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The recent decades have seen various attempts at accelerating the process of developing materials targeted towards specific applications. The performance required for a particular application leads to the choice of a particular material…
This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…
This paper presents a systematic literature review focusing on the application of machine learning techniques for deriving observational constraints in cosmology. The goal is to evaluate and synthesize existing research to identify…
A reasonable description of the degradation process is essential for credible reliability assessment in accelerated degradation testing. Existing methods usually use Markovian stochastic processes to describe the degradation process.…
Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…
Randomization is a powerful technique to create robust controllers, in particular in partially observable settings. The degrees of randomization have a significant impact on the system performance, yet they are intricate to get right. The…
Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…
Multilevel models (mixed-effect models or hierarchical linear models) are now a standard approach to analysing clustered and longitudinal data in the social, behavioural and medical sciences. This review article focuses on multilevel linear…
Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…
Laser degradation analysis is a crucial process for the enhancement of laser reliability. Here, we propose a data-driven fault detection approach based on Long Short-Term Memory (LSTM) recurrent neural networks to detect the different laser…
One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…
Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…
Estimating how a treatment affects different individuals, known as heterogeneous treatment effect estimation, is an important problem in empirical sciences. In the last few years, there has been a considerable interest in adapting machine…
From biological organs to soft robotics, highly deformable materials are essential components of natural and engineered systems. These highly deformable materials can have heterogeneous material properties, and can experience heterogeneous…
This paper introduces a novel model-based clustering approach for clustering time series which present changes in regime. It consists of a mixture of polynomial regressions governed by hidden Markov chains. The underlying hidden process for…
Statistical downscaling of global climate models (GCMs) allows researchers to study local climate change effects decades into the future. A wide range of statistical models have been applied to downscaling GCMs but recent advances in…
We study the data deletion problem for convex models. By leveraging techniques from convex optimization and reservoir sampling, we give the first data deletion algorithms that are able to handle an arbitrarily long sequence of adversarial…
The Markov chain Monte Carlo method as a statistical mechanics technique for the study of macroscopic systems has furnished the scientific community with great knowledge and advances in the theory of phase transitions. While a number of…
With the increasing availability of various sensor technologies, we now have access to large amounts of multi-block (also called multi-set, multi-relational, or multi-view) data that need to be jointly analyzed to explore their latent…
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…