Approximate Bayesian Computation Algorithm Research Articles

Unravelling the mystery of endemic versus translocated populations of the endangered Australian lungfish (Neoceratodus forsteri).

The Australian lungfish is a primitive and endangered representative of the subclass Dipnoi. The distribution of this species is limited to south-east Queensland, with some populations considered endemic and others possibly descending from translocations in the late nineteenth century shortly after European discovery. Attempts to resolve the historical distribution of this species have met with conflicting results based on descriptive genetic studies. Understanding if all populations are endemic or some are the result of, or influenced by, translocation events, has implications for conservation management. In this work, we analysed the genetic variation at three types of markers (mtDNA genomes, 11 STRs and 5196 nuclear SNPs) using the approximate Bayesian computation (ABC) algorithm to compare several demographic models. We postulated different contributions of Mary River and Burnett River gene pools into the Brisbane River and North Pine River populations, related to documented translocation events. We ran the analysis for each marker type separately, and we also estimated the posterior probabilities of the models combining the markers. Nuclear SNPs have the highest power to correctly identify the true model among the simulated datasets (where the model was known), but different marker types typically provided similar answers. The most supported demographic model able to explain the real dataset implies that an endemic gene pool is still present in the Brisbane and North Pine Rivers and coexists with the gene pools derived from past documented translocation events. These results support the view that ABC modelling can be useful to reconstruct complex historical translocation events with contemporary implications, and will inform ongoing conservation efforts for the endangered and iconic Australian lungfish.

Model-based estimation of AV-nodal refractory period and conduction delay trends from ECG.

Introduction: Atrial fibrillation (AF) is the most common arrhythmia, associated with significant burdens to patients and the healthcare system. The atrioventricular (AV) node plays a vital role in regulating heart rate during AF by filtering electrical impulses from the atria. However, it is often insufficient in regards to maintaining a healthy heart rate, thus the AV node properties are modified using rate-control drugs. Moreover, treatment selection during permanent AF is currently done empirically. Quantifying individual differences in diurnal and short-term variability of AV-nodal function could aid in personalized treatment selection. Methods: This study presents a novel methodology for estimating the refractory period (RP) and conduction delay (CD) trends, and their uncertainty in the two pathways of the AV node during 24 h using non-invasive data. This was achieved by utilizing a network model together with a problem-specific genetic algorithm and an approximate Bayesian computation algorithm. Diurnal variability in the estimated RP and CD was quantified by the difference between the daytime and nighttime estimates, and short-term variability was quantified by the Kolmogorov-Smirnov distance between adjacent 10-min segments in the 24-h trends. Additionally, the predictive value of the derived parameter trends regarding drug outcome was investigated using several machine learning tools. Results: Holter electrocardiograms from 51 patients with permanent AF during baseline were analyzed, and the predictive power of variations in RP and CD on the resulting heart rate reduction after treatment with four rate control drugs was investigated. Diurnal variability yielded no correlation to treatment outcome, and no prediction of drug outcome was possible using the machine learning tools. However, a correlation between the short-term variability for the RP and CD in the fast pathway and resulting heart rate reduction during treatment with metoprolol (ρ = 0.48, p < 0.005 in RP, ρ = 0.35, p < 0.05 in CD) were found. Discussion: The proposed methodology enables non-invasive estimation of the AV node properties during 24 h, which-indicated by the correlation between the short-term variability and heart rate reduction-may have the potential to assist in treatment selection.

Sequential Bayesian Planning for Accelerated Degradation Tests Considering Sensor Degradation

Most classical accelerated degradation test (ADT) planning models implicitly overlook the errors when measuring the degradation levels of the test units. However, the sensor measurement errors are inevitable and the magnitude of the errors may have a trend to increase over time due to sensor degradation. As a consequence improperly overlooking the sensor degradation in ADT planning could result in a test plan with unsatisfactory performance. This article addresses this issue by proposing a sequential ADT planning model that factors in sensor degradation. The system degradation level is periodically measured, based on which we dynamically adjust the stress level during ADT. We adopt a Bayesian framework that periodically updates the posterior distribution of model parameters considering the sensor degradation. An approximate Bayesian computation algorithm is developed to circumvent the difficulty of directly evaluating the complicated likelihood function in our problem. Numerical studies on a gas turbine reveal that our sequential model outperforms several traditional ADT designs that overlook the sensor degradation.

