complete information about the spectral and temporal properties of a photon pair. The technique, which relies on quantum interference, is applicable to biphoton states produced with a monochromatic pump when a shift of the pump frequency produces a shift in the relative frequencies contributing to the biphoton. We demonstrate an example of such a situation in type-II parametric down-conversion (SPDC) allowing arbitrary paraxial spatial pump and detection modes. Moreover, our test cases demonstrate the possibility to shape the spectral wavefunction. This is achieved by choosing the spatial mode of the pump and of the detection modes, and takes advantage of spatiotemporal correlations.

quant-ph↗
arXiv2013

Heralded Mapping of Photonic Entanglement into Single Atoms in Free Space: Proposal for a Loophole-Free Bell Test

An obvious way to entangle two atoms located at remote locations is to produce a pair of entangled photons half-way between the two atoms, to sent one photon to each location and to subsequently map the photonic entanglement into the atoms. The efficiency of this process is, however, fundamentally limited due to overall transmission losses. We propose a method to herald the success of the mapping operation in free space without destroying nor revealing the stored quantum state. Interestingly for a Bell test, the heralding signal does not open the detection loophole provided the measurement choice is performed once the heralding is obtained only. We show through a detailed feasibility study that this approach could provide an attractive alternative to Bell tests where the atom--atom entanglement is created from atom--photon entanglement using an entanglement swapping operation.

quant-ph↗
arXiv2010

Analysis of adiabatic transfer in cavity QED

A three-level atom in a $Λ$ configuration trapped in an optical cavity forms a basic unit in a number of proposed protocols for quantum information processing. Through control with an appropriate laser, this system allows for efficient storage of cavity photons into long-lived atomic excitations, and their retrieval with high fidelity. This process presumes an adiabatic transfer through the `dark state', a coherent superposition of the two lower levels of the $Λ$ system, by a slow variation of the intensity of the control laser. We study the full quantum mechanics of this transfer process with a view to examine the nonadiabatic effects, as the control laser is varied in time. The nonadiabatic effects arise due to inevitable excitations of the system to states involving the highest level of the $Λ$ configuration, which is radiative. We formulate the problem in terms of the instantaneous eigenstates and solve it numerically, allowing for spontaneous decays from the excited level. We present detailed results for both storage and retrieval for a suitable range of variation rates and intensity of the control laser, and examine optimum conditions for the transfer process.

quant-ph↗
arXiv2010

Heralded single photon absorption by a single atom

The emission and absorption of single photons by single atomic particles is a fundamental limit of matter-light interaction, manifesting its quantum mechanical nature. At the same time, as a controlled process it is a key enabling tool for quantum technologies, such as quantum optical information technology [1, 2] and quantum metrology [3, 4, 5, 6]. Controlling both emission and absorption will allow implementing quantum networking scenarios [1, 7, 8, 9], where photonic communication of quantum information is interfaced with its local processing in atoms. In studies of single-photon emission, recent progress includes control of the shape, bandwidth, frequency, and polarization of single-photon sources [10, 11, 12, 13, 14, 15, 16, 17], and the demonstration of atom-photon entanglement [18, 19, 20]. Controlled absorption of a single photon by a single atom is much less investigated; proposals exist but only very preliminary steps have been taken experimentally such as detecting the attenuation and phase shift of a weak laser beam by a single atom [21, 22], and designing an optical system that covers a large fraction of the full solid angle [23, 24, 25]. Here we report the interaction of single heralded photons with a single trapped atom. We find strong correlations of the detection of a heralding photon with a change in the quantum state of the atom marking absorption of the quantum-correlated heralded photon. In coupling a single absorber with a quantum light source, our experiment demonstrates previously unexplored matter-light interaction, while opening up new avenues towards photon-atom entanglement conversion in quantum technology.

quant-ph↗
arXiv2009

Realistic theory of electromagnetically-induced transparency and slow light in a hot vapor of atoms undergoing collisions

We present a realistic theoretical treatment of a three-level $Λ$ system in a hot atomic vapor interacting with a coupling and a probe field of arbitrary strengths, leading to electromagnetically-induced transparency and slow light under the two-photon resonance condition. We take into account all the relevant decoherence processes including col5Blisions. Velocity-changing collisions (VCCs) are modeled in the strong collision limit effectively, which helps in achieving optical pumping by the coupling beam across the entire Doppler profile. The steady-state expressions for the atomic density-matrix elements are numerically evaluated to yield the experimentally measured response characteristics. The predictions, taking into account a dynamic rate of influx of atoms in the two lower levels of the $Λ$, are in excellent agreement with the reported experimental results for $^4$He*. The role played by the VCC parameter is seen to be distinct from that by the transit time or Raman coherence decay rate.

quant-ph↗
arXiv2007

Phase diffusion pattern in quantum nondemolition systems

We quantitatively analyze the dynamics of the quantum phase distribution associated with the reduced density matrix of a system, as the system evolves under the influence of its environment with an energy-preserving quantum nondemolition (QND) type of coupling. We take the system to be either an oscillator (harmonic or anharmonic) or a two-level atom (or equivalently, a spin-1/2 system), and model the environment as a bath of harmonic oscillators, initially in a general squeezed thermal state. The impact of the different environmental parameters is explicitly brought out as the system starts out in various initial states. The results are applicable to a variety of physical systems now studied experimentally with QND measurements.

quant-ph↗