Approximate Bayesian Computation Approach Research Articles

An Approximate Bayesian Computation Approach for Embryonic Astrocyte Migration Model Reduction.

During embryonic development of the retina of the eye, astrocytes, a type of glial cell, migrate over the retinal surface and form a dynamic mesh. This mesh then serves as scaffolding for blood vessels to form the retinal vasculature network that supplies oxygen and nutrients to the inner portion of the retina. Astrocyte spreading proceeds in a radially symmetric manner over the retinal surface. Additionally, astrocytes mature from astrocyte precursor cells (APCs) to immature perinatal astrocytes (IPAs) during this embryonic stage. We extend a previously-developed continuum model that describes tension-driven migration and oxygen and growth factor influenced proliferation and differentiation. Comparing numerical simulations to experimental data, we identify model equation components that can be removed via model reduction using approximate Bayesian computation (ABC). Our results verify experimental studies indicating that the choroid oxygen supply plays a negligible role in promoting differentiation of APCs into IPAs and in promoting IPA proliferation, and the hyaloid artery oxygen supply and APC apoptosis play negligible roles in astrocyte spreading and differentiation.

Deep estimation of the intensity and timing of natural selection from ancient genomes.

Leveraging past allele frequencies has proven to be key for identifying the impact of natural selection across time. However, this approach suffers from imprecise estimations of the intensity (s) and timing (T) of selection, particularly when ancient samples are scarce in specific epochs. Here, we aimed to bypass the computation of allele frequencies across arbitrarily defined past epochs and refine the estimations of selection parameters by implementing convolutional neural networks (CNNs) algorithms that directly use ancient genotypes sampled across time. Using computer simulations, we first show that genotype-based CNNs consistently outperform an approximate Bayesian computation (ABC) approach based on past allele frequency trajectories, regardless of the selection model assumed and the number of available ancient genotypes. When applying this method to empirical data from modern and ancient Europeans, we replicated the reported increased number of selection events in post-Neolithic Europe, independently of the continental subregion studied. Furthermore, we substantially refined the ABC-based estimations of s and T for a set of positively and negatively selected variants, including iconic cases of positive selection and experimentally validated disease-risk variants. Our CNN predictions support a history of recent positive and negative selection targeting variants associated with host defence against pathogens, aligning with previous work that highlights the significant impact of infectious diseases, such as tuberculosis, in Europe. These findings collectively demonstrate that detecting the footprints of natural selection on ancient genomes is crucial for unravelling the history of severe human diseases.

Bayesian Model Updating of Multiscale Simulations Informing Corrosion Prognostics Using Conditional Invertible Neural Networks

Abstract Physics-based multi-scale corrosion simulation plays a vital role in predicting the evolution of pitting corrosion on large civil infrastructure such as miter gates, contributing to a model-informed structural health monitoring (SHM) strategy for risk-based asset health management. The physics-based analysis, however, may not accurately reflect the underlying true physics due to various uncertainty sources and needs to be updated using Bayesian inference methods based on observations to make the prediction closer to field observations. However, traditional Bayesian inference requires the evaluation of a likelihood function, which is often unavailable due to the complex model architecture and various surrogate models used in the analysis. Therefore, likelihood-free inference approaches are required for the updating of the multi-scale corrosion simulation models. This paper meets this need by proposing a conditional invertible neural network (cINN)-based Bayesian model updating method for an existing corrosion simulation model. We first train an cINN model based on simulated observations generated from a high-fidelity forward corrosion analysis model. A convolutional neural network (CNN)-based feature extraction algorithm is then employed to extract key features from corrosion images. After that, the extracted corrosion features from CNN is used as inputs of the cINN model to directly obtain posterior distributions of uncertain corrosion model parameters without evaluating the likelihood function. The results show that the proposed cINN-based model updating approach can provide more accurate inference results with a reduced computational cost in comparison to the classical approximate Bayesian computation (ABC) approach.

