ABC random forests for Bayesian parameter inference

This preprint has been reviewed and recommended by Peer Community In Evolutionary Biology (http://dx.doi.org/10.24072/pci.evolbiol.100036). Approximate Bayesian computation (ABC) has grown into a standard methodology that manages Bayesian inference for models associated with intractable likelihood functions. Most ABC implementations require the preliminary selection of a vector of informative statistics summarizing raw data. Furthermore, in almost all existing implementations, the tolerance level that separates acceptance from rejection of simulated parameter values needs to be calibrated. We propose to conduct likelihood-free Bayesian inferences about parameters with no prior selection of the relevant components of the summary statistics and bypassing the derivation of the associated tolerance level. The approach relies on the random forest methodology of Breiman (2001) applied in a (non parametric) regression setting. We advocate the derivation of a new random forest for each component of the parameter vector of interest. When compared with earlier ABC solutions, this method offers significant gains in terms of robustness to the choice of the summary statistics, does not depend on any type of tolerance level, and is a good trade-off in term of quality of point estimator precision and credible interval estimations for a given computing time. We illustrate the performance of our methodological proposal and compare it with earlier ABC methods on a Normal toy example and a population genetics example dealing with human population evolution. All methods designed here have been incorporated in the R package abcrf (version 1.7) available on CRAN.Comment: Main text: 24 pages, 6 figures Supplementary Information: 14 pages, 5 figure

Entropy-based parametric estimation of spike train statistics

We consider the evolution of a network of neurons, focusing on the asymptotic behavior of spikes dynamics instead of membrane potential dynamics. The spike response is not sought as a deterministic response in this context, but as a conditional probability : "Reading out the code" consists of inferring such a probability. This probability is computed from empirical raster plots, by using the framework of thermodynamic formalism in ergodic theory. This gives us a parametric statistical model where the probability has the form of a Gibbs distribution. In this respect, this approach generalizes the seminal and profound work of Schneidman and collaborators. A minimal presentation of the formalism is reviewed here, while a general algorithmic estimation method is proposed yielding fast convergent implementations. It is also made explicit how several spike observables (entropy, rate, synchronizations, correlations) are given in closed-form from the parametric estimation. This paradigm does not only allow us to estimate the spike statistics, given a design choice, but also to compare different models, thus answering comparative questions about the neural code such as : "are correlations (or time synchrony or a given set of spike patterns, ..) significant with respect to rate coding only ?" A numerical validation of the method is proposed and the perspectives regarding spike-train code analysis are also discussed.Comment: 37 pages, 8 figures, submitte

copulaedas: An R Package for Estimation of Distribution Algorithms Based on Copulas

The use of copula-based models in EDAs (estimation of distribution algorithms) is currently an active area of research. In this context, the copulaedas package for R provides a platform where EDAs based on copulas can be implemented and studied. The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known optimization problems, and utility functions to study the performance of the algorithms. Newly developed EDAs can be easily integrated into the package by extending an S4 class with generic functions for their main components. This paper presents copulaedas by providing an overview of EDAs based on copulas, a description of the implementation of the package, and an illustration of its use through examples. The examples include running the EDAs defined in the package, implementing new algorithms, and performing an empirical study to compare the behavior of different algorithms on benchmark functions and a real-world problem

A sharp interface isogeometric strategy for moving boundary problems

The proposed methodology is first utilized to model stationary and propagating cracks. The crack face is enriched with the Heaviside function which captures the displacement discontinuity. Meanwhile, the crack tips are enriched with asymptotic displacement functions to reproduce the tip singularity. The enriching degrees of freedom associated with the crack tips are chosen as stress intensity factors (SIFs) such that these quantities can be directly extracted from the solution without a-posteriori integral calculation. As a second application, the Stefan problem is modeled with a hybrid function/derivative enriched interface. Since the interface geometry is explicitly defined, normals and curvatures can be analytically obtained at any point on the interface, allowing for complex boundary conditions dependent on curvature or normal to be naturally imposed. Thus, the enriched approximation naturally captures the interfacial discontinuity in temperature gradient and enables the imposition of Gibbs-Thomson condition during solidification simulation. The shape optimization through configuration of finite-sized heterogeneities is lastly studied. The optimization relies on the recently derived configurational derivative that describes the sensitivity of an arbitrary objective with respect to arbitrary design modifications of a heterogeneity inserted into a domain. The THB-splines, which serve as the underlying approximation, produce sufficiently smooth solution near the boundaries of the heterogeneity for accurate calculation of the configurational derivatives. (Abstract shortened by ProQuest.

Autonomous search of an airborne release in urban environments using informed tree planning

The use of autonomous vehicles for chemical source localisation is a key enabling tool for disaster response teams to safely and efficiently deal with chemical emergencies. Whilst much work has been performed on source localisation using autonomous systems, most previous works have assumed an open environment or employed simplistic obstacle avoidance, separate to the estimation procedure. In this paper, we explore the coupling of the path planning task for both source term estimation and obstacle avoidance in a holistic framework. The proposed system intelligently produces potential gas sampling locations based on the current estimation of the wind field and the local map. Then a tree search is performed to generate paths toward the estimated source location that traverse around any obstacles and still allow for exploration of potentially superior sampling locations. The proposed informed tree planning algorithm is then tested against the Entrotaxis technique in a series of high fidelity simulations. The proposed system is found to reduce source position error far more efficiently than Entrotaxis in a feature rich environment, whilst also exhibiting vastly more consistent and robust results

Feedback control of parametrized PDEs via model order reduction and dynamic programming principle

In this paper, we investigate infinite horizon optimal control problems for parametrized partial differential equations. We are interested in feedback control via dynamic programming equations which is well-known to suffer from the curse of dimensionality. Thus, we apply parametric model order reduction techniques to construct low-dimensional subspaces with suitable information on the control problem, where the dynamic programming equations can be approximated. To guarantee a low number of basis functions, we combine recent basis generation methods and parameter partitioning techniques. Furthermore, we present a novel technique to construct non-uniform grids in the reduced domain, which is based on statistical information. Finally, we discuss numerical examples to illustrate the effectiveness of the proposed methods for PDEs in two space dimensions