Approximate Bayesian Computation for Discrete Spaces

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.

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

Sensors ◽

10.3390/s20113197 ◽

2020 ◽

Vol 20 (11) ◽

pp. 3197 ◽

Cited By ~ 1

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.

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Statistical Inference From Stem Cell Barcoding Data Using Adaptive Approximate Bayesian Computation

10.21203/rs.3.rs-187743/v1 ◽

2021 ◽

Author(s):

Siyi Chen ◽

Katherine Y. King ◽

Marek Kimmel

Keyword(s):

Stem Cell ◽

Dna Sequences ◽

Approximate Bayesian Computation ◽

Sequential Monte Carlo ◽

Real Life ◽

Lineage Tracing ◽

Bayesian Computation ◽

Multinomial Model ◽

Hematopoietic Stem ◽

Approximate Bayesian

Abstract Background: Barcodes that can be supplied to cells by transduction of a library of unique DNA sequences allow identification of heterogeneity in cell populations and lineage tracing applications. Estimation of the number of hematopoietic stem cell (HSC) clones is important since it also allows to approximate the number of hematopoietic stem cells from which the circulating blood cells descend. This problem is similar to the species problem, well-known to ecologists. However, an additional ”degree of freedom” exists, since different HSC generally give rise to clones with different growth rates. This adds credibility to sampling models based on different versions of Dirichlet-multinomial distributions. Results: We developed a truncated population approximate Bayesian computation (ABC) algorithm which is derived from sequential Monte Carlo ABC (SMC-ABC) and applied the method to the symmetric Dirichlet-multinomial model proposed by Zhang et al. (2005) and asymmetric Dirichlet-multinomial model we proposed. Methodology was tested using simulated and real-life data. Conclusions: Results suggest that flexibility of the asymmetric Dirichlet-multinomial helps to obtain insight into heterogeneity of proliferating cell systems such as HSC. Estimates based on experimental data approach the correct count of murine HSC.

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Bridging the gap between GLUE and formal statistical approaches: approximate Bayesian computation

Hydrology and Earth System Sciences ◽

10.5194/hess-17-4831-2013 ◽

2013 ◽

Vol 17 (12) ◽

pp. 4831-4850 ◽

Cited By ~ 34

Author(s):

M. Sadegh ◽

J. A. Vrugt

Keyword(s):

Approximate Bayesian Computation ◽

Likelihood Function ◽

Model Simulation ◽

The United States ◽

Bayesian Computation ◽

Calibration Data ◽

Data Set ◽

Simulation Techniques ◽

Approximate Bayesian ◽

Generalized Likelihood Uncertainty Estimation

Abstract. In recent years, a strong debate has emerged in the hydrologic literature regarding how to properly treat nontraditional error residual distributions and quantify parameter and predictive uncertainty. Particularly, there is strong disagreement whether such uncertainty framework should have its roots within a proper statistical (Bayesian) context using Markov chain Monte Carlo (MCMC) simulation techniques, or whether such a framework should be based on a quite different philosophy and implement informal likelihood functions and simplistic search methods to summarize parameter and predictive distributions. This paper is a follow-up of our previous work published in Vrugt and Sadegh (2013) and demonstrates that approximate Bayesian computation (ABC) bridges the gap between formal and informal statistical model–data fitting approaches. The ABC methodology has recently emerged in the fields of biology and population genetics and relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics that measure the distance of each model simulation to the data. This paper further studies the theoretical and numerical equivalence of formal and informal Bayesian approaches using discharge and forcing data from different watersheds in the United States, in particular generalized likelihood uncertainty estimation (GLUE). We demonstrate that the limits of acceptability approach of GLUE is a special variant of ABC if each discharge observation of the calibration data set is used as a summary diagnostic.

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

10.1101/050211 ◽

2016 ◽

Cited By ~ 1

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.

