scholarly journals Assessing the accuracy of Approximate Bayesian Computation approaches to infer epidemiological parameters from phylogenies

2016 ◽  
Author(s):  
Emma Saulnier ◽  
Olivier Gascuel ◽  
Samuel Alizon
Keyword(s):  
Machine Learning ◽  
Variable Selection ◽  
Approximate Bayesian Computation ◽  
Likelihood Function ◽  
Machine Learning Techniques ◽  
Bayesian Computation ◽  
Summary Statistics ◽  
Large Trees ◽  
Approximate Bayesian ◽  
Epidemiological Parameters

AbstractPhylodynamics typically rely on likelihood-based methods to infer epidemiological parameters from dated phylogenies. These methods are essentially based on simple epidemiological models because of the difficulty in expressing the likelihood function analytically. Computing this function numerically raises additional challenges, especially for large phylogenies. Here, we use Approximate Bayesian Computation (ABC) to circumvent these problems. ABC is a likelihood-free method of parameter inference, based on simulation and comparison between target data and simulated data, using summary statistics. We simulated target trees under several epidemiological scenarios in order to assess the accuracy of ABC methods for inferring epidemiological parameter such as the basic reproduction number (R0), the mean duration of infection, and the effective host population size. We designed many summary statistics to capture the information in a phylogeny and its corresponding lineage-through-time plot. We then used the simplest ABC method, called rejection, and its modern derivative complemented with adjustment of the posterior distribution by regression. The availability of machine learning techniques including variable selection, motivated us to compute many summary statistics on the phylogeny. We found that ABC-based inference reaches an accuracy comparable to that of likelihood-based methods for birth-death models and can even outperform existing methods for more refined models and large trees. By re-analysing data from the early stages of the recent Ebola epidemic in Sierra Leone, we also found that ABC provides more realistic estimates than the likelihood-based methods, for some parameters. This work shows that the combination of ABC-based inference using many summary statistics and sophisticated machine learning methods able to perform variable selection is a promising approach to analyse large phylogenies and non-trivial models.

scholarly journals Approximate Bayesian Computation for Discrete Spaces

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 312
Author(s):  
Ilze A. Auzina ◽  
Jakub M. Tomczak
Keyword(s):  
Approximate Bayesian Computation ◽  
Likelihood Function ◽  
Real Life ◽  
Random Variables ◽  
Bayesian Computation ◽  
Inference Problem ◽  
Markov Kernel ◽  
Inference Problems ◽  
Binary Neural Network ◽  
Approximate Bayesian

Many real-life processes are black-box problems, i.e., the internal workings are inaccessible or a closed-form mathematical expression of the likelihood function cannot be defined. For continuous random variables, likelihood-free inference problems can be solved via Approximate Bayesian Computation (ABC). However, an optimal alternative for discrete random variables is yet to be formulated. Here, we aim to fill this research gap. We propose an adjusted population-based MCMC ABC method by re-defining the standard ABC parameters to discrete ones and by introducing a novel Markov kernel that is inspired by differential evolution. We first assess the proposed Markov kernel on a likelihood-based inference problem, namely discovering the underlying diseases based on a QMR-DTnetwork and, subsequently, the entire method on three likelihood-free inference problems: (i) the QMR-DT network with the unknown likelihood function, (ii) the learning binary neural network, and (iii) neural architecture search. The obtained results indicate the high potential of the proposed framework and the superiority of the new Markov kernel.

scholarly journals Probabilistic Updating of Structural Models for Damage Assessment Using Approximate Bayesian Computation

Sensors ◽  
2020 ◽  
Vol 20 (11) ◽  
pp. 3197 ◽  
Author(s):  
Zhouquan Feng ◽  
Yang Lin ◽  
Wenzan Wang ◽  
Xugang Hua ◽  
Zhengqing Chen
Keyword(s):  
Damage Assessment ◽  
Approximate Bayesian Computation ◽  
Model Updating ◽  
Likelihood Function ◽  
Probabilistic Approach ◽  
Model Parameters ◽  
Bayesian Computation ◽  
The Novel ◽  
Subset Simulation ◽  
Approximate Bayesian

A novel probabilistic approach for model updating based on approximate Bayesian computation with subset simulation (ABC-SubSim) is proposed for damage assessment of structures using modal data. The ABC-SubSim is a likelihood-free Bayesian approach in which the explicit expression of likelihood function is avoided and the posterior samples of model parameters are obtained using the technique of subset simulation. The novel contributions of this paper are on three fronts: one is the introduction of some new stopping criteria to find an appropriate tolerance level for the metric used in the ABC-SubSim; the second one is the employment of a hybrid optimization scheme to find finer optimal values for the model parameters; and the last one is the adoption of an iterative approach to determine the optimal weighting factors related to the residuals of modal frequency and mode shape in the metric. The effectiveness of this approach is demonstrated using three illustrative examples.

scholarly journals A dimension-reduced neural network-assisted approximate Bayesian computation for inverse heat conduction problems

2021 ◽  
Author(s):  
Yang Zeng
Keyword(s):  
Neural Network ◽  
Approximate Bayesian Computation ◽  
Bayesian Method ◽  
Likelihood Function ◽  
Summary Statistics ◽  
Inverse Heat Conduction ◽  
Intractable Likelihood ◽  
Inverse Heat Conduction Problems ◽  
Approximate Bayesian ◽  
Low Dimensional

Abstract Due to the flexibility and feasibility of addressing ill-posed problems, the Bayesian method has been widely used in inverse heat conduction problems (IHCPs). However, in the real science and engineering IHCPs, the likelihood function of the Bayesian method is commonly computationally expensive or analytically unavailable. In this study, in order to circumvent this intractable likelihood function, the approximate Bayesian computation (ABC) is expanded to the IHCPs. In ABC, the high dimensional observations in the intractable likelihood function are equalized by their low dimensional summary statistics. Thus, the performance of the ABC depends on the selection of summary statistics. In this study, a machine learning-based ABC (ML-ABC) is proposed to address the complicated selections of the summary statistics. The Auto-Encoder (AE) is a powerful Machine Learning (ML) framework which can compress the observations into very low dimensional summary statistics with little information loss. In addition, in order to accelerate the calculation of the proposed framework, another neural network (NN) is utilized to construct the mapping between the unknowns and the summary statistics. With this mapping, given arbitrary unknowns, the summary statistics can be obtained efficiently without solving the time-consuming forward problem with numerical method. Furthermore, an adaptive nested sampling method (ANSM) is developed to further improve the efficiency of sampling. The performance of the proposed method is demonstrated with two IHCP cases.

scholarly journals Choice of Summary Statistic Weights in Approximate Bayesian Computation

2011 ◽  
Vol 10 (1) ◽  
Author(s):  
Hsuan Jung ◽  
Paul Marjoram
Keyword(s):  
Genetic Algorithm ◽  
Population Genetics ◽  
Approximate Bayesian Computation ◽  
Fundamental Problem ◽  
Bayesian Computation ◽  
Summary Statistics ◽  
Summary Statistic ◽  
Improved Performance ◽  
Approximate Bayesian ◽  
Computation Analysis

In this paper, we develop a Genetic Algorithm that can address the fundamental problem of how one should weight the summary statistics included in an approximate Bayesian computation analysis built around an accept/reject algorithm, and how one might choose the tolerance for that analysis. We then demonstrate that using weighted statistics, and a well-chosen tolerance, in such an approximate Bayesian computation approach can result in improved performance, when compared to unweighted analyses, using one example drawn purely from statistics and two drawn from the estimation of population genetics parameters.

scholarly journals Choosing summary statistics by least angle regression for approximate Bayesian computation

2016 ◽  
Vol 43 (12) ◽  
pp. 2191-2202 ◽  
Author(s):  
Muhammad Faisal ◽  
Andreas Futschik ◽  
Ijaz Hussain ◽  
Mitwali Abd-el.Moemen
Keyword(s):  
Approximate Bayesian Computation ◽  
Bayesian Computation ◽  
Summary Statistics ◽  
Least Angle Regression ◽  
Approximate Bayesian

scholarly journals Component-wise Approximate Bayesian Computation via Gibbs-like steps

Biometrika ◽  
2020 ◽  
Author(s):  
Grégoire Clarté ◽  
Christian P Robert ◽  
Robin J Ryder ◽  
Julien Stoehr
Keyword(s):  
Markov Chain ◽  
Posterior Distribution ◽  
Approximate Bayesian Computation ◽  
Generative Models ◽  
Bayesian Computation ◽  
Summary Statistics ◽  
Posterior Distributions ◽  
Reduced Dimensions ◽  
Standard Solution ◽  
Approximate Bayesian

Abstract 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 Approximate Bayesian computation 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.

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