scholarly journals A Nested Sampling Algorithm for Cosmological Model Selection

2006 ◽  
Vol 638 (2) ◽  
pp. L51-L54 ◽  
Author(s):  
Pia Mukherjee ◽  
David Parkinson ◽  
Andrew R. Liddle
Keyword(s):  
Model Selection ◽  
Cosmological Model ◽  
Sampling Algorithm ◽  
Nested Sampling

scholarly journals Nested sampling cross-checks using order statistics

2020 ◽  
Vol 497 (4) ◽  
pp. 5256-5263
Author(s):  
Andrew Fowlie ◽  
Will Handley ◽  
Liangliang Su
Keyword(s):  
Data Analysis ◽  
Model Selection ◽  
Cosmological Model ◽  
Gravitational Wave ◽  
Order Statistics ◽  
Particle Physics ◽  
Likelihood Function ◽  
Nested Sampling ◽  
Invaluable Tool ◽  
The Cross

ABSTRACT Nested sampling (NS) is an invaluable tool in data analysis in modern astrophysics, cosmology, gravitational wave astronomy, and particle physics. We identify a previously unused property of NS related to order statistics: the insertion indexes of new live points into the existing live points should be uniformly distributed. This observation enabled us to create a novel cross-check of single NS runs. The tests can detect when an NS run failed to sample new live points from the constrained prior and plateaus in the likelihood function, which break an assumption of NS and thus leads to unreliable results. We applied our cross-check to NS runs on toy functions with known analytic results in 2–50 dimensions, showing that our approach can detect problematic runs on a variety of likelihoods, settings, and dimensions. As an example of a realistic application, we cross-checked NS runs performed in the context of cosmological model selection. Since the cross-check is simple, we recommend that it become a mandatory test for every applicable NS run.

scholarly journals Metamodel-Based Nested Sampling for Model Selection in Eddy-Current Testing

2017 ◽  
Vol 53 (4) ◽  
pp. 1-12 ◽  
Author(s):  
Caifang Cai ◽  
Sandor Bilicz ◽  
Thomas Rodet ◽  
Marc Lambert ◽  
Dominique Lesselier
Keyword(s):  
Model Selection ◽  
Eddy Current ◽  
Eddy Current Testing ◽  
Nested Sampling ◽  
Current Testing

The ellipsoidal nested sampling and the expression of the model uncertainty in measurements

2016 ◽  
Vol 30 (15) ◽  
pp. 1541002
Author(s):  
Gianpiero Gervino ◽  
Giovanni Mana ◽  
Carlo Palmisano
Keyword(s):  
Model Selection ◽  
Measurement Uncertainty ◽  
Model Uncertainty ◽  
Physical System ◽  
Bayesian Model ◽  
Model Averaging ◽  
Nested Sampling ◽  
Contour Lines ◽  
The Many ◽  
Numerical Strategy

In this paper, we consider the problems of identifying the most appropriate model for a given physical system and of assessing the model contribution to the measurement uncertainty. The above problems are studied in terms of Bayesian model selection and model averaging. As the evaluation of the “evidence” [Formula: see text], i.e., the integral of Likelihood × Prior over the space of the measurand and the parameters, becomes impracticable when this space has [Formula: see text] dimensions, it is necessary to consider an appropriate numerical strategy. Among the many algorithms for calculating [Formula: see text], we have investigated the ellipsoidal nested sampling, which is a technique based on three pillars: The study of the iso-likelihood contour lines of the integrand, a probabilistic estimate of the volume of the parameter space contained within the iso-likelihood contours and the random samplings from hyperellipsoids embedded in the integration variables. This paper lays out the essential ideas of this approach.

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