A simulation-based comparison of maximum entropy and copula methods for capturing non-linear probability dependence

2016 ◽  
Author(s):  
Ehsan Salimi ◽  
Ali E. Abbas
Keyword(s):  
Maximum Entropy ◽  
Simulation Based ◽  
Non Linear ◽  
Linear Probability

Distribution of Maxima of Non-Linear Rolling in Case of Coupled Sway and Roll Motions of a Floating Body in Irregular Waves

2008 ◽  
Author(s):  
Ignace D. Mendoume Minko ◽  
Marc Prevosto ◽  
Marc Le Boulluec
Keyword(s):  
Irregular Waves ◽  
Floating Body ◽  
Time Domain Simulation ◽  
Single Degree Of Freedom ◽  
Simulation Based ◽  
Non Linear ◽  
Circular Frequency ◽  
The Time Domain ◽  
Gaussian Closure ◽  
Made In

The so-called Linearize & Match (L&M), which gives a good approximation of the exact distribution of maxima roll angle of non-linear systems, was studied some years ago by Armand and Duthoit (1990) and by Prevosto (2001). The developments within this method were made in the case of single degree of freedom dynamic systems. Moreover, the terms (mass, damping, stiffness) of the non-linear transfer function did not depend on the circular frequency. In this paper, first, the L&M method is improved by adding a last step in the procedure which correct the Gaussian closure technique of the method, secondly is generalized to a coupled sway and roll dynamic system in which the hydrodynamic coefficients are frequency-dependent. The system is modelled by a set of ordinary differential equations in which the non linearity is only in the roll motion. In order to validate the results obtained in this case by the L&M method, a Monte Carlo method with long simulations of the response of the system was carried out. Hence, some aspects of the time domain simulation, based on Cummins equations, are also discussed.

scholarly journals Cosmological Evidence Modelling: a new simulation-based approach to constrain cosmology on non-linear scales

2019 ◽  
Vol 490 (2) ◽  
pp. 1870-1878 ◽  
Author(s):  
Johannes U Lange ◽  
Frank C van den Bosch ◽  
Andrew R Zentner ◽  
Kuan Wang ◽  
Andrew P Hearin ◽  
...  
Keyword(s):  
Parameter Space ◽  
Cosmological Parameters ◽  
Computational Cost ◽  
Simulation Based ◽  
Non Linear ◽  
Bayesian Evidence ◽  
The Galaxy ◽  
Complex Models ◽  
Galaxy Halo ◽  
Galaxy Assembly

ABSTRACT Extracting accurate cosmological information from galaxy–galaxy and galaxy–matter correlation functions on non-linear scales (${\lesssim } 10 \, h^{-1}{\rm {Mpc}}$) requires cosmological simulations. Additionally, one has to marginalize over several nuisance parameters of the galaxy–halo connection. However, the computational cost of such simulations prohibits naive implementations of stochastic posterior sampling methods like Markov chain Monte Carlo (MCMC) that would require of order $\mathcal {O}(10^6)$ samples in cosmological parameter space. Several groups have proposed surrogate models as a solution: a so-called emulator is trained to reproduce observables for a limited number of realizations in parameter space. Afterwards, this emulator is used as a surrogate model in an MCMC analysis. Here, we demonstrate a different method called Cosmological Evidence Modelling (CEM). First, for each simulation, we calculate the Bayesian evidence marginalized over the galaxy–halo connection by repeatedly populating the simulation with galaxies. We show that this Bayesian evidence is directly related to the posterior probability of cosmological parameters. Finally, we build a physically motivated model for how the evidence depends on cosmological parameters as sampled by the simulations. We demonstrate the feasibility of CEM by using simulations from the Aemulus simulation suite and forecasting cosmological constraints from BOSS CMASS measurements of redshift-space distortions. Our analysis includes exploration of how galaxy assembly bias affects cosmological inference. Overall, CEM has several potential advantages over the more common approach of emulating summary statistics, including the ability to easily marginalize over highly complex models of the galaxy–halo connection and greater accuracy, thereby reducing the number of simulations required.

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