Related papers: Model error covariance estimation in particle and …
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…
We consider the problem of an ensemble Kalman filter when only partial observations are available. In particular we consider the situation where the observational space consists of variables which are directly observable with known…
Estimating the state of a dynamical system from partial and noisy observations is a ubiquitous problem in a large number of applications, such as probabilistic weather forecasting and prediction of epidemics. Particle filters are a widely…
We present a computational motivation for restricted maximum likelihood (REML) estimation in linear mixed models using an expectation--maximization (EM) algorithm. At each iteration, maximum likelihood (ML) and REML solve the same…
A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…
The Expectation-Maximization (EM) algorithm is one of the most popular methods used to solve the problem of parametric distribution-based clustering in unsupervised learning. In this paper, we propose to analyze a generalized EM (GEM)…
Data assimilation (DA) plays a pivotal role in diverse applications, ranging from climate predictions and weather forecasts to trajectory planning for autonomous vehicles. A prime example is the widely used ensemble Kalman filter (EnKF),…
We show that a large class of Estimation of Distribution Algorithms, including, but not limited to, Covariance Matrix Adaption, can be written as a Monte Carlo Expectation-Maximization algorithm, and as exact EM in the limit of infinite…
The sample covariance matrix of a random vector is a good estimate of the true covariance matrix if the sample size is much larger than the length of the vector. In high-dimensional problems, this condition is never met. As a result, in…
We consider the problem of conditioning a geological process-based computer simulation, which produces basin models by simulating transport and deposition of sediments, to data. Emphasising uncertainty quantification, we frame this as a…
We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on $n$ i.i.d. samples are known to have lower accuracy than the classical $n^{- \frac{1}{2}}$ error. We investigate…
The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. It converts a complicated one-time calculation for the MLE of the incomplete data…
This paper deals with the identification of piecewise affine state-space models. These models are obtained by partitioning the state or input domain into a finite number of regions and by considering affine submodels in each region. The…
The Ensemble Kalman Filter (EnKF), as a fundamental data assimilation approach, has been widely used in many fields of the sciences and engineering. When the state variable is of high dimensional accompanied with high resolution…
We propose a modified version of the three-step estimation method for the latent class model with covariates, which may be used to estimate latent Markov models for longitudinal data. The three-step estimation approach we propose is based…
We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…
In inverse problems, the goal is to estimate unknown model parameters from noisy observational data. Traditionally, inverse problems are solved under the assumption of a fixed forward operator describing the observation model. In this…
Interval-censored multi-state data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur…
In data assimilation, an ensemble provides a way to propagate the probability density of a system described by a nonlinear prediction model. Although a large ensemble size is required for statistical accuracy, the ensemble size is typically…