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While the design of automated knowledge-based sensor scheduling is relevant to many multi-target detection and tracking problems, tracking algorithms are rarely built for this purpose and their outputs provide little flexibility for the…
Since the early 1970s, stellar population modelling has been one of the basic tools for understanding the physics of unresolved systems from observation of their integrated light. Models allow us to relate the integrated spectra (or…
In several environmental applications data are functions of time, essentially con- tinuous, observed and recorded discretely, and spatially correlated. Most of the methods for analyzing such data are extensions of spatial statistical tools…
Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data.…
Despite extensive research, time series classification and forecasting on noisy data remain highly challenging. The main difficulties lie in finding suitable mathematical concepts to describe time series and effectively separate noise from…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
Stochastic linearization is a method used in Quasilinear Control (QLC) to replace a nonlinearity by an equivalent gain and a bias, utilizing the statistical properties of random inputs. In this paper, the theory of stochastic linearization…
Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open…
The Metropolis-Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement.…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…
We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
Functional time series whose sample elements are recorded sequentially over time are frequently encountered with increasing technology. Recent studies have shown that analyzing and forecasting of functional time series can be performed…
In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general time-varying random demand. Our main goal is to study the optimal policies, which can be…
In sampling theory, stratification corresponds to a technique used in surveys, which allows segmenting a population into homogeneous subpopulations (strata) to produce statistics with a higher level of precision. In particular, this article…
In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…
We develop a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby. A stochastic algorithm is constructed to move the walkers up the surface through the…
We present and implement a probabilistic (Bayesian) method for producing catalogs from images of stellar fields. The method is capable of inferring the number of sources N in the image and can also handle the challenges introduced by noise,…
Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…