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In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…
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…
We consider the problem of detecting abrupt changes (i.e., large jump discontinuities) in the rate function of a point process. The rate function is assumed to be fully unknown, non-stationary, and may itself be a random process that…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from…
The problem of quickest detection of a change in distribution is considered under the assumption that the pre-change distribution is known, and the post-change distribution is only known to belong to a family of distributions…
Model-based algorithms are deeply rooted in modern control and systems theory. However, they usually come with a critical assumption - access to an accurate model of the system. In practice, models are far from perfect. Even precisely tuned…
This article describes posterior maximization for topic models, identifying computational and conceptual gains from inference under a non-standard parametrization. We then show that fitted parameters can be used as the basis for a novel…
We addressed the problem of detecting the change in behavior of information diffusion from a small amount of observation data, where the behavior changes were assumed to be effectively reflected in changes in the diffusion parameter value.…
Modeling univariate block maxima by the generalized extreme value distribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying stationary time series,…
Empirical risk minimization (ERM) is a fundamental learning rule for statistical learning problems where the data is generated according to some unknown distribution $\mathsf{P}$ and returns a hypothesis $f$ chosen from a fixed class…
We consider an expected-value ranking and selection (R&S) problem where all k solutions' simulation outputs depend on a common parameter whose uncertainty can be modeled by a distribution. We define the most probable best (MPB) to be the…
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…
We discuss the conditions under which Scan Statistics can be fruitfully implemented to signal a departure from the underlying probability model that describes the experimental data. It is shown that local perturbations (``bumps'' or…
Estimating the parameters of max-stable parametric models poses significant challenges, particularly when some parameters lie on the boundary of the parameter space. This situation arises when a subset of variables exhibits extreme values…
In the fields of statistics and unsupervised machine learning a fundamental and well-studied problem is anomaly detection. Anomalies are difficult to define, yet many algorithms have been proposed. Underlying the approaches is the nebulous…
Oftentimes in practice, the observed process changes statistical properties at an unknown point in time and the duration of a change is substantially finite, in which case one says that the change is intermittent or transient. We provide an…
Theory and algorithms are developed for detecting changes in the distribution of statistically periodic random processes. The statistical periodicity is modeled using independent and periodically identically distributed processes, a new…
Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is {\it complex}. Nevertheless, even according to this restricted definition, a general…
We study the parameter estimation problem in mixture models with observational nonidentifiability: the full model (also containing hidden variables) is identifiable, but the marginal (observed) model is not. Hence global maxima of the…