Approximate Bayesian Computation and novel Bayesian approaches in cosmostatistics

vendredi 20 sept. 2019, 08:00 → 23:30 Europe/Paris

Clermont-Ferrand

Topics

The role of Bayesian inference in cosmological data processing has never ceased to grow and the need for always more sophisticated methods is dire. However making new statistical methods accepted by the research community is still a slow process. This workshop aims to present the recent progress made in this field, in particular in the implementation of approximate Bayesian computation for astrophysical data.

Registration is free and can be made here.

Invited speakers

Martin Kilbinger (CEA Saclay)

Florent Leclercq (Imperial College London)

Jean-Michel Marin (Université de Montpellier) (Absent)

Christian P. Robert (Université Paris-Dauphine)

Grégoire Aufort (Université Aix-Marseille)

Venue

Laboratoire de Mathématiques Blaise Pascal, Université Clermont-Auvergne, salle 2222

Organizers

Emmanuel Gangler (LPC, Université Clermont-Auvergne)

Arnaud Guillin (LMBP, Université Clermont-Auvergne)

Emille Ishida (LPC, Université Clermont-Auvergne)

Manon Michel (LMBP, Université Clermont-Auvergne)

 

09:00 Welcome and coffee

1 Gibbs-ABC

Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this dimension grows. To tackle this difficulty, we explore a Gibbs version of the ABC approach that runs component-wise approximate Bayesian computation steps aimed at the corresponding conditional posterior distributions, and based on summary statistics of reduced dimensions. While lacking the standard justifications for the Gibbs sampler, the resulting Markov chain is shown to converge in distribution under some partial independence conditions. The associated stationary distribution can further be shown to be close to the true posterior distribution and some hierarchical versions of the proposed mechanism enjoy a closed form limiting distribution. Experiments also demonstrate the gain in efficiency brought by the Gibbs version over the standard solution.

https://arxiv.org/abs/1905.13599

Orateur: Prof. Christian Robert (CEREMADE, Paris)

2 Bayesian inference with black-box cosmological models

Large-scale astronomical surveys carry opportunities for testing physical theories about the origin and evolution of the Universe. Advancing the research frontier requires solving challenging and unique statistical problems, to unlock the information content of massive and complex data streams. In this talk, I will present recent methodological advances, aiming at fitting cosmological data with "black-box" numerical models. I will discuss two different solutions, depending on the scenario: Bayesian optimisation (BOLFI) and Taylor-expansion of the simulator (SELFI).

References:
http://arxiv.org/abs/1805.07152
http://arxiv.org/abs/1902.10149

Orateur: Dr Florent Leclercq (Imperial Centre for Inference and Cosmology, London)

11:15 Coffee break

3 ABC for galaxy star formation history model choice

We are interested in the bayesian model choice problem when a large number of objects have to be processed. We propose an extension of the ABC-RandomForest algorithm for model choice, based on crossentropy minimization on the ABC simulation catalogue. This learning algorithm allows us to bypass the use of summary statistics for ABC. We present an application in astrophysics. From photometric data, we show the relevance of the complexification of a stellar formation history model for an important part of the datasets among tens of thousands of galaxies.

Orateur: Grégoire Aufort (Institut de Mathématiques de Marseille (I2M) Aix-Marseille Université)

12:15 Lunch break

4 ABC in cosmology: Likelihood-free inference without the inverse covariance matrix

In traditional likelihood-based parameter inference methods, the inverse of the data covariance matrix has to be computed. In cosmology, the covariance is often estimated from expensive numerical simulations. Limits on the allowed biases on parameter constraints from the inversion of the noisy, high-dimensional covariance matrix sets strong requirements on the necessary number of simulations, which has to be much larger than the data dimension. For a realistic setting of typical cosmological data, this number can be in the thousands, making the use of time-consuming N-body simulations prohibitive.

In this talk I propose to use Approximate Bayesian Computation (ABC) as a likelihood-free inference method to obtain constraints on cosmological parameters. Model simulations of the data vector are obtained quickly by drawing from an analytical multi-variate distribution, requiring only a covariance matrix but not its inverse. Using toy models, I show that the number of simulations can be much smaller than the data dimension. I present first results from applying ABC to weak gravitational lensing, which is one of the main cosmological probes to explore dark energy and the dark-matter distribution in the universe.

Orateur: Dr Martin Kilbinger (CEA Saclay)

15:15 Coffee break

Discussion