Approximate Bayesian Computation Algorithm Research Articles

Using Rate Transient Analysis and Bayesian Algorithms for Reservoir Characterization in Unconventional Gas Wells during Linear Flow

Summary The main objective of this work is to improve robust, repeatable interpretation of reservoir characteristics using rate transient analysis (RTA). This is to generate probabilistic credible intervals for key reservoir and completion variables. This resulting data-driven algorithm was applied to production data from both synthetic and actual case histories. Synthetic production data from a multistage, hydraulically fractured horizontal completion in a reservoir modeled after the Marcellus Shale reservoir were generated using a reservoir model. The synthetic production data were analyzed using a combination of RTA and Bayesian techniques. First, the traditional log-log plot was produced to identify the linear flow production regime. Using the linear flow production data and traditional RTA equations, Bayesian inversion was carried out using two distinct Bayesian methods. The “rjags” and “EasyABC” packages in the open-source statistical software R were used for the traditional and approximate inversion, respectively. Model priors were based on (1) information available about the Marcellus Shale from technical literature and (2) results from a hydraulic fracturing forward model. Posterior distributions and credible intervals were produced for the fracture length, matrix permeability, and skin factor. These credible intervals were then compared with true reservoir and hydraulic fracturing data. The methodology was also repeated for an actual case in the Barnett shale. The most substantial finding was that for nearly all the investigated cases—including complicated scenarios (such as including finite fracture conductivity, fracturing fluid flowback, and heterogeneity in fracture length in the reservoir/hydraulic fracturing forward model)—the combined RTA-Bayesian model provided a 95% credible interval that encompassed the true values of the reservoir/hydraulic fracture parameters. We also found that the choice of the prior distribution did not affect the posterior distribution/credible interval in a significant manner as long as it was moderately concentrated and consistent with engineering science. Also, a comparison of the approximate Bayesian computation (ABC) and the traditional Bayesian algorithms showed that the ABC algorithm reduced computational time by at least an order of magnitude with minimal loss in accuracy. In addition, the production history used, the number of iterations, and the tolerance of fitting in the ABC analysis had a minimal impact on the posterior distribution after an optimal point, which were determined to be at least 1-year production history, 10,000 iterations, and 0.001, respectively. In summary, the RTA-Bayesian production analysis method was implemented using relatively user-friendly computational platforms [R and Excel® (Microsoft Corporation, Redmond, Washington, USA)]. This methodology provided reasonable characterization of all key variables such as matrix permeability, fracture length, and skin when compared to results obtained from analytical methods. This probabilistic characterization has the potential to enable better understanding of well performance ranges expected from shale gas wells. The methodology described here can also be generalized to shale oil systems during linear flow.

Application of Distributed Agent-based Modeling to Investigate Opioid Use Outcomes in Justice Involved Populations.

Criminal justice involved (CJI) individuals with a history of opioid use disorder (OUD) are at high risk of overdose and death in the weeks following release from jail. We developed the Justice-Community Circulation Model (JCCM) to investigate OUD/CJI dynamics post-release and the effects of interventions on overdose deaths. The JCCM uses a synthetic agent-based model population of approximately 150,000 unique individuals that is generated using demographic information collected from multiple Chicago-area studies and data sets. We use a high-performance computing (HPC) workflow to implement a sequential approximate Bayesian computation algorithm for calibrating the JCCM. The calibration results in the simulated joint posterior distribution of the JCCM input parameters. The calibrated model is used to investigate the effects of a naloxone intervention for a mass jail release. The simulation results show the degree to which a targeted intervention focusing on recently released jail inmates can help reduce the risk of death from opioid overdose.

Inference of brain networks with approximate Bayesian computation – assessing face validity with an example application in Parkinsonism

This paper describes and validates a novel framework using the Approximate Bayesian Computation (ABC) algorithm for parameter estimation and model selection in models of mesoscale brain network activity. We provide a proof of principle, first pass validation of this framework using a set of neural mass models of the cortico-basal ganglia thalamic circuit inverted upon spectral features from experimental, in vivo recordings. This optimization scheme relaxes an assumption of fixed-form posteriors (i.e. the Laplace approximation) taken in previous approaches to inverse modelling of spectral features. This enables the exploration of model dynamics beyond that approximated from local linearity assumptions and so fit to explicit, numerical solutions of the underlying non-linear system of equations. In this first paper, we establish a face validation of the optimization procedures in terms of: (i) the ability to approximate posterior densities over parameters that are plausible given the known causes of the data; (ii) the ability of the model comparison procedures to yield posterior model probabilities that can identify the model structure known to generate the data; and (iii) the robustness of these procedures to local minima in the face of different starting conditions. Finally, as an illustrative application we show (iv) that model comparison can yield plausible conclusions given the known neurobiology of the cortico-basal ganglia-thalamic circuit in Parkinsonism. These results lay the groundwork for future studies utilizing highly nonlinear or brittle models that can explain time dependant dynamics, such as oscillatory bursts, in terms of the underlying neural circuits.

