Related papers: An Approximate Maximum Likelihood Estimator for Di…
The saddlepoint approximation gives an approximation to the density of a random variable in terms of its moment generating function. When the underlying random variable is itself the sum of $n$ unobserved i.i.d. terms, the basic classical…
Birth-and-death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, because the likelihood can become numerically…
This paper proposes a novel exact maximum likelihood (ML) estimation method for general Gaussian processes, where all parameters are estimated jointly. The exact ML estimator (MLE) is consistent and asymptotically normally distributed. We…
Birth-death processes (BDPs) are continuous-time Markov chains that track the number of "particles" in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle…
Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…
We consider statistical models driven by Gaussian and non-Gaussian self-similar processes with long memory and we construct maximum likelihood estimators (MLE) for the drift parameter. Our approach is based on the approximation by random…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…
This work studies the properties of the maximum likelihood estimator (MLE) of a non-linear model with Gaussian errors and multidimensional parameter. The observations are collected in a two-stage experimental design and are dependent since…
The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
The saddlepoint approximation to the likelihood, and its corresponding maximum likelihood estimate (MLE), offer an alternative estimation method when the true likelihood is intractable or computationally expensive. However, maximizing this…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…
Temporal Point Processes (TPP) with partial likelihoods involving a latent structure often entail an intractable marginalization, thus making inference hard. We propose a novel approach to Maximum Likelihood Estimation (MLE) involving…
The challenges posed by complex stochastic models used in computational ecology, biology and genetics have stimulated the development of approximate approaches to statistical inference. Here we focus on Synthetic Likelihood (SL), a…
Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…
The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…
Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution that best explain the observed data. In the context of text generation, MLE is often used to train generative language…
In this letter, we revisit the problem of maximum likelihood estimation (MLE) of parameters of Gaussian Mixture Model (GMM) and show a new derivation for its parameters. The new derivation, unlike the classical approach employing the…
We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and…