Bayesian optimisation for likelihood-free cosmological inference

Many cosmological models have only a finite number of parameters of interest, but a very expensive data-generating process and an intractable likelihood function. We address the problem of performing likelihood-free Bayesian inference from such black-box simulation-based models, under the constraint of a very limited simulation budget (typically a few thousand). To do so, we adopt an approach based on the likelihood of an alternative parametric model. Conventional approaches to approximate Bayesian computation such as likelihood-free rejection sampling are impractical for the considered problem, due to the lack of knowledge about how the parameters affect the discrepancy between observed and simulated data. As a response, we make use of a strategy previously developed in the machine learning literature (Bayesian optimisation for likelihood-free inference, BOLFI), which combines Gaussian process regression of the discrepancy to build a surrogate surface with Bayesian optimisation to actively acquire training data. We extend the method by deriving an acquisition function tailored for the purpose of minimising the expected uncertainty in the approximate posterior density, in the parametric approach. The resulting algorithm is applied to the problems of summarising Gaussian signals and inferring cosmological parameters from the Joint Lightcurve Analysis supernovae data. We show that the number of required simulations is reduced by several orders of magnitude, and that the proposed acquisition function produces more accurate posterior approximations, as compared to common strategies.Comment: 16+9 pages, 12 figures. Matches PRD published version after minor modification

Bayesian inference of the initial conditions from large-scale structure surveys

Analysis of three-dimensional cosmological surveys has the potential to answer outstanding questions on the initial conditions from which structure appeared, and therefore on the very high energy physics at play in the early Universe. We report on recently proposed statistical data analysis methods designed to study the primordial large-scale structure via physical inference of the initial conditions in a fully Bayesian framework, and applications to the Sloan Digital Sky Survey data release 7. We illustrate how this approach led to a detailed characterization of the dynamic cosmic web underlying the observed galaxy distribution, based on the tidal environment.Comment: 4 pages, 3 figures. Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", Tallinn, Estonia, June 23-28, 2014 (eds R. van de Weygaert, S. Shandarin, E. Saar, J. Einasto). Draws from arXiv:1409.6308. arXiv admin note: substantial text overlap with arXiv:1410.154

Bayesian inference of dark matter voids in galaxy surveys

We apply the BORG algorithm to the Sloan Digital Sky Survey Data Release 7 main sample galaxies. The method results in the physical inference of the initial density field at a scale factor $a~=~10^{-3}$, evolving gravitationally to the observed density field at a scale factor $a~=~1$, and provides an accurate quantification of corresponding uncertainties. Building upon these results, we generate a set of constrained realizations of the present large-scale dark matter distribution. As a physical illustration, we apply a void identification algorithm to them. In this fashion, we access voids defined by the inferred dark matter field, not by galaxies, greatly alleviating the issues due to the sparsity and bias of tracers. In addition, the use of full-scale physical density fields yields a drastic reduction of statistical uncertainty in void catalogs. These new catalogs are enhanced data sets for cross-correlation with other cosmological probes.Comment: 4 pages, 3 figures. Proceedings of the "49th Rencontres de Moriond" Cosmology Session, La Thuile, Italy, March 22-29, 2014. Draws from arXiv:1409.6308 and arXiv:1410.0355. One more figure, updated figures and references with respect to the published versio

Democracy and Deliberation: Two Models of Public Justification

El compromiso con la necesidad de ofrecer una “justificación adecuada” de las decisiones políticas vinculantes que sea aceptada o resulte aceptable para todos los ciudadanos afectados, constituye uno de los rasgos distintivos de la idea de deliberación política tal como es concebida por muchas teorías deliberativas de la democracia. Dicho esto, sin embargo, no sólo no resulta claro qué podría calificar como una “justificación adecuada”, sino tampoco algo mucho más básico: ¿cómo debemos interpretar el término “justificación” en contextos políticos? En este ensayo presentaré dos modelos de justificación pública. El primero está asociado con una concepción tradicional en epistemología de la noción de justificación de creencias e involucra algunas ideas de sentido común acerca de la cuestión. El segundo modelo, particularmente influyente en la filosofía polí- tica liberal reciente, estipula que ofrecer buenas razones (evidencia relevante, argumentos libres de defectos formales, intuiciones o juicios morales considerados, etc.) no resulta suficiente para justificar una creencia o un conjunto de creencias frente a otros sujetos. Es necesaria, además, la apelación a razones que ya son aceptadas –o pueden serlo como resultado del proceso deliberativos mismo– por parte tanto del agente que ofrece la justificación como de aquellos a quienes va dirigida. La meta de este ensayo es desarrollar un argumento en apoyo de este último modelo de justificación pública.The commitment to provide an “adequate justification” of binding political decisions that is accepted or proves acceptable by all citizens concerned, appears to be one of the distinctive features of the idea of deliberation in the public arena as it is conceived by many deliberative conceptions of democracy. Having said that, however, not only is it not at all clear what exactly would qualify as “adequate justification” but also something even more basic: how are we to interpret the term “justification” in political contexts? In this essay I shall present two models of public justification. The first one, is associated with a traditional epistemological idea of justification of beliefs and involve some common sense notions about the subject. The second model, particularly influential in recent liberal political philosophy, stipulates that providing good reasons (relevant evidence, arguments with no formal flaws, intuitions or duly considered moral convictions, etc.) does not suffice to justify a belief or set of beliefs before others. There must be an appeal to reasons that are accepted –or may come to be accepted as a result of the deliberative process itself– by the subject providing the justification as well as by those he addresses. The aim of this essay is to develop an argument in support of this second model of public justification.Fil: Garreta Leclercq, Mariano Raul. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin