scholarly journals Fast Compression of MCMC Output

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1017
Author(s):  
Nicolas Chopin ◽  
Gabriel Ducrocq
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Equality Constraints ◽  
Survey Sampling ◽  
Monte Carlo Algorithm ◽  
Control Variates ◽  
Novel Method

We propose cube thinning, a novel method for compressing the output of an MCMC (Markov chain Monte Carlo) algorithm when control variates are available. It allows resampling of the initial MCMC sample (according to weights derived from control variates), while imposing equality constraints on the averages of these control variates, using the cube method (an approach that originates from survey sampling). The main advantage of cube thinning is that its complexity does not depend on the size of the compressed sample. This compares favourably to previous methods, such as Stein thinning, the complexity of which is quadratic in that quantity.

scholarly journals Star formation law in the epoch of reionization from [C ii] and C iii] lines

2020 ◽  
Vol 495 (1) ◽  
pp. L22-L26 ◽  
Author(s):  
L Vallini ◽  
A Ferrara ◽  
A Pallottini ◽  
S Carniani ◽  
S Gallerani
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Star Formation ◽  
Markov Chain Monte Carlo ◽  
Star Formation Rate ◽  
Formation Rate ◽  
Average Density ◽  
Monte Carlo Algorithm ◽  
James Webb Space Telescope ◽  
Novel Method

ABSTRACT We present a novel method to simultaneously characterize the star formation law and the interstellar medium properties of galaxies in the epoch of reionization (EoR) through the combination of [C ii] 158 μm (and its known relation with star formation rate) and C iii] λ1909 Å emission line data. The method, based on a Markov chain Monte Carlo algorithm, allows us to determine the target galaxy average density, n, gas metallicity, Z, and ‘burstiness’ parameter, κs, quantifying deviations from the Kennicutt–Schmidt relation. As an application, we consider COS-3018 (z = 6.854), the only EoR Lyman Break Galaxy so far detected in both [C ii] and C iii]. We show that COS-3018 is a moderate starburst (κs ≈ 3), with $Z \approx 0.4 \, \mathrm{Z}_{\odot }$, and $n \approx 500\, {\rm cm^{-3}}$. Our method will be optimally applied to joint ALMA and James Webb Space Telescope targets.

scholarly journals Estimation of trace gas fluxes with objectively determined basis functions using reversible-jump Markov chain Monte Carlo

2016 ◽  
Vol 9 (9) ◽  
pp. 3213-3229 ◽  
Author(s):  
Mark F. Lunt ◽  
Matt Rigby ◽  
Anita L. Ganesan ◽  
Alistair J. Manning
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Space ◽  
Spatial Domain ◽  
Monte Carlo Algorithm ◽  
Trace Gas ◽  
Reversible Jump ◽  
Pseudo Data ◽  
Atmospheric Trace Gas

Abstract. Atmospheric trace gas inversions often attempt to attribute fluxes to a high-dimensional grid using observations. To make this problem computationally feasible, and to reduce the degree of under-determination, some form of dimension reduction is usually performed. Here, we present an objective method for reducing the spatial dimension of the parameter space in atmospheric trace gas inversions. In addition to solving for a set of unknowns that govern emissions of a trace gas, we set out a framework that considers the number of unknowns to itself be an unknown. We rely on the well-established reversible-jump Markov chain Monte Carlo algorithm to use the data to determine the dimension of the parameter space. This framework provides a single-step process that solves for both the resolution of the inversion grid, as well as the magnitude of fluxes from this grid. Therefore, the uncertainty that surrounds the choice of aggregation is accounted for in the posterior parameter distribution. The posterior distribution of this transdimensional Markov chain provides a naturally smoothed solution, formed from an ensemble of coarser partitions of the spatial domain. We describe the form of the reversible-jump algorithm and how it may be applied to trace gas inversions. We build the system into a hierarchical Bayesian framework in which other unknown factors, such as the magnitude of the model uncertainty, can also be explored. A pseudo-data example is used to show the usefulness of this approach when compared to a subjectively chosen partitioning of a spatial domain. An inversion using real data is also shown to illustrate the scales at which the data allow for methane emissions over north-west Europe to be resolved.

scholarly journals Fitting Spectral Energy Distributions of AGN A Markov Chain Monte Carlo Approach

2013 ◽  
Vol 9 (S304) ◽  
pp. 228-229
Author(s):  
Gabriela Calistro Rivera ◽  
Elisabeta Lusso ◽  
Joseph F. Hennawi ◽  
David W. Hogg
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Galactic Nuclei ◽  
Physical Models ◽  
Monte Carlo Algorithm ◽  
Spectral Energy ◽  
Spectral Energy Distributions ◽  
Energy Distributions ◽  
Multiple Parameters

AbstractWe present AGNfitter: a Markov Chain Monte Carlo algorithm developed to fit the spectral energy distributions (SEDs) of active galactic nuclei (AGN) with different physical models of AGN components. This code is well suited to determine in a robust way multiple parameters and their uncertainties, which quantify the physical processes responsible for the panchromatic nature of active galaxies and quasars. We describe the technicalities of the code and test its capabilities in the context of X-ray selected obscured AGN using multiwavelength data from the XMM-COSMOS survey.

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