Variable Selection with ABC Bayesian Forests

AbstractFew problems in statistics are as perplexing as variable selection in the presence of very many redundant covariates. The variable selection problem is most familiar in parametric environments such as the linear model or additive variants thereof. In this work, we abandon the linear model framework, which can be quite detrimental when the covariates impact the outcome in a non-linear way, and turn to tree-based methods for variable selection. Such variable screening is traditionally done by pruning down large trees or by ranking variables based on some importance measure. Despite heavily used in practice, these ad hoc selection rules are not yet well understood from a theoretical point of view. In this work, we devise a Bayesian tree-based probabilistic method and show that it is consistent for variable selection when the regression surface is a smooth mix of p > n covariates. These results are the first model selection consistency results for Bayesian forest priors. Probabilistic assessment of variable importance is made feasible by a spike-and-slab wrapper around sum-of-trees priors. Sampling from posterior distributions over trees is inherently very difficult. As an alternative to Markov Chain Monte Carlo (MCMC), we propose approximate Bayesian computation (ABC) Bayesian forests, a new ABC sampling method based on data-splitting that achieves higher ABC acceptance rate. We show that the method is robust and successful at finding variables with high marginal inclusion probabilities. Our ABC algorithm provides a new avenue towards approximating the median probability model in non-parametric setups where the marginal likelihood is intractable.

Weighted approximate Bayesian computation via Sanov\u2019s theorem

We 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.

Complex genetic admixture histories reconstructed with Approximate Bayesian Computation.

Admixture is a fundamental evolutionary process that has influenced genetic patterns in numerous species. Maximum‐likelihood approaches based on allele frequencies and linkage‐disequilibrium have been extensively used to infer admixture processes from genome‐wide data sets, mostly in human populations. Nevertheless, complex admixture histories, beyond one or two pulses of admixture, remain methodologically challenging to reconstruct. We developed an Approximate Bayesian Computation (ABC) framework to reconstruct highly complex admixture histories from independent genetic markers. We built the software package methis to simulate independent SNPs or microsatellites in a two‐way admixed population for scenarios with multiple admixture pulses, monotonically decreasing or increasing recurring admixture, or combinations of these scenarios. methis allows users to draw model‐parameter values from prior distributions set by the user, and, for each simulation, methis can calculate numerous summary statistics describing genetic diversity patterns and moments of the distribution of individual admixture fractions. We coupled methis with existing machine‐learning ABC algorithms and investigated the admixture history of admixed populations. Results showed that random forest ABC scenario‐choice could accurately distinguish among most complex admixture scenarios, and errors were mainly found in regions of the parameter space where scenarios were highly nested, and, thus, biologically similar. We focused on African American and Barbadian populations as two study‐cases. We found that neural network ABC posterior parameter estimation was accurate and reasonably conservative under complex admixture scenarios. For both admixed populations, we found that monotonically decreasing contributions over time, from Europe and Africa, explained the observed data more accurately than multiple admixture pulses. This approach will allow for reconstructing detailed admixture histories when maximum‐likelihood methods are intractable.

ABCpy: A High-Performance Computing Perspective to Approximate Bayesian Computation

ABCpy is a highly modular scientific library for Approximate Bayesian Computation (ABC) written in Python. The main contribution of this paper is to document a software engineering effort that enables domain scientists to easily apply ABC to their research without being ABC experts; using ABCpy they can easily run large parallel simulations without much knowledge about parallelization. Further, ABCpy enables ABC experts to easily develop new inference schemes and evaluate them in a standardized environment and to extend the library with new algorithms. These benefits come mainly from the modularity of ABCpy. We give an overview of the design of ABCpy and provide a performance evaluation concentrating on parallelization. This points us towards the inherent imbalance in some of the ABC algorithms. We develop a dynamic scheduling MPI implementation to mitigate this issue and evaluate the various ABC algorithms according to their adaptability towards high-performance computing.