Hubble constant by natural selection: Evolution chips in the Hubble tension

The Approximate Bayesian Computation (ABC) algorithm considers natural selection in biology as a guiding principle for statistical model selection and parameter estimation. We take this ABC approach to cosmology and use it to infer which ΛCDM model anchored on a choice of a Hubble constant prior would be preferred by the data. We find in all of our runs that the Planck Hubble constant (H0=67.4±0.5 km s−1Mpc−1) always emerges naturally selected by the ABC over the SH0ES estimate (H0=73.30±1.04 km s−1Mpc−1). The result holds regardless of how we mix our data sets, including supernovae, cosmic chronometers, baryon acoustic oscillations, and growth data. Compared with the traditional MCMC, we find that the ABC always results with narrower cosmological constraints, but remain consistent inside the corresponding MCMC posteriors.

Estimating mutation rates in a Markov branching process using approximate Bayesian computation

Estimating microbial mutation rates is an essential task in evolutionary biology, with wide range applications in related fields such as virology, epidemiology, clinic and public health, and antibiotic research. Significant progress has been made on this research since 1943 when Luria–Delbrück fluctuation analysis was first introduced. However, existing estimators of mutation rates are heavily reliant on model assumptions in fluctuation analysis, and become less applicable to real microbial experiments which deviate from the model assumptions. To overcome this difficulty, we propose to model fluctuation experimental data by a two-type Markov branching process (MBP) and use approximate Bayesian computation (ABC) to estimate the mutation probability parameters. Such an ABC-based mutation rate estimator is based on intensive simulations from the mutation process, thereby taking advantage of modern computing power. Most importantly, its likelihood-free feature allows more complex and realistic setups of the mutation process, especially when the distribution of the number of mutants cannot be easily derived. To further improve computation efficiency, we use a Gaussian process surrogate to substitute the simulator in the ABC algorithm, and call the resulting estimator GPS-ABC. Simulation studies show that, when used to estimate constant mutation rate in MBP, ABC-based estimators generally outperform traditional moment or likelihood-based estimators. When mutations occur in two stages, i.e., in MBP with a piece-wise constant mutation rate function, traditional mutation rate estimators become not applicable, yet GPS-ABC still achieves reasonable estimates. Finally, the proposed GPS-ABC estimator is used to analyze real fluctuation experimental datasets for studying drug resistance.

Discrimination between accelerated life models via Approximate Bayesian Computation

Accelerated life testing (ALT) is widely used in high-reliability product estimation to get relevant information about an item's performance and its failure mechanisms. To analyse the observed ALT data, reliability practitioners need to select a suitable accelerated life model based on the nature of the stress and the physics involved. A statistical model consists of (i) a lifetime distribution that represents the scatter in product life and (ii) a relationship between life and stress. In practice, several accelerated life models could be used for the same failure mode and the choice of the best model is far from trivial. For this reason, an efficient selection procedure to discriminate between a set of competing accelerated life models is of great importance for practitioners. In this paper, accelerated life model selection is approached by using the Approximate Bayesian Computation (ABC) method and a likelihood-based approach for comparison purposes. To demonstrate the efficiency of the ABC method in calibrating and selecting accelerated life model, an extensive Monte Carlo simulation study is carried out using different distances to measure the discrepancy between the empirical and simulated times of failure data. Then, the ABC algorithm is applied to real accelerated fatigue life data in order to select the most likely model among five plausible models. It has been demonstrated that the ABC method outperforms the likelihood-based approach in terms of reliability predictions mainly at lower percentiles particularly useful in reliability engineering and risk assessment applications. Moreover, it has shown that ABC could mitigate the effects of model misspecification through an appropriate choice of the distance function.

FlywayNet: A hidden semi‐Markov model for inferring the structure of migratory bird networks from count data

Abstract Every year, millions of birds migrate between breeding and nonbreeding habitat, but the relative numbers of animals moving between sites are difficult to observe directly. Here we propose FlywayNet, a discrete network model based on observed count data, to determine the most likely migration links between regions using statistical modelling and efficient inference tools. Our approach advances on previous studies by accounting for noisy observations and flexible stopover durations by modelling using interacting hidden semi‐Markov Models. In FlywayNet, individual birds sojourn in stopover nodes for a period of time before moving to other nodes with an unknown probability that we aim to estimate. Exact estimation using existing approaches is not possible, so we designed customised versions of the Monte Carlo expectation‐maximisation and approximate Bayesian computation algorithms for our model. We compare the efficiency and quality of estimation of these approaches on synthetic data and an applied case study. Our algorithms performed well on benchmark problems, with low absolute error and strong correlation between estimated and known parameters. On a case study using citizen science count data of the Far Eastern Curlew (Numenius madagascariensis), an endangered shorebird from the East Asian–Australasian Flyway, the ABC and MCEM algorithms generated contrasting recommendations due to a difference in optimisation criteria and noise in the data. For ABC, we recovered key features of population‐level movements predicted by experts despite the challenges of noisy unstructured data. Understanding connectivity places local conservation efforts and threat mitigation in the global context, yet it has proven difficult to rigorously quantify connectivity at the population level. Our approach provides a flexible framework to infer the structure of migratory networks in birds and other organisms.