Dynamic Exploration-Exploitation Trade-Off in Active Learning Regression with Bayesian Hierarchical Modeling

Active learning provides a framework to adaptively query the most informative experiments towards learning an unknown black-box function. Various approaches of active learning have been proposed in the literature, however, they either focus on exploration or exploitation in the design space. Methods that do consider exploration-exploitation simultaneously employ fixed or ad-hoc measures to control the trade-off that may not be optimal. In this paper, we develop a Bayesian hierarchical approach, referred as BHEEM, to dynamically balance the exploration-exploitation trade-off as more data points are queried. To sample from the posterior distribution of the trade-off parameter, We subsequently formulate an approximate Bayesian computation approach based on the linear dependence of queried data in the feature space. Simulated and real-world examples show the proposed approach achieves at least 21 % and 11 % average improvement when compared to pure exploration and exploitation strategies respectively. More importantly, we note that by optimally balancing the trade-off between exploration and exploitation, BHEEM performs better or at least as well as either pure exploration or pure exploitation.

Selection among site-dependent structurally constrained substitution models of protein evolution by approximate Bayesian computation.

The selection among substitution models of molecular evolution is fundamental for obtaining accurate phylogenetic inferences. At the protein level, evolutionary analyses are traditionally based on empirical substitution models but these models make unrealistic assumptions and are being surpassed by structurally constrained substitution (SCS) models. The SCS models often consider site-dependent evolution, a process that provides realism but complicates their implementation into likelihood functions that are commonly used for substitution model selection. We present a method to perform selection among site-dependent SCS models, also among empirical and site-dependent SCS models, based on the approximate Bayesian computation (ABC) approach and its implementation into the computational framework ProteinModelerABC. The framework implements ABC with and without regression adjustments and includes diverse empirical and site-dependent SCS models of protein evolution. Using extensive simulated data, we found that it provides selection among SCS and empirical models with acceptable accuracy. As illustrative examples, we applied the framework to analyze a variety of protein families observing that SCS models fit them better than the corresponding best-fitting empirical substitution models. ProteinModelerABC is freely available from https://github.com/DavidFerreiro/ProteinModelerABC, can run in parallel and includes a graphical user interface. The framework is distributed with detailed documentation and ready-to-use examples.

Probabilistic model updating of civil structures with a decentralized variational inference approach

The quantification of uncertainties in civil structures poses a significant challenge due to the need to update a large number of unknown parameters, which can significantly increase the computational workload. A potential solution to this problem is the use of Approximate Bayesian Computation (ABC) approaches, which have gained attention in recent years. However, most existing ABC methods are limited in their ability to handle a large number of unknowns. To address this limitation, this study proposes a decentralized approach for uncertainty quantification in civil structures. In this approach, the structure is divided into several parts, and the uncertainties in each part are estimated independently. The proposed method utilizes the wavelet domain technique to eliminate the interfacial force of the target part and employs a recently developed variational inference approach to quantify the uncertainty in the target substructure. A three-span beam, a 2D truss, and an eight-story building were tested to evaluate the efficiency and feasibility of this approach. The results show that uncertainties in large structures can be estimated and that the proposed method is robust to high levels of measurement noise.

Body size evolution in otters distinguished from terrestrial mustelids.

Some taxa of mammals live in water, all of which evolved from land-dwelling ancestors. In the family Mustelidae (Mammalia: Carnivora), most species live on land, while otters, comprising the subfamily Lutrinae, inhabit aquatic environments, which include the almost exclusively aquatic sea otters (Enhydra lutris). Thus, the transition from a terrestrial to an aquatic lifestyle has occurred within this family. Despite potentially different selection pressures on body size in aquatic and terrestrial habitats, no divergence in the evolutionary pattern of body size between otters and other mustelids has previously been shown using models of trait evolution on a phylogeny. We applied models that explicitly incorporated lineage-specific directional selection to the evolution of body mass in living mustelids. Using a simulation-based likelihood and approximate Bayesian computation approach, we demonstrated lineage-specific directional selection for larger body mass in otters, which is distinct from other mustelids. There was no evidence of a difference between sea otters and other otters in the strength of directional selection for larger body mass. Additionally, our analyses supported no difference in the rate at which body mass evolves in both directions between otters and other mustelids. These findings suggest that the evolution of body mass in otters is associated with selective advantages of larger size rather than the relaxation of constraints on body size in aquatic habitats, like other aquatic mammals such as sirenians, cetaceans, and pinnipeds.

Cophylogeny Reconstruction Allowing for Multiple Associations Through Approximate Bayesian Computation.