Analysis of Coronal Mass Ejection Flux Rope Signatures Using 3DCORE and Approximate Bayesian Computation

Abstract We present a major update to the 3D coronal rope ejection (3DCORE) technique for modeling coronal mass ejection flux ropes in conjunction with an approximate Bayesian computation (ABC) algorithm that is used for fitting the model to in situ magnetic field measurements. The model assumes an empirically motivated torus-like flux rope structure that expands self-similarly within the heliosphere, is influenced by a simplified interaction with the solar wind environment, and carries along an embedded analytical magnetic field. The improved 3DCORE implementation allows us to generate extremely large ensemble simulations that we then use to find global best-fit model parameters using an ABC sequential Monte Carlo algorithm. The usage of this algorithm, under some basic assumptions on the uncertainty of the magnetic field measurements, allows us to furthermore generate estimates on the uncertainty of model parameters using only a single in situ observation. We apply our model to synthetically generated measurements to prove the validity of our implementation for the fitting procedure. We also present a brief analysis, within the scope of our model, of an event captured by the Parker Solar Probe shortly after its first flyby of the Sun on 2018 November 12 at 0.25 au. The presented toolset is also easily extendable to the analysis of events captured by multiple spacecraft and will therefore facilitate future multipoint studies.

Quantification of the weight of fingerprint evidence using a ROC-based Approximate Bayesian Computation algorithm for model selection

For more than a century, fingerprints have been used with considerable success to identify criminals or verify the identity of individuals. The categorical conclusion scheme used by fingerprint examiners, and more generally the inference process followed by forensic scientists, have been heavily criticised in the scientific and legal literature. Instead, scholars have proposed to characterise the weight of forensic evidence using the Bayes factor as the key element of the inference process. In forensic science, quantifying the magnitude of support is equally as important as determining which model is supported. Unfortunately, the complexity of fingerprint patterns render likelihood-based inference impossible. In this paper, we use an Approximate Bayesian Computation (ABC) model selection algorithm to quantify the weight of fingerprint evidence. We supplement the original ABC model selection algorithm using a Receiver Operating Characteristic curve to mitigate its known shortcomings with respect to the choice of a suitable threshold and the curse of dimensionality. In a sense, we offer an alternative to other methods that have tried to address the same issues. Our method is straightforward to implement, computationally efficient, and visually intuitive for lay individuals (i.e., jurors). We apply our method to quantify the weight of fingerprint evidence in forensic science, but we note that it can be applied to any other forensic pattern evidence.

Corrigendum to “Quantification of the weight of fingerprint evidence using a ROC-based Approximate Bayesian Computation algorithm for model selection”

In this correction, we provide an acknowledgment for the source of several images in the paper: J. Hendricks, C. Neumann, C.P. Saunders (2021) “Quantification of the weight of fingerprint evidence using a ROC-based Approximate Bayesian Computation algorithm for model selection”, Electronic Journal of Statistics (15)1, pp. 1228–1262.

A bivariate two-state Markov modulated Poisson process for failure modeling

Motivated by a real failure dataset in a two-dimensional context, this paper presents an extension of the Markov modulated Poisson process (MMPP) to two dimensions. The one-dimensional MMPP has been proposed for the modeling of dependent and non-exponential inter-failure times (in contexts as queuing, risk or reliability, among others). The novel two-dimensional MMPP allows for dependence between the two sequences of inter-failure times, while at the same time preserves the MMPP properties, marginally. The generalization is based on the Marshall–Olkin exponential distribution. Inference is undertaken for the new model through a method combining a matching moments approach with an Approximate Bayesian Computation (ABC) algorithm. The performance of the method is shown on simulated and real datasets representing times and distances covered between consecutive failures in a public transport company. For the real dataset, some quantities of importance associated with the reliability of the system are estimated as the probabilities and expected number of failures at different times and distances covered by trains until the occurrence of a failure.

Application of the Approximate Bayesian Computation Algorithm to Gamma-Ray Spectroscopy

Radioisotope identification (RIID) algorithms for gamma-ray spectroscopy aim to infer what isotopes are present and in what amounts in test items. RIID algorithms either use all energy channels in the analysis region or only energy channels in and near identified peaks. Because many RIID algorithms rely on locating peaks and estimating each peak’s net area, peak location and peak area estimation algorithms continue to be developed for gamma-ray spectroscopy. This paper shows that approximate Bayesian computation (ABC) can be effective for peak location and area estimation. Algorithms to locate peaks can be applied to raw or smoothed data, and among several smoothing options, the iterative bias reduction algorithm (IBR) is recommended; the use of IBR with ABC is shown to potentially reduce uncertainty in peak location estimation. Extracted peak locations and areas can then be used as summary statistics in a new ABC-based RIID. ABC allows for easy experimentation with candidate summary statistics such as goodness-of-fit scores and peak areas that are extracted from relatively high dimensional gamma spectra with photopeaks (1024 or more energy channels) consisting of count rates versus energy for a large number of gamma energies.

