Approximate Bayesian Computation Research Articles

A random-effect Wiener process degradation model with transmuted normal distribution and ABC-Gibbs algorithm for parameter estimation

Degradation modeling is a widely used technique for evaluating the reliability of high-quality products. However, unit-to-unit variability, stemming from material fluctuations during manufacturing and environmental factors, can significantly impact the accuracy of this assessment. To tackle this issue, we propose a novel time-transformed Wiener process with a transmuted normal distribution to represent unit-to-unit variability. This distribution extends the normal distribution, offering greater flexibility by capturing a wide range of non-normal, asymmetric behaviors in unit-to-unit variability. We derive closed-form expressions for the probability density function and reliability function for the model in two scenarios: (i) assuming the degradation process observations remain unaffected by measurement errors, and (ii) assuming the degradation process observations influenced by measurement errors. Due to the complexity of the likelihood functions, we employ the Gibbs version of approximate Bayesian computation (ABC-Gibbs) for parameter estimation. The effectiveness and application of the proposed method were demonstrated through numerical examples and practical application with light-emitting diode degradation data. Moreover, we use approximate Bayesian computation model choice (ABC-MC) for model comparison studies. The results indicated that our model offers improved approximations to observed degradation results compared to existing models, showcasing its superiority in generating data under the smallest tolerance threshold.

Model parameter estimation with imprecise information

ABSTRACT Model parameter estimation is a well-known inverse problem, as long as single-value point data are available as observations of system performance measurement. However, classical statistical methods, such as the minimization of an objective function or maximum likelihood, are no longer straightforward, when measurements are imprecise in nature. Typical examples of the latter include censored data and binary information. Here, we explore Approximate Bayesian Computation as a simple method to perform model parameter estimation with such imprecise information. We demonstrate the method for the example of a plain rainfall–runoff model and illustrate the advantages and shortcomings. Last, we outline the value of Shapley values to determine which type of observation contributes to the parameter estimation and which are of minor importance.

Homologous Recombination Shapes the Architecture and Evolution of Bacterial Genomes.

Homologous recombination is a key evolutionary force that varies considerably across bacterial species. However, how the landscape of homologous recombination varies across genes and within individual genomes has only been studied in a few species. Here, we used Approximate Bayesian Computation to estimate the recombination rate along the genomes of 145 bacterial species. Our results show that homologous recombination varies greatly along bacterial genomes and shapes many aspects of genome architecture and evolution. The genomic landscape of recombination presents several key signatures: rates are highest near the origin of replication in most species, patterns of recombination generally appear symmetrical in both replichores (i.e. replicational halves of circular chromosomes) and most species have genomic hotpots of recombination. Furthermore, many closely related species share conserved landscapes of recombination across orthologs indicating that recombination landscapes are conserved over significant evolutionary distances. We show evidence that recombination drives the evolution of GC-content through increasing the effectiveness of selection and not through biased gene conversion, thereby contributing to an ongoing debate. Finally, we demonstrate that the rate of recombination varies across gene function and that many hotspots of recombination are associated with adaptive and mobile regions often encoding genes involved in pathogenicity.

Rotational Evolution of Classical T Tauri Stars: Models and Observations

We developed a grid of stellar rotation models for low-mass and solar-type classical T Tauri stars (CTTS; 0.3M ⊙ < M * < 1.2M ⊙). These models incorporate the star–disk interaction and magnetospheric ejections to investigate the evolution of the stellar rotation rate as a function of the mass of the star M *, the magnetic field (B *), and stellar wind ( Ṁwind ). We compiled and determined stellar parameters for 208 CTTS, such as projected rotational velocity vsin(i) , mass accretion rate Ṁacc , stellar mass M *, ages, and estimated rotational periods using Transiting Exoplanet Survey Satellite (TESS) data. We also estimated a representative value of the mass-loss rate for our sample using the [O i] λ 6300 spectral line. Our results confirm that vsin(i) measurements in CTTS agree with the rotation rates provided by our spin models in the accretion-powered stellar winds picture. In addition, we used the approximate Bayesian computation technique to explore the connection between the model parameters and the observational properties of CTTS. We find that the evolution of vsin(i) with age might be regulated by variations in (1) the intensity of B * and (2) the fraction of the accretion flow ejected in magnetic winds, removing angular momentum from these systems. The youngest stars in our sample (∼1 Myr) show a median branching ratio Ṁwind/Ṁacc∼0.16 and median B * ∼ 2000 G, in contrast to ∼0.01 and 1000 G, respectively, for stars with ages ≳3 Myr.