Sequential time-window learning with approximate Bayesian computation: an application to epidemic forecasting.

The long duration of the COVID-19 pandemic allowed for multiple bursts in the infection and death rates, the so-called epidemic waves. This complex behavior is no longer tractable by simple compartmental model and requires more sophisticated mathematical techniques for analyzing epidemic data and generating reliable forecasts. In this work, we propose a framework for analyzing complex dynamical systems by dividing the data in consecutive time-windows to be separately analyzed. We fit parameters for each time-window through an approximate Bayesian computation (ABC) algorithm, and the posterior distribution of parameters obtained for one window is used as the prior distribution for the next window. This Bayesian learning approach is tested with data on COVID-19 cases in multiple countries and is shown to improve ABC performance and to produce good short-term forecasting. Supplementary InformationThe online version contains supplementary material available at 10.1007/s11071-022-07865-x.

Population genomics reveal multiple introductions and admixture of Sonchus oleraceus in Australia

AbstractAimThe goal of this study was to investigate the invasion history of the weed Sonchus oleraceus in Australia by comparing the population genetic structure of individuals at different locations in Australia, and in the most likely areas of origin in the native range.LocationSamples were collected in Europe and Morocco, North Africa (27 locations), and Australia (17 locations).MethodsWe performed population genetic analyses using a large dataset comprising 2883 single nucleotide polymorphism markers from 547 plant samples and investigated the invasion history of S. oleraceus with Approximate Bayesian Computation and Random Forest classification algorithms. We compared single and multiple invasion scenarios considering admixture having occurred before and after introduction.ResultsOur results revealed high levels of inbreeding within sampling locations in the two ranges. Analyses also showed that S. oleraceus was possibly introduced to Australia at least twice: a first introduction around 1000 years ago before British settlement and a more recent introduction (~65 years ago) from Europe and North Africa. We also found evidence of post‐introduction admixture and a potential reintroduction of S. oleraceus from Australia back to its native range.Main conclusionsWe conclude that the invasion history of S. oleraceus into Australia is probably historic (i.e. prior to British settlements) and complex showing recent evidence of post‐introduction admixture. The complex invasion history of S. oleraceus in Australia poses challenges for the search of potential biological control agents.

Approximate Bayesian computation approach on the maximal offspring and parameters in controlled branching processes

Our purpose is to estimate the posterior distribution of the parameters of interest for controlled branching processes (CBPs) without prior knowledge of the maximum number of offspring that an individual can give birth to and without explicit likelihood calculations. We consider that only the population sizes at each generation and at least the number of progenitors of the last generation are observed, but the number of offspring produced by any individual at any generation is unknown. The proposed approach is twofold. Firstly, to estimate the maximum progeny per individual we make use of an approximate Bayesian computation (ABC) algorithm for model choice and based on sequential importance sampling with the raw data. Secondly, given such an estimate and taking advantage of the simulated values of the previous stage, we approximate the posterior distribution of the main parameters of a CBP by applying the rejection ABC algorithm with an appropriate summary statistic and a post-processing adjustment. The accuracy of the proposed method is illustrated by means of simulated examples developed with the statistical software R. Moreover, we apply the methodology to two real datasets describing populations with logistic growth. To this end, different population growth models based on CBPs are proposed for the first time.

Identifying cell-to-cell variability in internalization using flow cytometry.

Biological heterogeneity is a primary contributor to the variation observed in experiments that probe dynamical processes, such as the internalization of material by cells. Given that internalization is a critical process by which many therapeutics and viruses reach their intracellular site of action, quantifying cell-to-cell variability in internalization is of high biological interest. Yet, it is common for studies of internalization to neglect cell-to-cell variability. We develop a simple mathematical model of internalization that captures the dynamical behaviour, cell-to-cell variation, and extrinsic noise introduced by flow cytometry. We calibrate our model through a novel distribution-matching approximate Bayesian computation algorithm to flow cytometry data of internalization of anti-transferrin receptor antibody in a human B-cell lymphoblastoid cell line. This approach provides information relating to the region of the parameter space, and consequentially the nature of cell-to-cell variability, that produces model realizations consistent with the experimental data. Given that our approach is agnostic to sample size and signal-to-noise ratio, our modelling framework is broadly applicable to identify biological variability in single-cell data from internalization assays and similar experiments that probe cellular dynamical processes.