Phylogenetic tree reconciliation is extensively employed for the examination of coevolution between host and symbiont species. An important concern is the requirement for dependable cost values when selecting event-based parsimonious reconciliation. Although certain approaches deduce event probabilities unique to each pair of host and symbiont trees, which can subsequently be converted into cost values, a significant limitation lies in their inability to model the invasion of diverse host species by the same symbiont species (termed as a spread event), which is believed to occur in symbiotic relationships. Invasions lead to the observation of multiple associations between symbionts and their hosts (indicating that a symbiont is no longer exclusive to a single host), which are incompatible with the existing methods of coevolution. Here, we present a method called AmoCoala (an enhanced version of the tool Coala) that provides a more realistic estimation of cophylogeny event probabilities for a given pair of host and symbiont trees, even in the presence of spread events. We expand the classical 4-event coevolutionary model to include 2 additional outcomes, vertical and horizontal spreads, that lead to multiple associations. In the initial step, we estimate the probabilities of spread events using heuristic frequencies. Subsequently, in the second step, we employ an approximate Bayesian computation approach to infer the probabilities of the remaining 4 classical events (cospeciation, duplication, host switch, and loss) based on these values. By incorporating spread events, our reconciliation model enables a more accurate consideration of multiple associations. This improvement enhances the precision of estimated cost sets, paving the way to a more reliable reconciliation of host and symbiont trees. To validate our method, we conducted experiments on synthetic datasets and demonstrated its efficacy using real-world examples. Our results showcase that AmoCoala produces biologically plausible reconciliation scenarios, further emphasizing its effectiveness.

Integrating Pool-seq uncertainties into demographic inference.

Next-generation sequencing of pooled samples (Pool-seq) is a popular method to assess genome-wide diversity patterns in natural and experimental populations. However, Pool-seq is associated with specific sources of noise, such as unequal individual contributions. Consequently, using Pool-seq for the reconstruction of evolutionary history has remained underexplored. Here we describe a novel Approximate Bayesian Computation (ABC) method to infer demographic history, explicitly modelling Pool-seq sources of error. By jointly modelling Pool-seq data, demographic history and the effects of selection due to barrier loci, we obtain estimates of demographic history parameters accounting for technical errors associated with Pool-seq. Our ABC approach is computationally efficient as it relies on simulating subsets of loci (rather than the whole-genome) and on using relative summary statistics and relative model parameters. Our simulation study results indicate Pool-seq data allows distinction between general scenarios of ecotype formation (single versus parallel origin) and to infer relevant demographic parameters (e.g. effective sizes and split times). We exemplify the application of our method to Pool-seq data from the rocky-shore gastropod Littorina saxatilis, sampled on a narrow geographical scale at two Swedish locations where two ecotypes (Wave and Crab) are found. Our model choice and parameter estimates show that ecotypes formed before colonization of the two locations (i.e. single origin) and are maintained despite gene flow. These results indicate that demographic modelling and inference can be successful based on pool-sequencing using ABC, contributing to the development of suitable null models that allow for a better understanding of the genetic basis of divergent adaptation.

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.

Phylogeography of 912 Cherry Accessions Insight into Independent Origins of Fruiting Cherries and Domestication Footprints of Cultivated Chinese Cherry (Prunus pseudocerasus Lindl.).

The subgenus Cerasus (Rosaceae) contain numerous fruit trees and ornamentals with high economic values. The origin and genetic divergence among various types of fruiting cherries always remain a perplexing issue. We employed three plastom fragments and ITS sequence matrices derived from 912 cherry accessions to elucidate the phylogeographic structure and genetic relationship among fruiting cherries, as well as the origin and domestication of cultivated Chinese cherry. The integration of haplotype genealogies, Approximate Bayesian computation (ABC) approach and estimation of genetic differentiation within and between different groups and lineages has facilitated the resolution of several previously unresolved questions. Firstly, distant phylogenetic relationships between Cerasus and Microcerasus accessions, as indicated by both nuclear and chloroplast data, suggested independent origins and evolution for these two taxa. Moreover, two distinct geographic origin centers (Europe and China) have been confirmed, with significant phylogeographic signals and high genetic differentiation observed between cherries from these regions. This may be attributed to long-term geographic isolation caused by Himalaya-Hengduan Mountains. Our phylogeographic analyses and ABC analysis suggested that cherries inhabiting in China may have undergone multiple hybridization events during the glacial refugia of the eastern edge and southern Himalaya-Hengduan Mountains, followed by rapid radiation throughout their current habitats during interglacial period. The discrepancy between nuclear and chloroplast data may be attributed to hybridization events and incomplete lineage sorting. Furthermore, we speculated that the domesticated Chinese cherries were derived from wild accessions in Longmenshan Fault Zones approximately 2600 years ago. We have also traced the domestication processes and dispersal routes of cultivated Chinese cherries.

