716 research outputs found
An optimal transportation approach for assessing almost stochastic order
When stochastic dominance does not hold, we can improve
agreement to stochastic order by suitably trimming both distributions. In this
work we consider the Wasserstein distance, , to stochastic
order of these trimmed versions. Our characterization for that distance
naturally leads to consider a -based index of disagreement with
stochastic order, . We provide asymptotic
results allowing to test vs , that,
under rejection, would give statistical guarantee of almost stochastic
dominance. We include a simulation study showing a good performance of the
index under the normal model
Informative Features for Model Comparison
Given two candidate models, and a set of target observations, we address the
problem of measuring the relative goodness of fit of the two models. We propose
two new statistical tests which are nonparametric, computationally efficient
(runtime complexity is linear in the sample size), and interpretable. As a
unique advantage, our tests can produce a set of examples (informative
features) indicating the regions in the data domain where one model fits
significantly better than the other. In a real-world problem of comparing GAN
models, the test power of our new test matches that of the state-of-the-art
test of relative goodness of fit, while being one order of magnitude faster.Comment: Accepted to NIPS 201
On some goodness of fit tests fornormality based on the optimal transport distance
We apply the optimal transport distance to construct two goodness of fit tests for (univariate) normality. The derived statistics are then compared with those used by the Shapiro-Wilk, the Anderson-Darling and the Cramer-von Mises tests. In particular, we preform Monte Carlo experiments, involving computations of the test power against some selected alternatives and wide range of sample sizes, which show efficiency of the obtained test procedures
Critical Transitions In a Model of a Genetic Regulatory System
We consider a model for substrate-depletion oscillations in genetic systems,
based on a stochastic differential equation with a slowly evolving external
signal. We show the existence of critical transitions in the system. We apply
two methods to numerically test the synthetic time series generated by the
system for early indicators of critical transitions: a detrended fluctuation
analysis method, and a novel method based on topological data analysis
(persistence diagrams).Comment: 19 pages, 8 figure
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