Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology

@article{Alsing2018MassiveOD,
  title={Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology},
  author={Justin Alsing and Benjamin Dan Wandelt and Stephen M. Feeney},
  journal={Monthly Notices of the Royal Astronomical Society},
  year={2018},
  volume={477},
  pages={2874-2885}
}
Many statistical models in cosmology can be simulated forwards but have intractable likelihood functions. Likelihood-free inference methods allow us to perform Bayesian inference from these models using only forward simulations, free from any likelihood assumptions or approximations. Likelihood-free inference generically involves simulating mock data and comparing to the observed data; this comparison in data space suffers from the curse of dimensionality and requires compression of the data to… 

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References

SHOWING 1-10 OF 62 REFERENCES
LIKELIHOOD-FREE COSMOLOGICAL INFERENCE WITH TYPE Ia SUPERNOVAE: APPROXIMATE BAYESIAN COMPUTATION FOR A COMPLETE TREATMENT OF UNCERTAINTY
TLDR
Approximate Bayesian computation (ABC) methods are presented and discussed in the context of supernova cosmology using data from the SDSS-II Supernova Survey and it is demonstrated that ABC can recover an accurate posterior distribution.
Approximate Bayesian computation in large-scale structure : constraining the galaxy-halo connection
TLDR
This work demonstrates that ABC is feasible for LSS parameter inference by using it to constrain parameters of the halo occupation distribution (HOD) model for populating dark matter halos with galaxies and suggests that ABC can and should be applied in parameter inference for L SS analyses.
cosmoabc: Likelihood-free inference via Population Monte Carlo Approximate Bayesian Computation
Likelihood-Free Inference in Cosmology: Potential for the Estimation of Luminosity Functions
TLDR
This paper will present an overview of methods that allow a likelihood-free approach to inference, with emphasis on approximate Bayesian computation, a class of procedures originally motivated by similar inference problems in population genetics.
Massive data compression for parameter-dependent covariance matrices
TLDR
MOPED can be used to reduce, by orders of magnitude, the number of simulated datasets that are required to estimate the covariance matrix required for the analysis of gaussian-distributed data, making an otherwise intractable analysis feasible.
Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses
TLDR
Three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies in very high dimensions are presented, leading to a further substantial improvement in sampling efficiency and robustness and an even more efficient technique for estimating the uncertainty on the evaluated evidence.
Accelerating Approximate Bayesian Computation with Quantile Regression: application to cosmological redshift distributions
TLDR
A novel method, which is called qABC, to accelerate ABC with Quantile Regression, which creates a model of quantiles of distance measure as a function of input parameters and applies it to the practical problem of estimation of redshift distribution of cosmological samples.
Massive lossless data compression and multiple parameter estimation from galaxy spectra
We present a method for radical linear compression of data sets where the data are dependent on some number M of parameters. We show that, if the noise in the data is independent of the parameters,
Generalized massive optimal data compression
TLDR
This paper provides a general procedure for optimally compressing data down to summary statistics, showing that compression to the score function -- the gradient of the log-likelihood with respect to the parameters -- yields compressed statistics that are optimal in the sense that they preserve the Fisher information content of the data.
...
...