Approximate Bayesian Computation Techniques Research Articles

A Parameter Correction method of CFD based on the Approximate Bayesian Computation technique

Numerical simulation and modeling techniques are becoming the primary research tools for aerodynamic analysis and design. However, various uncertainties in physical modeling and numerical simulation seriously affect the credibility of Computational Fluid Dynamics (CFD) simulation results. Therefore, CFD models need to be adjusted and modified with consideration of uncertainties to improve the prediction accuracy and confidence level of CFD numerical simulations. This paper presents a parameter correction method of CFD for aerodynamic analysis by making full use of the advantages of the Approximate Bayesian Computation (ABC) technique in dealing with the analysis and inference of complex statistical models, in which the parameters of turbulence models for CFD are inferenced. The proposed parameter correction method is applied to the aerodynamic prediction of the NACA0012 airfoil. The results show the feasibility and effectiveness of the proposed approach in improving CFD prediction accuracy.

Data-driven approach for post-earthquake condition and reliability assessment with approximate Bayesian computation

Estimating the reliability of civil structures after earthquake events is a challenging problem because the uncertainties of random variables are usually unknown. This paper presents a data-driven approach for post-earthquake reliability assessments of civil structures. The measured vibration data are used to update the probability density functions of random variables. Two approximate Bayesian computation techniques are introduced to generate the posterior probability density functions of structural parameters. One is the likelihood-free Bayesian inference method, in which the weighted sum of squared errors term in the likelihood function is approximated by a Gaussian process model and the posterior probability density functions is generated using the Metropolis–Hastings algorithm. The second method is the variational inference approach, in which the posterior probability density function is approximated by a Gaussian mixture model. Both the proposed techniques can provide an approximation of the posterior probability density functions of the unknown parameters. Furthermore, the updated probability density functions are applied for reliability assessments. Numerical studies on a steel frame structure and a reinforced concrete structure are conducted to verify the accuracy and efficiency of the proposed techniques. Results show that the posterior probability density functions of unknown structural parameters can be updated and the reliability of the structure and components can be estimated.

Application of Approximate Bayesian Computational technique to characterize the breakthrough of paracetamol adsorption in fixed bed column

Drugs in general have been responsible for water contamination when there is no adequate treatment. An alternative for decontamination is the use of a fixed bed to carry out adsorption and thus prevent such contaminants from being released into the environment. This work aims to evaluate different models (Clark, Yan, Yoon-Nelson, Gompertz and Log-Gompertz) to simulate the breakthrough curve of the adsorption of the drug paracetamol on activated carbon under different operational conditions. Parameter estimates and model selection were performed using the Approximate Bayesian Computation (ABC) technique, in which it was found that the Yan model was the one that best represented the behavior of the evaluated breakthrough curve.

Back to the brink: Phylogeography and demographic history of the endangered Torreya jackii

AbstractBoth paleoclimatic change and anthropogenic habitat destruction can have adverse effects on species demography and, in turn, could lead a species towards being endangered and rare. Understanding the relative importance of these natural and anthropogenic factors driving species endangerment and rarity is thus crucial for effective conservation planning but remains elusive. Here, we examine the phylogeography and demographic history of an endangered conifer species in China, Torreya jackii Chun, and assess the relative importance of natural and anthropogenic factors that might have put the species in its endangered state. We collected tissue samples from all the 13 extant wild populations, and analyzed the genetic variation using eight nuclear microsatellites and four chloroplast and one mitochondrial DNA fragments. We found low genetic and nucleotide diversities, which could explain the absence of spatial and phylogeographic structure. Using a hierarchical approximate Bayesian computation technique, we identified the demographic scenario that best fits the genetic data and found that effective population size was low at least 200 000 years ago but expanded after the last glacial maximum (LGM). The paleoclimatic niche model revealed a profound effect of precipitation on the distribution of T. jackii and predicted that the current distribution areas were suitable during the LGM. Despite the post‐LGM expansion, the best‐supported scenario showed a dramatic population collapse during the past 300 years, when anthropogenic disturbances also increased dramatically. Overall, our study sheds light on how historical factors and human impacts jointly threaten the persistence of a species, and these aspects should be duly considered in species conservation planning.