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Approximate Bayesian Computation Algorithms for Estimating Network Model Parameters

10.1101/106450 ◽

2017 ◽

Author(s):

Ye Zheng ◽

Stéphane Aris-Brosou

Keyword(s):

Monte Carlo ◽

Approximate Bayesian Computation ◽

Sequential Monte Carlo ◽

Likelihood Function ◽

Model Parameters ◽

Human Populations ◽

Bayesian Computation ◽

Transmission Networks ◽

General Network ◽

Approximate Bayesian

AbstractStudies on Approximate Bayesian Computation (ABC) replacing the intractable likelihood function in evaluation of the posterior distribution have been developed for several years. However, their field of application has to date essentially been limited to inference in population genetics. Here, we propose to extend this approach to estimating the structure of transmission networks of viruses in human populations. In particular, we are interested in estimating the transmission parameters under four very general network structures: random, Watts-Strogatz, Barabasi-Albert and an extension that incorporates aging. Estimation was evaluated under three approaches, based on ABC, ABC-Markov chain Monte Carlo (ABC-MCMC) and ABC-Sequential Monte Carlo (ABC-SMC) samplers. We show that ABC-SMC samplers outperform both ABC and ABC-MCMC, achieving high accuracy and low variance in simulations. This approach paves the way to estimating parameters of real transmission networks of transmissible diseases.

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Approximate Bayesian Computation in hydrologic modeling: equifinality of formal and informal approaches

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-10-4739-2013 ◽

2013 ◽

Vol 10 (4) ◽

pp. 4739-4797 ◽

Cited By ~ 6

Author(s):

M. Sadegh ◽

J. A. Vrugt

Keyword(s):

Approximate Bayesian Computation ◽

Likelihood Function ◽

Model Simulation ◽

The United States ◽

Bayesian Computation ◽

Calibration Data ◽

Bayesian Approaches ◽

Data Set ◽

Using Data ◽

Approximate Bayesian

Abstract. In recent years, a strong debate has emerged in the hydrologic literature how to properly treat non-traditional error residual distributions and quantify parameter and predictive uncertainty. Particularly, there is strong disagreement whether such uncertainty framework should have its roots within a proper statistical (Bayesian) context using Markov chain Monte Carlo (MCMC) simulation techniques, or whether such a framework should be based on a quite different philosophy and implement informal likelihood functions and simplistic search methods to summarize parameter and predictive distributions. In this paper we introduce an alternative framework, called Approximate Bayesian Computation (ABC) that summarizes the differing viewpoints of formal and informal Bayesian approaches. This methodology has recently emerged in the fields of biology and population genetics and relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics that measure the distance of each model simulation to the data. This paper is a follow up of the recent publication of Nott et al. (2012) and further studies the theoretical and numerical equivalence of formal (DREAM) and informal (GLUE) Bayesian approaches using data from different watersheds in the United States. We demonstrate that the limits of acceptability approach of GLUE is a special variant of ABC in which each discharge observation of the calibration data set is used as a summary diagnostic.

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Gaussian process enhanced semi-automatic approximate Bayesian computation: parameter inference in a stochastic differential equation system for chemotaxis

Journal of Computational Physics ◽

10.1016/j.jcp.2020.109999 ◽

2020 ◽

pp. 109999

Author(s):

Agnieszka Borowska ◽

Diana Giurghita ◽

Dirk Husmeier

Keyword(s):

Differential Equation ◽

Stochastic Differential Equation ◽

Gaussian Process ◽

Approximate Bayesian Computation ◽

Equation System ◽

Bayesian Computation ◽

Differential Equation System ◽

Parameter Inference ◽

Approximate Bayesian

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Weighted approximate Bayesian computation via Sanov’s theorem

Computational Statistics ◽

10.1007/s00180-021-01093-4 ◽

2021 ◽

Author(s):

Cecilia Viscardi ◽

Michele Boreale ◽

Fabio Corradi

Keyword(s):

Large Deviations ◽

Posterior Distribution ◽

Approximate Bayesian Computation ◽

Bayesian Computation ◽

Information Theoretic ◽

Discrete Random Variables ◽

Positive Weights ◽

Approximate Bayesian ◽

Information Theoretic Method ◽

Computational Resources

AbstractWe consider the problem of sample degeneracy in Approximate Bayesian Computation. It arises when proposed values of the parameters, once given as input to the generative model, rarely lead to simulations resembling the observed data and are hence discarded. Such “poor” parameter proposals do not contribute at all to the representation of the parameter’s posterior distribution. This leads to a very large number of required simulations and/or a waste of computational resources, as well as to distortions in the computed posterior distribution. To mitigate this problem, we propose an algorithm, referred to as the Large Deviations Weighted Approximate Bayesian Computation algorithm, where, via Sanov’s Theorem, strictly positive weights are computed for all proposed parameters, thus avoiding the rejection step altogether. In order to derive a computable asymptotic approximation from Sanov’s result, we adopt the information theoretic “method of types” formulation of the method of Large Deviations, thus restricting our attention to models for i.i.d. discrete random variables. Finally, we experimentally evaluate our method through a proof-of-concept implementation.

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