Fuzzy Linear regression based on approximate Bayesian computation

Fuzzy linear regression with crisp inputs and fuzzy output data constitutes an important modeling problem. Basic strategies used to solve this problem, i.e., the possibilistic method and the least squares method, together with their extensions, have some drawbacks. The possibilistic methods put emphasis on an inclusion property while the least squares methods focus on a central tendency property. Therefore, many researchers work on combining these two methods to obtain a better performance. In this paper, in contrast to most existing techniques which treat fuzzy linear regression as an optimization problem, we set the problem of constructing a fuzzy linear regression model in Bayesian statistics and propose a new fuzzy linear regression method based on approximate Bayesian computation (ABC). The method applies the likelihood-free inference algorithm ABC to generate independent samples of unknown model coefficients from Bayesian posterior distribution. This overcomes difficulty of defining likelihood function in fuzzy environment. By adjusting a prior distribution and a threshold of the ABC algorithm, the proposed approach can flexibly balance the inclusion property of the possibilistic methods and the central tendency property of the least squares methods. The convergence property of the proposed ABC algorithm is verified by a numerical example. Two measuring criteria, i.e., a distance metric and a degree of fitting index, which indicate the central tendency property and the inclusion property, respectively, are introduced to evaluate the quality of regression results. Three numerical examples are applied to show the performances of the proposed method. The numerical results are also compared with those obtained by some classical and recently proposed approaches. Additionally, a practical engineering application example is used to illustrate effectiveness of the proposed method.

Uncertainty calibration of building energy models by combining approximate Bayesian computation and machine learning algorithms

Bayesian analysis has attracted more attention in calibrating building energy models since it can naturally account for uncertainty of input parameters. However, standard Bayesian analysis requires to compute likelihood functions to represent the probability of the observed data under a statistical energy model. This makes the implementation of standard Bayesian analysis difficult for calibrating dynamic building energy models. Therefore, this research proposes a new Bayesian method by combining the approximate Bayesian computation with machine learning techniques in calibrating building models without computing likelihood functions. The results indicate that this new Bayesian computation approach combined with the machine learning algorithms can provide fast and reliable calibration for building energy models created using the EnergyPlus program. The calibration metrics in terms of the coefficient variations of root mean square errors from this new Bayesian method are well below the threshold value (15%) recommended from the ASHRAE standard for monthly energy data. Moreover, the better calibration results can be obtained by using linear or nonlinear post-adjustment techniques to account for the differences between the simulated and observed energy data. The method proposed here can significantly extend the application of Bayesian analysis in calibrating building energy models under uncertainty due to its simplicity and fast computation. Furthermore, the new Bayesian approach combined with machine learning technique can also be used to calibrate the simulation-based models for various types of energy systems.

Approximate Bayesian computation (ABC) method for estimating parameters of the gamma process using noisy data

The stochastic gamma process (GP) has emerged as a versatile model of degradation processes affecting the performance of engineering structures and components. The GP model captures the temporal uncertainty in the degradation process, whereas the Bayesian approach is used to account for uncertainty in the model parameters. Although the conceptual approach to GP parameter estimation is straightforward, its practical implementation is quite challenging. The reason is that degradation data required for parameter estimation are invariably contaminated by measurement noise, which turns the likelihood function into a high-dimensional multivariate integral. To circumvent this difficulty, the paper presents a novel and practical approach based on the approximate Bayesian computation (ABC) technique. The ABC method is a simulation-based approach that does not require an explicit formulation of the likelihood function. Instead, ABC uses an “accept-reject” mechanism to perform the posterior computation. To reduce the rejection rate, the Markov chain Monte Carlo (MCMC) approach is used within the ABC algorithm. The proposed ABC-MCMC algorithm is shown to be computationally more efficient than the traditional likelihood-based method without compromising the numerical accuracy. A case study involving the modelling of corrosion in nuclear piping systems is presented, which confirms the practical usefulness of the proposed method.