Occurrence rates of planets orbiting M Stars: applying ABC to Kepler DR25, Gaia DR2, and 2MASS data

ABSTRACT We present robust planet occurrence rates for Kepler planet candidates around M stars for planet radii Rp = 0.5–4 R⊕ and orbital periods P = 0.5–256 d using the approximate Bayesian computation technique. This work incorporates the final Kepler DR25 planet candidate catalogue and data products and augments them with updated stellar properties using Gaia DR2 and 2MASS point source catalogue. We apply a set of selection criteria to select a sample of 1746 Kepler M dwarf targets that host 89 associated planet candidates. These early-type M dwarfs and late K dwarfs were selected from cross-referenced targets using several photometric quality flags from Gaia DR2 and colour–magnitude cuts using 2MASS magnitudes. We estimate a habitable zone occurrence rate of $f_{\textrm {M,HZ}} = 0.33^{+0.10}_{-0.12}$ for planets with 0.75–1.5 R⊕ size. We caution that occurrence rate estimates for Kepler M stars are sensitive to the choice of prior due to the small sample of target stars and planet candidates. For example, we find an occurrence rate of $4.2^{+0.6}_{-0.6}$ or $8.4^{+1.2}_{-1.1}$ planets per M dwarf (integrating over Rp = 0.5–4 R⊕ and P = 0.5–256 d) for our two choices of prior. These occurrence rates are greater than those for FGK dwarf target when compared at the same range of orbital periods, but similar to occurrence rates when computed as a function of equivalent stellar insolation. Combining our result with recent studies of exoplanet architectures indicates that most, and potentially all, early-type M dwarfs harbour planetary systems.

Likelihood-free approximate Gibbs sampling

Likelihood-free methods such as approximate Bayesian computation (ABC) have extended the reach of statistical inference to problems with computationally intractable likelihoods. Such approaches perform well for small-to-moderate dimensional problems, but suffer a curse of dimensionality in the number of model parameters. We introduce a likelihood-free approximate Gibbs sampler that naturally circumvents the dimensionality issue by focusing on lower-dimensional conditional distributions. These distributions are estimated by flexible regression models either before the sampler is run, or adaptively during sampler implementation. As a result, and in comparison to Metropolis-Hastings based approaches, we are able to fit substantially more challenging statistical models than would otherwise be possible. We demonstrate the sampler's performance via two simulated examples, and a real analysis of Airbnb rental prices using a intractable high-dimensional multivariate non-linear state space model containing 13,140 parameters, which presents a real challenge to standard ABC techniques.

Adjustment for exploratory cut-off selection in randomized clinical trials with survival endpoint.

Defining the target population based on predictive biomarkers plays an important role during clinical development. After establishing a relationship between a biomarker candidate and response to treatment in exploratory phases, a subsequent confirmatory trial ideally involves only subjects with high potential of benefiting from the new compound. In order to identify those subjects in case of a continuous biomarker, a cut-off is needed. Usually, a cut-off is chosen that resulted in a subgroup with a large observed treatment effect in an exploratory trial. However, such a data-driven selection may lead to overoptimistic expectations for the subsequent confirmatory trial. Treatment effect estimates, probability of success, and posterior probabilities are useful measures for deciding whether or not to conduct a confirmatory trial enrolling the biomarker-defined population. These measures need to be adjusted for selection bias. We extend previously introduced Approximate Bayesian Computation techniques for adjustment of subgroup selection bias to a time-to-event setting with cut-off selection. Challenges in this setting are that treatment effects become time-dependent and that subsets are defined by the biomarker distribution. Simulation studies show that the proposed method provides adjusted statistical measures which are superior to naïve Maximum Likelihood estimators as well as simple shrinkage estimators.

AKL-ABC: An Automatic Approximate Bayesian Computation Approach Based on Kernel Learning

Bayesian statistical inference under unknown or hard to asses likelihood functions is a very challenging task. Currently, approximate Bayesian computation (ABC) techniques have emerged as a widely used set of likelihood-free methods. A vast number of ABC-based approaches have appeared in the literature; however, they all share a hard dependence on free parameters selection, demanding expensive tuning procedures. In this paper, we introduce an automatic kernel learning-based ABC approach, termed AKL-ABC, to automatically compute posterior estimations from a weighting-based inference. To reach this goal, we propose a kernel learning stage to code similarities between simulation and parameter spaces using a centered kernel alignment (CKA) that is automated via an Information theoretic learning approach. Besides, a local neighborhood selection (LNS) algorithm is used to highlight local dependencies over simulations relying on graph theory. Attained results on synthetic and real-world datasets show our approach is a quite competitive method compared to other non-automatic state-of-the-art ABC techniques.