Computationally efficient parameter estimation for spatial individual-level models of infectious disease transmission

Individual-level models incorporate individual-specific covariate information, such as spatial location, to model infectious disease transmission. However, fitting these models with traditional Bayesian methods becomes cumbersome as model complexity or population size increases. We consider a spatial individual-level model with a binary susceptibility covariate. A method for fitting this model to aggregate-level data using traditional Metropolis–Hastings MCMC and then disaggregating the results to obtain individual-level estimates for epidemic metrics is proposed. This so-called “Cluster–Aggregate–Disaggregate” (CAD) method is compared to two approximate Bayesian computation (ABC) algorithms in a simulation study. The methods are also applied to a data set from the 2001 U.K. foot and mouth disease epidemic. While the CAD and ABC methods both performed reasonably well at capturing epidemic metrics, the CAD method was found to be much easier to implement and reduced computation time (relative to the traditional model-fitting method) more consistently than the ABC methods.

Microsimulation Model Calibration with Approximate Bayesian Computation in R: A Tutorial

Mathematical health policy models, including microsimulation models (MSMs), are widely used to simulate complex processes and predict outcomes consistent with available data. Calibration is a method to estimate parameter values such that model predictions are similar to observed outcomes of interest. Bayesian calibration methods are popular among the available calibration techniques, given their strong theoretical basis and flexibility to incorporate prior beliefs and draw values from the posterior distribution of model parameters and hence the ability to characterize and evaluate parameter uncertainty in the model outcomes. Approximate Bayesian computation (ABC) is an approach to calibrate complex models in which the likelihood is intractable, focusing on measuring the difference between the simulated model predictions and outcomes of interest in observed data. Although ABC methods are increasingly being used, there is limited practical guidance in the medical decision-making literature on approaches to implement ABC to calibrate MSMs. In this tutorial, we describe the Bayesian calibration framework, introduce the ABC approach, and provide step-by-step guidance for implementing an ABC algorithm to calibrate MSMs, using 2 case examples based on a microsimulation model for dementia. We also provide the R code for applying these methods.

Predicting the time to detect moderately virulent African swine fever virus in finisher swine herds using a stochastic disease transmission model

BackgroundAfrican swine fever (ASF) is a highly contagious and devastating pig disease that has caused extensive global economic losses. Understanding ASF virus (ASFV) transmission dynamics within a herd is necessary in order to prepare for and respond to an outbreak in the United States. Although the transmission parameters for the highly virulent ASF strains have been estimated in several articles, there are relatively few studies focused on moderately virulent strains. Using an approximate Bayesian computation algorithm in conjunction with Monte Carlo simulation, we have estimated the adequate contact rate for moderately virulent ASFV strains and determined the statistical distributions for the durations of mild and severe clinical signs using individual, pig-level data. A discrete individual based disease transmission model was then used to estimate the time to detect ASF infection based on increased mild clinical signs, severe clinical signs, or daily mortality.ResultsOur results indicate that it may take two weeks or longer to detect ASF in a finisher swine herd via mild clinical signs or increased mortality beyond levels expected in routine production. A key factor contributing to the extended time to detect ASF in a herd is the fairly long latently infected period for an individual pig (mean 4.5, 95% P.I., 2.4 - 7.2 days).ConclusionThese transmission model parameter estimates and estimated time to detection via clinical signs provide valuable information that can be used not only to support emergency preparedness but also to inform other simulation models of evaluating regional disease spread.

A simulation-based Bayesian approach to predict the distribution of maximum pit depth in steam generator tubes

Accurate prediction of the distribution of maximum pit depth is necessary for life-cycle management of the steam generator (SG) tubes in a nuclear power plant. However, probabilistic modeling of the pitting corrosion data often becomes computationally prohibitive once measurement and detection issues are taken into account. This happens because the noise in degradation data turns model likelihoods into complicated functions that are difficult to evaluate. This paper presents an approach based on the approximate Bayesian computation (ABC) method which avoids the evaluation of the likelihood function with the help of forward simulation. Using the underlying model as a simulator, the ABC method generates samples from a target posterior distribution by simulating pseudo data sets and comparing them with the observed data set using a distance function and a tolerance threshold. A new ABC algorithm is proposed in this study which is based on the subset simulation method. The proposed method is applied to a real data set, and the results show that it can efficiently estimate the model parameters from noisy data and accurately predict the distribution of the maximum pit depth in SG tubes. The parameter uncertainties are further integrated for the prediction of the 95th percentile of maximum pit depth along time.