On predictive inference for intractable models via approximate Bayesian computation

Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based statistical models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility of ABC as a generic approximate method for predictive inference, in particular, for computing the posterior predictive distribution of future observations or missing data of interest. We consider three complementary ABC approaches for this goal, each based on different assumptions regarding which predictive density of the intractable model can be sampled from. The case where only simulation from the joint density of the observed and future data given the model parameters can be used for inference is given particular attention and it is shown that the ideal summary statistic in this setting is minimal predictive sufficient instead of merely minimal sufficient (in the ordinary sense). An ABC prediction approach that takes advantage of a certain latent variable representation is also investigated. We additionally show how common ABC sampling algorithms can be used in the predictive settings considered. Our main results are first illustrated by using simple time-series models that facilitate analytical treatment, and later by using two common intractable dynamic models.

Using mechanistic model-based inference to understand and project epidemic dynamics with time-varying contact and vaccination rates

Epidemiological models range in complexity from relatively simple statistical models that make minimal assumptions about the variables driving epidemic dynamics to more mechanistic models that include effects such as vaccine-derived and infection-derived immunity, population structure and heterogeneity. The former are often fitted to data in real-time and used for short-term forecasting, while the latter are more suitable for comparing longer-term scenarios under differing assumptions about control measures or other factors. Here, we present a mechanistic model of intermediate complexity that can be fitted to data in real-time but is also suitable for investigating longer-term dynamics. Our approach provides a bridge between primarily empirical approaches to forecasting and assumption-driven scenario models. The model was developed as a policy advice tool for New Zealand’s 2021 outbreak of the Delta variant of SARS-CoV-2 and includes the effects of age structure, non-pharmaceutical interventions, and the ongoing vaccine rollout occurring during the time period studied. We use an approximate Bayesian computation approach to infer the time-varying transmission coefficient from real-time data on reported cases. We then compare projections of the model with future, out-of-sample data. We find that this approach produces a good fit with in-sample data and reasonable forward projections given the inherent limitations of predicting epidemic dynamics during periods of rapidly changing policy and behaviour. Results from the model helped inform the New Zealand Government’s policy response throughout the outbreak.

Reprint of: Bayesian inference using Gaussian process surrogates in cancer modeling

Parametric multiscale tumor models have been used nowadays as tools to understand and predict the behavior of tumor onset, development, and decrease under treatments. In order to obtain a useful model, its parameters have to be accurately estimated, often requiring numerous model evaluations. This can be computationally prohibitive for complex problems. In this work, we propose an approximate Bayesian computation approach for estimating model parameters using a low-fidelity Gaussian Process Regression metamodel. We develop an adaptive procedure to build the data-driven surrogate model by sequentially enriching the data set in the parametric space regions where the surrogate is not accurate enough. At the end of the process, we obtain good emulators of the original models over the entire parametric space at a low computational cost. We investigate the use of the proposed framework for the calibration of two tumor growth models, reaching high accuracy and computational efficiency, which may be key issues in many complex problems.

An Approximate Bayesian Computation Approach for Modeling Genome Rearrangements.

The inference of genome rearrangement events has been extensively studied, as they play a major role in molecular evolution. However, probabilistic evolutionary models that explicitly imitate the evolutionary dynamics of such events, as well as methods to infer model parameters, are yet to be fully utilized. Here, we developed a probabilistic approach to infer genome rearrangement rate parameters using an Approximate Bayesian Computation (ABC) framework. We developed two genome rearrangement models, a basic model, which accounts for genomic changes in gene order, and a more sophisticated one which also accounts for changes in chromosome number. We characterized the ABC inference accuracy using simulations and applied our methodology to both prokaryotic and eukaryotic empirical datasets. Knowledge of genome-rearrangement rates can help elucidate their role in evolution as well as help simulate genomes with evolutionary dynamics that reflect empirical genomes.