The Quetzal Coalescence template library: A C++ programmers resource for integrating distributional, demographic and coalescent models.

Genetic samples can be used to understand and predict the behaviour of species living in a fragmented and temporally changing environment. In this regard, models of coalescence conditioned to an environment through an explicit modelling of population growth and migration have been developed in recent years, and simulators implementing these models have been developed, enabling biologists to estimate parameters of interest with Approximate Bayesian Computation techniques. However, model choice remains limited, and developing new coalescence simulators is extremely time consuming because code re-use is limited. We present Quetzal, a C++ library composed of re-usable components, which is sufficiently general to efficiently implement a wide range of spatially explicit coalescence-based environmental models of population genetics and to embed the simulation in an Approximate Bayesian Computation framework. Quetzal is not a simulation program, but a toolbox for programming simulators aimed at the community of scientific coders and research software engineers in molecular ecology and phylogeography. This new code resource is open-source and available at https://becheler.github.io/pages/quetzal.html along with other documentation resources.

Approximate Bayesian inference for discretely observed continuous-time multi-state models.

Inference for continuous time multi-state models presents considerable computational difficulties when the process is only observed at discrete time points with no additional information about the state transitions. In fact, for general multi-state Markov model, evaluation of the likelihood function is possible only via intensive numerical approximations. Moreover, in real applications, transitions between states may depend on the time since entry into the current state, and semi-Markov models, where the likelihood function is not available in closed form, should be fitted to the data. Approximate Bayesian Computation (ABC) methods, which make use only of comparisons between simulated and observed summary statistics, represent a solution to intractable likelihood problems and provide alternative algorithms when the likelihood calculation is computationally too costly. In this article we investigate the potentiality of ABC techniques for multi-state models both to obtain the posterior distributions of the model parameters and to compare Markov and semi-Markov models. In addition, we will also exploit ABC methods to estimate and compare hidden Markov and semi-Markov models when observed states are subject to classification errors. We illustrate the performance of the ABC methodology both with simulated data and with a real data example.

Dissociating visuo-spatial and verbal working memory: It\u2019s all in the features

Echoing many of the themes of the seminal work of Atkinson and Shiffrin (The Psychology of Learning and Motivation, 2; 89–195, 1968), this paper uses the feature model (Nairne, Memory & Cognition, 16, 343–352, 1988; Nairne, Memory & Cognition, 18; 251–269, 1990; Neath & Nairne, Psychonomic Bulletin & Review, 2; 429–441, 1995) to account for performance in working-memory tasks. The Brooks verbal and visuo-spatial matrix tasks were performed alone, with articulatory suppression, or with a spatial suppression task; the results produced the expected dissociation. We used approximate Bayesian computation techniques to fit the feature model to the data and showed that the similarity-based interference process implemented in the model accounted for the data patterns well. We then fit the model to data from Guérard and Tremblay (2008, Journal of Experimental Psychology: Learning, Memory, and Cognition, 34, 556–569); the latter study produced a double dissociation while calling upon more typical order reconstruction tasks. Again, the model performed well. The findings show that a double dissociation can be modelled without appealing to separate systems for verbal and visuo-spatial processing. The latter findings are significant as the feature model had not been used to model this type of dissociation before; importantly, this is also the first time the model is quantitatively fit to data. For the demonstration provided here, modularity was unnecessary if two assumptions were made: (1) the main difference between spatial and verbal working-memory tasks is the features that are encoded; (2) secondary tasks selectively interfere with primary tasks to the extent that both tasks involve similar features. It is argued that a feature-based view is more parsimonious (see Morey, 2018, Psychological Bulletin, 144, 849–883) and offers flexibility in accounting for multiple benchmark effects in the field.

