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The Hidden Markov Model (HMM) is one of the mainstays of statistical modeling of discrete time series, with applications including speech recognition, computational biology, computer vision and econometrics. Estimating an HMM from its…
The group synchronization problem involves estimating a collection of group elements from noisy measurements of their pairwise ratios. This task is a key component in many computational problems, including the molecular reconstruction…
We consider the problem of collaborative personalized mean estimation under a privacy constraint in an environment of several agents continuously receiving data according to arbitrary unknown agent-specific distributions. In particular, we…
The expectation-maximization (EM) algorithm introduced by Dempster et al in 1977 is a very general method to solve maximum likelihood estimation problems. In this informal report, we review the theory behind EM as well as a number of EM…
In this paper, we propose a dynamical systems perspective of the Expectation-Maximization (EM) algorithm. More precisely, we can analyze the EM algorithm as a nonlinear state-space dynamical system. The EM algorithm is widely adopted for…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
We propose convenient inferential methods for potentially nonstationary multivariate unobserved components models with fractional integration and cointegration. Based on finite-order ARMA approximations in the state space representation,…
We propose sequential Monte Carlo based algorithms for maximum likelihood estimation of the static parameters in hidden Markov models with an intractable likelihood using ideas from approximate Bayesian computation. The static parameter…
In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
Mixtures of generalized normal distributions (MGND) have gained popularity for modelling datasets with complex statistical behaviours. However, the estimation of the shape parameter within the maximum likelihood framework is quite complex,…
Data augmentation improves the convergence of iterative algorithms, such as the EM algorithm and Gibbs sampler by introducing carefully designed latent variables. In this article, we first propose a data augmentation scheme for the…
It was known from Metropolis et al. [J. Chem. Phys. 21 (1953) 1087--1092] that one can sample from a distribution by performing Monte Carlo simulation from a Markov chain whose equilibrium distribution is equal to the target distribution.…
The performance of ensemble-based data assimilation techniques that estimate the state of a dynamical system from partial observations depends crucially on the prescribed uncertainty of the model dynamics and of the observations. These are…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
The Poisson log-normal model is a latent variable model that provides a generic framework for the analysis of multivariate count data. Inferring its parameters can be a daunting task since the conditional distribution of the latent…
Model-based clustering approaches concern the paradigm of exploratory data analysis relying on the finite mixture model to automatically find a latent structure governing observed data. They are one of the most popular and successful…
Risk management is particularly concerned with extreme events, but analysing these events is often hindered by the scarcity of data, especially in a multivariate context. This data scarcity complicates risk management efforts. Various tools…
This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…
Rank data arises frequently in marketing, finance, organizational behavior, and psychology. Most analysis of rank data reported in the literature assumes the presence of one or more variables (sometimes latent) based on whose values the…