The emergence of a cryptic lineage and cytonuclear discordance through past hybridization in the Japanese fire-bellied newt,Cynops pyrrhogaster(Amphibia: Urodela)

AbstractDiscrepancies in geographic variation patterns between nuclear DNA and mitochondrial DNA (mtDNA) are the result of the complicated differentiation processes in organisms and are the key to understanding their true evolutionary processes. The genetic differentiation of the northern and Southern-Izu lineages of the Japanese newt, Cynops pyrrhogaster, was investigated through their single nucleotide polymorphism variations obtained via multiplexed ISSR genotyping by sequencing (MIG-seq). We found three genetic groups (Tohoku, N-Kanto and S-Kanto), that were not detected by mtDNA variations, in the northern lineage. N-Kanto has intermediate genetic characteristics between Tohoku and S-Kanto. The genetic groups are now moderately isolated from each other and have unique genetic characteristics. An estimation of the evolutionary history using the approximate Bayesian computation (ABC) approach suggested that Tohoku diverged from the common ancestor of S-Kanto and S-Izu. Then, S-Kanto and S-Izu split, and the recent hybridization between Tohoku and S-Kanto gave rise to N-Kanto. The origin of N-Kanto through the hybridization is relatively young and seems to be related to changes in the distributions of Tohoku and S-Kanto as a result of climatic oscillation in the Pleistocene. We conclude that the mitochondrial genome of S-Kanto was captured in Tohoku and that the original mitochondrial genome of Tohoku was entirely removed through hybridization.

Approximate Bayesian computation design for phase I clinical trials.

In the development of new cancer treatment, an essential step is to determine the maximum tolerated dose in a phase I clinical trial. In general, phase I trial designs can be classified as either model-based or algorithm-based approaches. Model-based phase I designs are typically more efficient by using all observed data, while there is a potential risk of model misspecification that may lead to unreliable dose assignment and incorrect maximum tolerated dose identification. In contrast, most of the algorithm-based designs are less efficient in using cumulative information, because they tend to focus on the observed data in the neighborhood of the current dose level for dose movement. To use the data more efficiently yet without any model assumption, we propose a novel approximate Bayesian computation approach to phase I trial design. Not only is the approximate Bayesian computation design free of any dose-toxicity curve assumption, but it can also aggregate all the available information accrued in the trial for dose assignment. Extensive simulation studies demonstrate its robustness and efficiency compared with other phase I trial designs. We apply the approximate Bayesian computation design to the MEK inhibitor selumetinib trial to demonstrate its satisfactory performance. The proposed design can be a useful addition to the family of phase I clinical trial designs due to its simplicity, efficiency and robustness.

Bayesian inference using Gaussian process surrogates in cancer modeling

Parametric multiscale tumor models have been used nowadays as tools to understand and predict the behavior of tumor onset, development, and decrease under treatments. In order to obtain a useful model, its parameters have to be accurately estimated, often requiring numerous model evaluations. This can be computationally prohibitive for complex problems. In this work, we propose an approximate Bayesian computation approach for estimating model parameters using a low-fidelity Gaussian Process Regression metamodel. We develop an adaptive procedure to build the data-driven surrogate model by sequentially enriching the data set in the parametric space regions where the surrogate is not accurate enough. At the end of the process, we obtain good emulators of the original models over the entire parametric space at a low computational cost. We investigate the use of the proposed framework for the calibration of two tumor growth models, reaching high accuracy and computational efficiency, which may be key issues in many complex problems.

Automatic model calibration of combined hydrologic, hydraulic and stormwater quality models using approximate Bayesian computation

A range of automatic model calibration techniques are used in water engineering practice. However, use of these techniques can be problematic due to the requirement of evaluating the likelihood function. This paper presents an innovative approach for overcoming this issue using a calibration framework developed based on Approximate Bayesian Computation (ABC) technique. Use of ABC in automatic model calibration was undertaken for a combined urban hydrologic, hydraulic and stormwater quality model. The simulated runoff hydrograph and total suspended solid (TSS) pollutograph were compared with observed data for multiple events from three different catchments, and found to be within 95% confidence intervals of the simulated results. The R programmed model was validated by comparing simulated flow with similar commercially available modeling software, MIKE URBAN output determined using mean value of parameters obtained from the calibration exercise, and performed well by satisfying statistical criteria's such as coefficient of determination (CD), root mean square error (RMSE) and maximum error (ME). The developed framework is useful for automatic calibration and uncertainty estimation using ABC approach in complex hydrologic, hydraulic and stormwater quality models with multi-input-output systems.

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.