Calibration of forest 137Cs cycling model ”FoRothCs” via approximate Bayesian computation based on 6-year observations from plantation forests in Fukushima

Predicting the environmental fate of 137Cs in forest ecosystems along with the concentrations of 137Cs in tree parts are important for the managements of radioactively contaminated forests. In this study, we calibrate the Forest RothC and Cs model (FoRothCs), a forest ecosystem 137Cs dynamics model, using observational data obtained over six years from four forest sites with different levels of 137Cs contamination from Fukushima Prefecture. To this end, we applied an approximate Bayesian computation (ABC) technique based on the observed 137Cs concentrations (Bq kg−1) of five compartments (leaf, branch, stem, litter, and soil) in a Japanese cedar plantation. The environmental decay (increment) constants of the five compartments were used as the summary statistics (i.e., the metric for model performance) to infer the five parameters related to 137Cs transfer processes in FoRothCs. The ABC technique successfully reconciled the model outputs with the observed trends in 137Cs concentrations at all sites during the study period. Furthermore, the estimated parameters are in agreement with the literature values (e.g., the root uptake rates of 137Cs). Our study demonstrates that model calibration with ABC based on the trends in 137Cs concentrations of multi compartments is useful for reducing the prediction uncertainty of 137Cs dynamics in forest ecosystems.

Inference-based assessment of parameter identifiability in nonlinear biological models

As systems approaches to the development of biological models become more mature, attention is increasingly focusing on the problem of inferring parameter values within those models from experimental data. However, particularly for nonlinear models, it is not obvious, either from inspection of the model or from the experimental data, that the inverse problem of parameter fitting will have a unique solution, or even a non-unique solution that constrains the parameters to lie within a plausible physiological range. Where parameters cannot be constrained they are termed 'unidentifiable'. We focus on gaining insight into the causes of unidentifiability using inference-based methods, and compare a recently developed measure-theoretic approach to inverse sensitivity analysis to the popular Markov chain Monte Carlo and approximate Bayesian computation techniques for Bayesian inference. All three approaches map the uncertainty in quantities of interest in the output space to the probability of sets of parameters in the input space. The geometry of these sets demonstrates how unidentifiability can be caused by parameter compensation and provides an intuitive approach to inference-based experimental design.

Approximate Bayesian computation techniques for optical characterization of nanoparticle clusters.

Characterization of nanoparticle aggregates from observed scattered light leads to a highly complex inverse problem. Even the forward model is so complex that it prohibits the use of classical likelihood-based inference methods. In this study, we compare four so-called likelihood-free methods based on approximate Bayesian computation (ABC) that requires only numeric simulation of the forward model without the need of evaluating a likelihood. In particular, rejection, Markov chain Monte Carlo, population Monte Carlo, and adaptive population Monte Carlo (APMC) are compared in terms of accuracy. In the current model, we assume that the nanoparticle aggregates are mutually well separated and made up of particles of same size. Filippov's particle-cluster algorithm is used to generate aggregates, and discrete dipole approximation is used to estimate scattering behavior. It is found that the APMC algorithm is superior to others in terms of time and acceptance rates, although all algorithms produce similar posterior distributions. Using ABC techniques and utilizing unpolarized light experiments at 266nm wavelength, characterization of soot aggregates is performed with less than 2nm deviation in nanoparticle radius and 3-4 deviation in number of nanoparticles forming the monodisperse aggregates. Promising results are also observed for the polydisperse aggregate with log-normal particle size distribution.

Simulation-based adjustment after exploratory biomarker subgroup selection in phase II.

As part of the evaluation of phase II trials, it is common practice to perform exploratory subgroup analyses with the aim of identifying patient populations with a beneficial treatment effect. When investigating targeted therapies, these subgroups are typically defined by biomarkers. Promising results may lead to the decision to select the respective subgroup as the target population for a subsequent phase III trial. However, a selection based on a large observed treatment effect may potentially induce an upwards-bias leading to over-optimistic expectations on the success probability of the phase III trial. We describe how Approximate Bayesian Computation techniques can be used to derive a simulation-based bias adjustment method in this situation. Recommendations for the implementation of the approach are given. Simulation studies show that the proposed method reduces bias substantially compared with the maximum likelihood estimator. The procedure is illustrated with data from an oncology trial. Copyright © 2017 John Wiley & Sons, Ltd.

