Approximate Bayesian Computation and novel Bayesian approaches in cosmostatistics
Friday, September 20, 2019 
8:00 AM
Monday, September 16, 2019
Tuesday, September 17, 2019
Wednesday, September 18, 2019
Thursday, September 19, 2019
Friday, September 20, 2019
9:00 AM
Welcome and coffee
Welcome and coffee
9:00 AM  9:15 AM
9:15 AM
GibbsABC

Christian Robert
(
CEREMADE, Paris
)
GibbsABC
Christian Robert
(
CEREMADE, Paris
)
9:15 AM  10:15 AM
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 componentwise 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
10:15 AM
Bayesian inference with blackbox cosmological models

Florent Leclercq
(
Imperial Centre for Inference and Cosmology, London
)
Bayesian inference with blackbox cosmological models
Florent Leclercq
(
Imperial Centre for Inference and Cosmology, London
)
10:15 AM  11:15 AM
Largescale 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 "blackbox" numerical models. I will discuss two different solutions, depending on the scenario: Bayesian optimisation (BOLFI) and Taylorexpansion of the simulator (SELFI). References: http://arxiv.org/abs/1805.07152 http://arxiv.org/abs/1902.10149
11:15 AM
Coffee break
Coffee break
11:15 AM  11:30 AM
11:30 AM
ABC for galaxy star formation history model choice

Grégoire Aufort
(
Institut de Mathématiques de Marseille (I2M) AixMarseille Université
)
ABC for galaxy star formation history model choice
Grégoire Aufort
(
Institut de Mathématiques de Marseille (I2M) AixMarseille Université
)
11:30 AM  12:15 PM
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 ABCRandomForest 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.
12:15 PM
Lunch break
Lunch break
12:15 PM  2:15 PM
2:15 PM
ABC in cosmology: Likelihoodfree inference without the inverse covariance matrix

Martin Kilbinger
(
CEA Saclay
)
ABC in cosmology: Likelihoodfree inference without the inverse covariance matrix
Martin Kilbinger
(
CEA Saclay
)
2:15 PM  3:15 PM
In traditional likelihoodbased 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, highdimensional 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 timeconsuming Nbody simulations prohibitive. In this talk I propose to use Approximate Bayesian Computation (ABC) as a likelihoodfree inference method to obtain constraints on cosmological parameters. Model simulations of the data vector are obtained quickly by drawing from an analytical multivariate 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 darkmatter distribution in the universe.
3:15 PM
Coffee break
Coffee break
3:15 PM  3:45 PM
3:45 PM
3:45 PM  4:45 PM