Distance-learning For Approximate Bayesian Computation To Model a Volcanic Eruption

Approximate Bayesian computation (ABC) provides us with a way to infer parameters of models, for which the likelihood function is not available, from an observation. Using ABC, which depends on many simulations from the considered model, we develop an inferential framework to learn parameters of a stochastic numerical simulator of volcanic eruption. Moreover, the model itself is parallelized using Message Passing Interface (MPI). Thus, we develop a nested-parallelized MPI communicator to handle the expensive numerical model with ABC algorithms. ABC usually relies on summary statistics of the data in order to measure the discrepancy model output and observation. However, informative summary statistics cannot be found for the considered model. We therefore develop a technique to learn a distance between model outputs based on deep metric-learning. We use this framework to learn the plume characteristics (eg. initial plume velocity) of the volcanic eruption from the tephra deposits collected by field-work associated with the 2450 BP Pululagua (Ecuador) volcanic eruption.

The discrepancy measures in approximate Bayesian computation and applications in bioscience

Background and Objective: Approximate Bayesian computation (ABC), identifying the parameters that yield simulated data resembling the observed data, is a powerful likelihood-free inference framework, and has been widely applied in bioscience including population model, epidemic model and so on. A major difficulty in ABC is how to accurately determine the level of the discrepancy for it has a crucial impact on the inference results of algorithms. In this paper, our aim is to propose a novel and valid discrepancy measure approach. Methods: By analyzing and comparing existing discrepancy measure methods, one finds they have obvious shortcomings including narrow adaptability and high computational cost. To overcome these deficiencies, an improved cosine similarity to assess the discrepancy in ABC is designed. First, both simulated data and observed data are converted into vectors, and then in virtue of the angle of them and the modulus of vectors, the similarity between the two data sets are measure. Results: The proposed discrepancy measure method achieves a comparable or higher posterior quality compared with the existing methods through four examples including Gaussian, Gaussian mixture, predator-prey and epidemic models. Conclusions: The statistical inference of complex biological models is a challenging task, and ABC algorithm can solve this problem well, but it needs to choose appropriate discrepancy measures. The results show that the improved cosine similarity is a extremely efficient discrepancy measurement method. Moreover, our work facilitates researchers to choose an appropriate discrepancy measure in practice.

Thermal Characterization of Ex Vivo Tissue.

Cancer treatment strategies require mathematical modeling of different coupled phenomena as well as uncertainty quantification of resulting computational solutions. Due to variability in thermophysical tissue properties among individuals, and even for the same individual under different physiological conditions, uncertainties in such parameters must appropriately be taken into account for accurate planning and control of hyperthermia and thermal ablation. The objective of this work is to estimate thermophysical properties of ex vivo tissue, with bovine muscle used for experiments. The Markov chain Monte Carlo method and approximate Bayesian computation algorithm are used to find solutions of the inverse problems examined in this work. These techniques provide a framework for not only solving the inverse problem but also finding uncertainty quantification.

Information Geometry for Approximate Bayesian Computation

The goal of this paper is to explore the basic approximate Bayesian computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of t...

Approximate Bayesian Computation Via the Energy Statistic

Approximate Bayesian computation (ABC) has become an essential part of the Bayesian toolbox for addressing problems in which the likelihood is prohibitively expensive or entirely unknown, making it intractable. ABC defines a pseudo-posterior by comparing observed data with simulated data, traditionally based on some summary statistics, the elicitation of which is regarded as a key difficulty. Recently, using data discrepancy measures has been proposed in order to bypass the construction of summary statistics. Here we propose to use the importance-sampling ABC (IS-ABC) algorithm relying on the so-called two-sample energy statistic. We establish a new asymptotic result for the case where both the observed sample size and the simulated data sample size increase to infinity, which highlights to what extent the data discrepancy measure impacts the asymptotic pseudo-posterior. The result holds in the broad setting of IS-ABC methodologies, thus generalizing previous results that have been established only for rejection ABC algorithms. Furthermore, we propose a consistent V-statistic estimator of the energy statistic, under which we show that the large sample result holds, and prove that the rejection ABC algorithm, based on the energy statistic, generates pseudo-posterior distributions that achieves convergence to the correct limits, when implemented with rejection thresholds that converge to zero, in the finite sample setting. Our proposed energy statistic based ABC algorithm is demonstrated on a variety of models, including a Gaussian mixture, a moving-average model of order two, a bivariate beta and a multivariate g-and-k distribution. We find that our proposed method compares well with alternative discrepancy measures.