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Title: astroABC : An Approximate Bayesian Computation Sequential Monte Carlo sampler for cosmological parameter estimation

Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:
AC02-07CH11359; De-AC02-07CH11359
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Astronomy and Computing
Additional Journal Information:
Journal Volume: 19; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-12-26 19:36:24; Journal ID: ISSN 2213-1337
Country of Publication:

Citation Formats

Jennings, E., and Madigan, M.. astroABC : An Approximate Bayesian Computation Sequential Monte Carlo sampler for cosmological parameter estimation. Netherlands: N. p., 2017. Web. doi:10.1016/j.ascom.2017.01.001.
Jennings, E., & Madigan, M.. astroABC : An Approximate Bayesian Computation Sequential Monte Carlo sampler for cosmological parameter estimation. Netherlands. doi:10.1016/j.ascom.2017.01.001.
Jennings, E., and Madigan, M.. Sat . "astroABC : An Approximate Bayesian Computation Sequential Monte Carlo sampler for cosmological parameter estimation". Netherlands. doi:10.1016/j.ascom.2017.01.001.
title = {astroABC : An Approximate Bayesian Computation Sequential Monte Carlo sampler for cosmological parameter estimation},
author = {Jennings, E. and Madigan, M.},
abstractNote = {},
doi = {10.1016/j.ascom.2017.01.001},
journal = {Astronomy and Computing},
number = C,
volume = 19,
place = {Netherlands},
year = {Sat Apr 01 00:00:00 EDT 2017},
month = {Sat Apr 01 00:00:00 EDT 2017}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.ascom.2017.01.001

Citation Metrics:
Cited by: 2works
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  • Given the complexity of modern cosmological parameter inference where we arefaced with non-Gaussian data and noise, correlated systematics and multi-probecorrelated data sets, the Approximate Bayesian Computation (ABC) method is apromising alternative to traditional Markov Chain Monte Carlo approaches in thecase where the Likelihood is intractable or unknown. The ABC method is called"Likelihood free" as it avoids explicit evaluation of the Likelihood by using aforward model simulation of the data which can include systematics. Weintroduce astroABC, an open source ABC Sequential Monte Carlo (SMC) sampler forparameter estimation. A key challenge in astrophysics is the efficient use oflarge multi-probe datasets to constrainmore » high dimensional, possibly correlatedparameter spaces. With this in mind astroABC allows for massive parallelizationusing MPI, a framework that handles spawning of jobs across multiple nodes. Akey new feature of astroABC is the ability to create MPI groups with differentcommunicators, one for the sampler and several others for the forward modelsimulation, which speeds up sampling time considerably. For smaller jobs thePython multiprocessing option is also available. Other key features include: aSequential Monte Carlo sampler, a method for iteratively adapting tolerancelevels, local covariance estimate using scikit-learn's KDTree, modules forspecifying optimal covariance matrix for a component-wise or multivariatenormal perturbation kernel, output and restart files are backed up everyiteration, user defined metric and simulation methods, a module for specifyingheterogeneous parameter priors including non-standard prior PDFs, a module forspecifying a constant, linear, log or exponential tolerance level,well-documented examples and sample scripts. This code is hosted online at« less
  • Cited by 12
  • Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing, and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo (MCMC) technique built upon the basic principle of Hamiltonian mechanics. Hamiltonian dynamics allows the chain to move along trajectories of constant energy, taking large jumps in the parameter space with relatively inexpensive computations. This new technique improves the acceptance rate by a factor of 4 while reducing the correlations and boosts up the efficiency by almost a factor of Dmore » in a D-dimensional parameter space. Therefore shorter chains will be needed for a reliable parameter estimation comparing to a traditional MCMC chain yielding the same performance. Besides that, the HMC is well suited for sampling from non-Gaussian and curved distributions which are very hard to sample from using the traditional MCMC methods. The method is very simple to code and can be easily plugged into standard parameter estimation codes such as CosmoMC. In this paper we demonstrate how the HMC can be efficiently used in cosmological parameter estimation. Also we discuss possible ways of getting good estimates of the derivatives of (the log of) posterior which is needed for HMC.« less
  • Cosmological parameter estimation techniques that robustly account for systematic measurement uncertainties will be crucial for the next generation of cosmological surveys. We present a new analysis method, superABC, for obtaining cosmological constraints from Type Ia supernova (SN Ia) light curves using Approximate Bayesian Computation (ABC) without any likelihood assumptions. The ABC method works by using a forward model simulation of the data where systematic uncertainties can be simulated and marginalized over. A key feature of the method presented here is the use of two distinct metrics, the `Tripp' and `Light Curve' metrics, which allow us to compare the simulated data to the observed data set. The Tripp metric takes as input the parameters of models fit to each light curve with the SALT-II method, whereas the Light Curve metric uses the measured fluxes directly without model fitting. We apply the superABC sampler to a simulated data set ofmore » $$\sim$$1000 SNe corresponding to the first season of the Dark Energy Survey Supernova Program. Varying $$\Omega_m, w_0, \alpha$$ and $$\beta$$ and a magnitude offset parameter, with no systematics we obtain $$\Delta(w_0) = w_0^{\rm true} - w_0^{\rm best \, fit} = -0.036\pm0.109$$ (a $$\sim11$$% 1$$\sigma$$ uncertainty) using the Tripp metric and $$\Delta(w_0) = -0.055\pm0.068$$ (a $$\sim7$$% 1$$\sigma$$ uncertainty) using the Light Curve metric. Including 1% calibration uncertainties in four passbands, adding 4 more parameters, we obtain $$\Delta(w_0) = -0.062\pm0.132$$ (a $$\sim14$$% 1$$\sigma$$ uncertainty) using the Tripp metric. Overall we find a $17$% increase in the uncertainty on $$w_0$$ with systematics compared to without. We contrast this with a MCMC approach where systematic effects are approximately included. We find that the MCMC method slightly underestimates the impact of calibration uncertainties for this simulated data set.« less
  • Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modeled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is an increasing burden placed on adequate modeling; systematic errors in the model will dominate where previously these were swamped by statistical errors. For example, Gaussian distributions are an insufficient representation for errors in quantities like photometric redshifts. Likewise, it can be difficult to quantify analytically the distribution of errors that are introduced in complex fitting codes. Without a simple form for these distributions, it becomes difficult to accurately construct a likelihood function formore » the data as a function of parameters of interest. Approximate Bayesian computation (ABC) provides a means of probing the posterior distribution when direct calculation of a sufficiently accurate likelihood is intractable. ABC allows one to bypass direct calculation of the likelihood but instead relies upon the ability to simulate the forward process that generated the data. These simulations can naturally incorporate priors placed on nuisance parameters, and hence these can be marginalized in a natural way. We present and discuss ABC methods in the context of supernova cosmology using data from the SDSS-II Supernova Survey. Assuming a flat cosmology and constant dark energy equation of state, we demonstrate that ABC can recover an accurate posterior distribution. Finally, we show that ABC can still produce an accurate posterior distribution when we contaminate the sample with Type IIP supernovae.« less