Related papers: Stochastic measure distortions induced by quantile…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…
In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in [1], which addressed…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
As a physical fact, randomness is an inherent and ineliminable aspect in all physical measurements and engineering production. As a consequence, material parameters, serving as input data, are only known in a stochastic sense and thus, also…
Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite dimensional) Wiener…
Probabilistic values, including Shapley values and semivalues, provide a model-agnostic framework to attribute the behavior of a black-box model to data points or features, with a wide range of applications including explainable artificial…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
We study stochastic motion planning problems which involve a controlled process, with possibly discontinuous sample paths, visiting certain subsets of the state-space while avoiding others in a sequential fashion. For this purpose, we first…
Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…
Proceeding from the concept of rational expectations, a new dynamic model of supply and demand in a single market with one supplier, one buyer, and one kind of commodity is developed. Unlike the cob-web dynamic theories with adaptive…
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…
The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…
Stochastic processes are encountered in many contexts, ranging from generation sizes of bacterial colonies and service times in a queueing system to displacements of Brownian particles and frequency fluctuations in an electrical power grid.…
In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…
Vecchia's approximate likelihood for Gaussian process parameters depends on how the observations are ordered, which can be viewed as a deficiency because the exact likelihood is permutation-invariant. This article takes the alternative…
In stochastic quantisation, quantum mechanical expectation values are computed as averages over the time history of a stochastic process described by a Langevin equation. Complex stochastic quantisation, though theoretically not rigorously…