Novel estimation of African swine fever transmission parameters within smallholder villages in Lao P.D.R

African Swine Fever (ASF) disease transmission parameters are crucial for making response and control decisions when faced with an outbreak, yet they are poorly quantified for smallholder and village contexts within Southeast Asia. Whilst disease-specific factors − such as latent and infectious periods − should remain reasonably consistent, host, environmental and management factors are likely to affect the rate of disease spread. These differences are investigated using Approximate Bayesian Computation with Sequential Monte-Carlo methods to provide disease parameter estimates in four naïve pig populations in villages of Lao People’s Democratic Republic. The villages represent smallholder pig farmers of the Northern province of Oudomxay and the Southern province of Savannakhet, and the model utilised field mortality data to validate the transmission parameter estimates over the course of multiple model generations. The basic reproductive number between-pigs was estimated to range from 3.08 to 7.80, whilst the latent and infectious periods were consistent with those published in the literature for similar genotypes in the region (4.72 to 6.19 days and 2.63 to 5.50 days, respectively). These findings demonstrate that smallholder village pigs interact similarly to commercial pigs, however the spread of disease may occur slightly slower than in commercial study groups. Furthermore, the findings demonstrated that despite diversity across the study groups, the disease behaved in a consistent manner. This data can be used in disease control programs or for future modelling of ASF in smallholder contexts.

Data-driven modelling makes quantitative predictions regarding bacteria surface motility.

In this work, we quantitatively compare computer simulations and existing cell tracking data of P. aeruginosa surface motility in order to analyse the underlying motility mechanism. We present a three dimensional twitching motility model, that simulates the extension, retraction and surface association of individual Type IV Pili (TFP), and is informed by recent experimental observations of TFP. Sensitivity analysis is implemented to minimise the number of model parameters, and quantitative estimates for the remaining parameters are inferred from tracking data by approximate Bayesian computation. We argue that the motility mechanism is highly sensitive to experimental conditions. We predict a TFP retraction speed for the tracking data we study that is in a good agreement with experimental results obtained under very similar conditions. Furthermore, we examine whether estimates for biologically important parameters, whose direct experimental determination is challenging, can be inferred directly from tracking data. One example is the width of the distribution of TFP on the bacteria body. We predict that the TFP are broadly distributed over the bacteria pole in both walking and crawling motility types. Moreover, we identified specific configurations of TFP that lead to transitions between walking and crawling states.

New sexually transmitted HIV infections from 2016 to 2050 in Guangdong Province, China: a study based on a dynamic compartmental model

BackgroundIn Guangdong Province, China, there is lack of information on the HIV epidemic among high-risk groups and the general population, particularly in relation to sexual transmission, which is a predominant route. The new HIV infections each year is also uncertain owing to HIV transmission from men who have sex with men (MSM) to women, as a substantial proportion of MSM also have female sexual partnerships to comply with social demands in China.MethodsA deterministic compartmental model was developed to predict new HIV infections in four risk groups, including heterosexual men and women and low- and high-risk MSM, in Guangdong Province from 2016 to 2050, considering HIV transmission from MSM to women. The new HIV infections and its 95% credible interval (CrI) were predicted. An adaptive sequential Monte Carlo method for approximate Bayesian computation (ABC-SMC) was used to estimate the unknown parameter, a mixing index. We calibrated our results based on new HIV diagnoses and proportions of late diagnoses. The Morris and Sobol methods were applied in the sensitivity analysis.ResultsNew HIV infections increased during and 2 years after the COVID-19 pandemic, then declined until 2050. New infections rose from 8,828 [95% credible interval (CrI): 6,435–10,451] in 2016 to 9,652 (95% CrI: 7,027–11,434) in 2019, peaking at 11,152 (95% CrI: 8,337–13,062) in 2024 before declining to 7,084 (95% CrI: 5,165–8,385) in 2035 and 4,849 (95% CrI: 3,524–5,747) in 2050. Women accounted for approximately 25.0% of new HIV infections, MSM accounted for 40.0% (approximately 55.0% of men), and high-risk MSM accounted for approximately 25.0% of the total. The ABC-SMC mixing index was 0.504 (95% CrI: 0.239–0.894).ConclusionsGiven that new HIV infections and the proportion of women were relatively high in our calibrated model, to some extent, the HIV epidemic in Guangdong Province remains serious, and services for HIV prevention and control are urgently needed to return to the levels before the COVID-19 epidemic, especially in promoting condom-based safe sex and increasing awareness of HIV prevention to general population.

