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We propose a new sampling algorithm combining two quite powerful ideas in the Markov chain Monte Carlo literature -- adaptive Metropolis sampler and two-stage Metropolis-Hastings sampler. The proposed sampling method will be particularly…

We consider the recently introduced Transformation-based Markov Chain Monte Carlo (TMCMC) (Dutta and Bhattacharya (2014)), a methodology that is designed to update all the parameters simultaneously using some simple deterministic…

This article addresses the challenge of validating the admission committee's decisions for undergraduate admissions. In recent years, the traditional review process has struggled to handle the overwhelmingly large amount of applicants'…

Classification is a common statistical task in many areas. In order to ameliorate the performance of the existing methods, there are always some new classification procedures proposed. These procedures, especially those raised in the…

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization…

A generalized method of moments (GMM) estimator is unreliable for a large number of moment conditions, that is, it is comparable, or larger than the sample size. While classical GMM literature proposes several provisions to this problem,…

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…

Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms to estimate system…

Finite element model updating is challenging because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield responses that are similar with respect to…

Bond rating Transition Probability Matrices (TPMs) are built over a one-year time-frame and for many practical purposes, like the assessment of risk in portfolios or the computation of banking Capital Requirements (e.g. the new IFRS 9…

Rubric-based reward shaping provides interpretable and editable reward signals for fine-tuning LLMs via reinforcement learning (RL), but existing adaptive rubric methods typically update criteria from local evidence such as the current…

We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model…

We introduce Prompt Curriculum Learning (PCL), a lightweight reinforcement learning (RL) algorithm that selects intermediate-difficulty prompts using a learned value model to post-train language models. Since post-training LLMs via RL…

Providing timely, consistent, and high-quality feedback in large-scale higher education courses remains a persistent challenge, often constrained by instructor workload and resource limitations. This study presents an LLM-powered, agentic…

Stochastic optimization in learning and inference often relies on Markov chain Monte Carlo (MCMC) to approximate gradients when exact computation is intractable. However, finite-time MCMC estimators are biased, and reducing this bias…

For a remote estimation system, we study age of incorrect information (AoII), which is a recently proposed semantic-aware freshness metric. In particular, we assume an information source observing a discrete-time finite-state Markov chain…

Despite the prevalence of retrieval-augmented language models (RALMs), the seamless integration of these models with retrieval mechanisms to enhance performance in document-based tasks remains challenging. While some post-retrieval…

The adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen [Bernoulli 7 (2001) 223-242] uses the estimated covariance of the target distribution in the proposal distribution. This paper introduces a new robust adaptive…

Most Markov chain Monte Carlo methods operate in discrete time and are reversible with respect to the target probability. Nevertheless, it is now understood that the use of non-reversible Markov chains can be beneficial in many contexts. In…

To combat the detrimental effects of the variability in wireless channels, we consider cross-layer rate adaptation based on limited feedback. In particular, based on limited feedback in the form of link-layer acknowledgements (ACK) and…