Related papers: Adaptive Penalized Likelihood method for Markov Ch…

Robust estimators for generalized linear models (GLMs) are not easy to develop due to the nature of the distributions involved. Recently, there has been growing interest in robust estimation methods, particularly in contexts involving a…

Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…

The pattern maximum likelihood (PML) estimate, introduced by Orlitsky et al., is an estimate of the multiset of probabilities in an unknown probability distribution $\mathbf{p}$, the estimate being obtained from $n$ i.i.d. samples drawn…

Large language models (LLMs) solve problems more accurately and interpretably when instructed to work out the answer step by step using a ``chain-of-thought'' (CoT) prompt. One can also improve LLMs' performance on a specific task by…

Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate…

In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…

Gaussian processes (GPs) are popular as nonlinear regression models for expensive computer simulations, yet GP performance relies heavily on estimation of unknown covariance parameters. Maximum likelihood estimation (MLE) is common, but it…

Jump Markov linear systems (JMLS) are a useful class which can be used to model processes which exhibit random changes in behavior during operation. This paper presents a numerically stable method for learning the parameters of jump Markov…

There are various parametric models for analyzing pairwise comparison data, including the Bradley-Terry-Luce (BTL) and Thurstone models, but their reliance on strong parametric assumptions is limiting. In this work, we study a flexible…

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…

We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the…

The design of the proposal distributions, and most notably the kernel parameters, are crucial for the performance of Markov chain Monte Carlo (MCMC) rendering. A poor selection of parameters can increase the correlation of the Markov chain…

Estimating model parameters is a crucial step in mathematical modelling and typically involves minimizing the disagreement between model predictions and experimental data. This calibration data can change throughout a study, particularly if…

The graphical Lasso (GLASSO) is a widely used algorithm for learning high-dimensional undirected Gaussian graphical models (GGM). Given i.i.d. observations from a multivariate normal distribution, GLASSO estimates the precision matrix by…

The pseudo-likelihood method is one of the most popular algorithms for learning sparse binary pairwise Markov networks. In this paper, we formulate the $L_1$ regularized pseudo-likelihood problem as a sparse multiple logistic regression…

We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed…

This work concerns estimation of linear autoregressive models with Markov-switching using expectation maximisation (E.M.) algorithm. Our method generalise the method introduced by Elliot for general hidden Markov models and avoid to use…

In this paper, we introduce a variant of hidden Markov models in which the transition probabilities between the states, as well as the emission distributions, are not constant in time but vary in a periodic manner. This class of models,…

The Future Elderly Model and related microsimulations are modeled as Markov chains. These simulations rely on longitudinal survey data to estimate their transition models. The use of survey data presents several incomplete data problems,…

Estimating the difficulty of input questions as perceived by large language models (LLMs) is essential for accurate performance evaluation and adaptive inference. Existing methods typically rely on repeated response sampling, auxiliary…