Bayesian estimation of agent-based models

We consider Bayesian inference techniques for agent-based (AB) models, as an alternative to simulated minimum distance (SMD). Three computationally heavy steps are involved: (i) simulating the model, (ii) estimating the likelihood and (iii) sampling from the posterior distribution of the parameters. Computational complexity of AB models implies that efficient techniques have to be used with respect to points (ii) and (iii), possibly involving approximations. We first discuss non-parametric (kernel density) estimation of the likelihood, coupled with Markov chain Monte Carlo sampling schemes. We then turn to parametric approximations of the likelihood, which can be derived by observing the distribution of the simulation outcomes around the statistical equilibria, or by assuming a specific form for the distribution of external deviations in the data. Finally, we introduce Approximate Bayesian Computation techniques for likelihood-free estimation. These allow embedding SMD methods in a Bayesian framework, and are particularly suited when robust estimation is needed. These techniques are first tested in a simple price discovery model with one parameter, and then employed to estimate the behavioural macroeconomic model of De Grauwe (2012), with nine unknown parameters.

Bayesian nonparametric forecasting of monotonic functional time series

We propose a Bayesian nonparametric approach to modelling and predicting a class of functional time series with application to energy markets, based on fully observed, noise-free functional data. Traders in such contexts conceive profitable strategies if they can anticipate the impact of their bidding actions on the aggregate demand and supply curves, which in turn need to be predicted reliably. Here we propose a simple Bayesian nonparametric method for predicting such curves, which take the form of monotonic bounded step functions. We borrow ideas from population genetics by defining a class of interacting particle systems to model the functional trajectory, and develop an implementation strategy which uses ideas from Markov chain Monte Carlo and approximate Bayesian computation techniques and allows to circumvent the intractability of the likelihood. Our approach shows great adaptation to the degree of smoothness of the curves and the volatility of the functional series, proves to be robust to an increase of the forecast horizon and yields an uncertainty quantification for the functional forecasts. We illustrate the model and discuss its performance with simulated datasets and on real data relative to the Italian natural gas market.

Reliable ABC model choice via random forests.

Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior probabilities may be poorly evaluated by standard ABC techniques. We propose a novel approach based on a machine learning tool named random forests (RF) to conduct selection among the highly complex models covered by ABC algorithms. We thus modify the way Bayesian model selection is both understood and operated, in that we rephrase the inferential goal as a classification problem, first predicting the model that best fits the data with RF and postponing the approximation of the posterior probability of the selected model for a second stage also relying on RF. Compared with earlier implementations of ABC model choice, the ABC RF approach offers several potential improvements: (i) it often has a larger discriminative power among the competing models, (ii) it is more robust against the number and choice of statistics summarizing the data, (iii) the computing effort is drastically reduced (with a gain in computation efficiency of at least 50) and (iv) it includes an approximation of the posterior probability of the selected model. The call to RF will undoubtedly extend the range of size of datasets and complexity of models that ABC can handle. We illustrate the power of this novel methodology by analyzing controlled experiments as well as genuine population genetics datasets. The proposed methodology is implemented in the R package abcrf available on the CRAN. jean-michel.marin@umontpellier.fr Supplementary data are available at Bioinformatics online.

Approximate Bayesian computation for forward modeling in cosmology

Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In many practical situations, the likelihood function may however be unavailable or intractable due to non-gaussian errors, non-linear measurements processes, or complex data formats such as catalogs and maps. In these cases, the simulation of mock data sets can often be made through forward modeling. We discuss how Approximate Bayesian Computation (ABC) can be used in these cases to derive an approximation to the posterior constraints using simulated data sets. This technique relies on the sampling of the parameter set, a distance metric to quantify the difference between the observation and the simulations and summary statistics to compress the information in the data. We first review the principles of ABC and discuss its implementation using a Population Monte-Carlo (PMC) algorithm and the Mahalanobis distance metric. We test the performance of the implementation using a Gaussian toy model. We then apply the ABC technique to the practical case of the calibration of image simulations for wide field cosmological surveys. We find that the ABC analysis is able to provide reliable parameter constraints for this problem and is therefore a promising technique for other applications in cosmology and astrophysics. Our implementation of the ABC PMC method is made available via a public code release.

Scalable inference for Markov processes with intractable likelihoods

Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo (MCMC) techniques can lead to exact inference in such models but in practice can suffer performance issues including long burn-in periods and poor mixing. On the other hand approximate Bayesian computation techniques can allow rapid exploration of a large parameter space but yield only approximate posterior distributions. Here we consider the combined use of approximate Bayesian computation and MCMC techniques for improved computational efficiency while retaining exact inference on parallel hardware.