New approximate Bayesian computation algorithm for censored data

New approximate Bayesian computation algorithm for censored data

Adaptive approximate Bayesian computation by subset simulation for structural model calibration

AbstractThis paper provides a new approximate Bayesian computation (ABC) algorithm with reduced hyper‐parameter scaling and its application to nonlinear structural model calibration problems. The algorithm initially takes the ABC‐SubSim algorithm structure and sequentially estimates the algorithm hyper‐parameter by autonomous adaptation following a Markov chain approach, thus avoiding the error associated to modeler's choice for these hyper‐parameters. The resulting algorithm, named BC‐SubSim, simplifies the application of ABC‐SubSim method for new users while ensuring better measure of accuracy in the posterior distribution and improved computational efficiency. A first numerical application example is provided for illustration purposes and to provide a comparative and sensitivity analysis of the algorithm with respect to initial ABC‐SubSim algorithm. Moreover, the efficiency of the method is demonstrated in two nonlinear structural calibration case studies where the BC‐SubSim is used as a tool to infer structural parameters with quantified uncertainty based on test data. The results confirm the suitability of the method to tackle with a real‐life damage parameter inference and its superiority in relation to the original ABC‐SubSim.

Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using approximate Bayesian computation

We develop a parameter estimation method based on approximate Bayesian computation (ABC) for a stochastic cell invasion model using fluorescent cell cycle labelling with proliferation, migration and crowding effects. Previously, inference has been performed on a deterministic version of the model fitted to cell density data, and not all parameters were identifiable. Considering the stochastic model allows us to harness more features of experimental data, including cell trajectories and cell count data, which we show overcomes the parameter identifiability problem. We demonstrate that, while difficult to collect, cell trajectory data can provide more information about the parameters of the cell invasion model. To handle the intractability of the likelihood function of the stochastic model, we use an efficient ABC algorithm based on sequential Monte Carlo. Rcpp and MATLAB implementations of the simulation model and ABC algorithm used in this study are available at https://github.com/michaelcarr-stats/FUCCI.

An improved approximate Bayesian computation scheme for parameter inference based on a recalibration post-processing method

Approximate Bayesian Computation algorithms (ABC), bypassing the intractable likelihood function, are commonly used to estimate the posterior distributions of parameters in practice. However ABC algorithms also have some inherent problems in the application, for example, when the algorithm maintains operating efficiency, it is difficult to obtain a more accurate approximation of the target distribution. To overcome these defects, an improved ABC algorithm is introduced in this article. The novel algorithm based on the ABC Sequential Monte Carlo (ABC-SMC) and a new recalibration post-processing methods is obtained to estimate the parameters of the biodynamic models, which is also called the ABC-SMCR algorithm. Through this article, it will be shown that the new algorithm is promising in processing the parameter inference problem. This algorithm not only offers high computational efficiency but also improves the quality estimate of the posterior distributions. To demonstrate its strengths, two examples are given. The first illustrative example on the basis of simulated data mainly demonstrates that it can be used to obtain accurate parameter inference of the Lotka-Volterra model. The second illustration based on actual flu outbreak data are given to show the computational efficiency of this algorithm in parameter estimation of the epidemic model.

ABCDP: Approximate Bayesian Computation with Differential Privacy.

We developed a novel approximate Bayesian computation (ABC) framework, ABCDP, which produces differentially private (DP) and approximate posterior samples. Our framework takes advantage of the sparse vector technique (SVT), widely studied in the differential privacy literature. SVT incurs the privacy cost only when a condition (whether a quantity of interest is above/below a threshold) is met. If the condition is sparsely met during the repeated queries, SVT can drastically reduce the cumulative privacy loss, unlike the usual case where every query incurs the privacy loss. In ABC, the quantity of interest is the distance between observed and simulated data, and only when the distance is below a threshold can we take the corresponding prior sample as a posterior sample. Hence, applying SVT to ABC is an organic way to transform an ABC algorithm to a privacy-preserving variant with minimal modification, but yields the posterior samples with a high privacy level. We theoretically analyzed the interplay between the noise added for privacy and the accuracy of the posterior samples. We apply ABCDP to several data simulators and show the efficacy of the proposed framework.