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We propose an attitude and gyro-bias estimation scheme for accelerated rigid body systems using an inertial measurement unit (IMU) and a global positioning system (GPS). The proposed scheme allows to obtain attitude estimates directly on…
The multivariate generalized Gaussian distribution (MGGD), also known as the multivariate exponential power (MEP) distribution, is widely used in signal and image processing. However, estimating MGGD parameters, which is required in…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
Many filters have been proposed in recent decades for the nonlinear state estimation problem. The linearization-based extended Kalman filter (EKF) is widely applied to nonlinear industrial systems. As EKF is limited in accuracy and…
Non-negative matrix factorization (NMF) is widely used as a feature extraction technique for matrices with non-negative entries, such as image data, purchase histories, and other types of count data. In NMF, a non-negative matrix is…
The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a…
Iterative methods for fitting a Gaussian Random Field (GRF) model via maximum likelihood (ML) estimation requires solving a nonconvex optimization problem. The problem is aggravated for anisotropic GRFs where the number of covariance…
Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a…
We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that…
Understanding $\textit{galaxy bias}$ -- that is the statistical relation between matter and galaxies -- is of key importance for extracting cosmological information from galaxy surveys. While the bias function $f$ -- that is the probability…
A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…
Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…
Ancestral graph models, introduced by Richardson and Spirtes (2002), generalize both Markov random fields and Bayesian networks to a class of graphs with a global Markov property that is closed under conditioning and marginalization. By…
We generalize the popular ensemble Kalman filter to an ensemble transform filter where the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
The inverse Gaussian (IG) is one of the most famous and considered distributions with positive support. We propose a convenient mode-based parameterization yielding the reparametrized IG (rIG) distribution; it allows/simplifies the use of…