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Remarks on a Multivariate Transformation

Murray Rosenblatt
- 01 Sep 1952 - 
- Vol. 23, Iss: 3, pp 470-472
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This article is published in Annals of Mathematical Statistics.The article was published on 1952-09-01 and is currently open access. It has received 2735 citations till now. The article focuses on the topics: Transformation (function).

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Simulation-based exploration of high-dimensional system models for identifying unexpected events

TL;DR: This paper presents a meta-modelling framework that automates the very labor-intensive and therefore time-heavy and expensive process of manually cataloging and cataloging the sequences of events or configurations that occur in a numerical model.
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Multidimensional Adaptive Relevance Vector Machines for Uncertainty Quantification

TL;DR: A Bayesian uncertainty quantification framework using a local binary tree surrogate model that is able to make use of arbitrary Bayesian regression methods and is demonstrated with examples in the solution of stochastic differential equations.
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Likelihood‐based Analysis of a Class of Generalized Long‐Memory Time Series Models

TL;DR: A Markov chain Monte Carlo sampling algorithm is introduced and developed which makes it possible, among other things, to carry out exact likelihood‐based analysis of a wide range of non‐Gaussian long‐memory models without resorting to the use of likelihood approximations.
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Evaluation of failure probability under parameter epistemic uncertainty: application to aerospace system reliability assessment

TL;DR: In this article, the authors compare two different approaches to perform a reliability analysis in a context of uncertainties affecting probability distribution parameters, namely the nested reliability approach (NRA) and the augmented reliability approach(ARA).
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On probability analysis in snow avalanche hazard zoning

TL;DR: In this article, the authors combine a mechanical probabilistic model for avalanche release with a statistical/topographical model for run-out distance to obtain the unconditional probability of extreme runout distance.