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In this article, we consider the problem of estimating the parameters of the Fr\'echet distribution from both frequentist and Bayesian points of view. First we briefly describe different frequentist approaches, namely, maximum likelihood,…

Quantum phase estimation based on Gaussian states plays a crucial role in many application fields. In this paper, we study the precision bound for the scheme using two-mode squeezed Gaussian states. The quantum Fisher information is…

Diffusion models often degrade when trained in latent spaces (e.g., VAEs), yet the formal causes remain poorly understood. We quantify latent-space diffusability through the rate of change of the Minimum Mean Squared Error (MMSE) along the…

This paper proposes a method for estimating and detecting optical signals in practical photon-counting receivers. There are two important aspects of non-perfect photon-counting receivers, namely, (i) dead time which results in blocking…

Parton distribution functions (PDFs) form an essential part of particle physics calculations. Currently, the most precise predictions for these non-perturbative functions are generated through fits to global data. A problem that several PDF…

We consider distributed estimation of a Gaussian vector with a linear observation model in an inhomogeneous wireless sensor network, where a fusion center (FC) reconstructs the unknown vector, using a linear estimator. Sensors employ…

Beam displacement measurements are widely used in optical sensing and communications; however, their performance is affected by numerous intrinsic and extrinsic factors including beam profile, propagation loss, and receiver architecture.…

Bayesian inference is a popular and widely-used approach to infer phylogenies (evolutionary trees). However, despite decades of widespread application, it remains difficult to judge how well a given Bayesian Markov chain Monte Carlo (MCMC)…

This Point spread function (PSF) plays a crucial role in many computational imaging applications, such as shape from focus/defocus, depth estimation, and fluorescence microscopy. However, the mathematical model of the defocus process is…

Message passing algorithms have been tailored for compressive imaging applications by plugging in different types of off-the-shelf image denoisers. These off-the-shelf denoisers mostly rely on some generic or hand-crafted priors for…

The problem of distributed estimation of a parametric physical field is stated as a maximum likelihood estimation problem. Sensor observations are distorted by additive white Gaussian noise. Prior to data transmission, each sensor quantizes…

We propose a method to map the conventional optical interferometry setup into quantum circuits. The unknown phase shift inside a Mach-Zehnder interferometer in the presence of photon loss is estimated by simulating the quantum circuits. For…

Optimality results for two outstanding Bayesian estimation problems are given in this paper: the estimation of the sampling distribution for the squared total variation function and the estimation of the density for the $L^1$-squared loss…

Bayesian low-rank matrix factorization techniques have become an essential tool for relational data analysis and matrix completion. A standard approach is to assign zero-mean Gaussian priors on the columns or rows of factor matrices to…

We propose a Bayesian image super-resolution (SR) method with a causal Gaussian Markov random field (MRF) prior. SR is a technique to estimate a spatially high-resolution image from given multiple low-resolution images. An MRF model with…

In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a…

In a wireless sensor network, multilevel quantization is necessary in order to find a compromise between the smallest possible power consumption of the sensors and the detection performance at the fusion center (FC). The general methodology…

Gaussian quantum channels constitute a cornerstone of continuous-variable quantum information science, underpinning a wide array of protocols in quantum optics and quantum metrology. While the action of such channels on arbitrary states is…

We examine codes, over the additive Gaussian noise channel, designed for reliable communication at some specific signal-to-noise ratio (SNR) and constrained by the permitted minimum mean-square error (MMSE) at lower SNRs. The maximum…

The multivariate extended skew-normal distribution allows for accommodating raw data which are skewed and heavy tailed, and has at least three appealing statistical properties, namely closure under conditioning, affine transformations, and…