A simulation-based approach for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data

Tracking pathogen transmissibility during infectious disease outbreaks is essential for assessing the effectiveness of public health measures and planning future control strategies. A key measure of transmissibility is the time-dependent reproduction number, which has been estimated in real-time during outbreaks of a range of pathogens from disease incidence time series data. While commonly used approaches for estimating the time-dependent reproduction number can be reliable when disease incidence is recorded frequently, such incidence data are often aggregated temporally (for example, numbers of cases may be reported weekly rather than daily). As we show, commonly used methods for estimating transmissibility can be unreliable when the timescale of transmission is shorter than the timescale of data recording. To address this, here we develop a simulation-based approach involving Approximate Bayesian Computation for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data. We first use a simulated dataset representative of a situation in which daily disease incidence data are unavailable and only weekly summary values are reported, demonstrating that our method provides accurate estimates of the time-dependent reproduction number under such circumstances. We then apply our method to two outbreak datasets consisting of weekly influenza case numbers in 2019–20 and 2022–23 in Wales (in the United Kingdom). Our simple-to-use approach will allow accurate estimates of time-dependent reproduction numbers to be obtained from temporally aggregated data during future infectious disease outbreaks.

A Novel Approach to Integrate Human Biomonitoring Data with Model Predicted Dietary Exposures: A Crop Protection Chemical Case Study Using Lambda-Cyhalothrin.

The appropriate use of human biomonitoring data to model population chemical exposures is challenging, especially for rapidly metabolized chemicals, such as agricultural chemicals. The objective of this study is to demonstrate a novel approach integrating model predicted dietary exposures and biomonitoring data to potentially inform regulatory risk assessments. We use lambda-cyhalothrin as a case study, and for the same representative U.S. population in the National Health and Nutrition Examination Survey (NHANES), an integrated exposure and pharmacokinetic model predicted exposures are calibrated to measurements of the urinary metabolite 3-phenoxybenzoic acid (3PBA), using an approximate Bayesian computing (ABC) methodology. We demonstrate that the correlation between modeled urinary 3PBA and the NHANES 3PBA measurements more than doubled as ABC thresholding narrowed the acceptable tolerance range for predicted versus observed urinary measurements. The median predicted urinary concentrations were closer to the median measured value using ABC than using current regulatory Monte Carlo methods.

Experimental Evaluation of a Direct Fitness Effect of the De Novo Evolved Mouse Gene Pldi.

De novo evolved genes emerge from random parts of noncoding sequences and have, therefore, no homologs from which a function could be inferred. While expression analysis and knockout experiments can provide insights into the function, they do not directly test whether the gene is beneficial for its carrier. Here, we have used a seminatural environment experiment to test the fitness of the previously identified de novo evolved mouse gene Pldi, which has been implicated to have a role in sperm differentiation. We used a knockout mouse strain for this gene and competed it against its parental wildtype strain for several generations of free reproduction. We found that the knockout (ko) allele frequency decreased consistently across three replicates of the experiment. Using an approximate Bayesian computation framework that simulated the data under a demographic scenario mimicking the experiment's demography, we could estimate a selection coefficient ranging between 0.21 and 0.61 for the wildtype allele compared to the ko allele in males, under various models. This implies a relatively strong selective advantage, which would fix the new gene in less than hundred generations after its emergence.

Simulation-based inference of deep fields: galaxy population model and redshift distributions

Accurate redshift calibration is required to obtain unbiased cosmological information from large-scale galaxy surveys. In a forward modelling approach, the redshift distribution n(z) of a galaxy sample is measured using a parametric galaxy population model constrained by observations. We use a model that captures the redshift evolution of the galaxy luminosity functions, colours, and morphology, for red and blue samples. We constrain this model via simulation-based inference, using factorized Approximate Bayesian Computation (ABC) at the image level. We apply this framework to HSC deep field images, complemented with photometric redshifts from COSMOS2020. The simulated telescope images include realistic observational and instrumental effects. By applying the same processing and selection to real data and simulations, we obtain a sample of n(z) distributions from the ABC posterior. The photometric properties of the simulated galaxies are in good agreement with those from the real data, including magnitude, colour and redshift joint distributions. We compare the posterior n(z) from our simulations to the COSMOS2020 redshift distributions obtained via template fitting photometric data spanning the wavelength range from UV to IR. We mitigate sample variance in COSMOS by applying a reweighting technique. We thus obtain a good agreement between the simulated and observed redshift distributions, with a difference in the mean at the 1σ level up to a magnitude of 24 in the i band. We discuss how our forward model can be applied to current and future surveys and be further extended. The ABC posterior and further material will be made publicly available at https://cosmology.ethz.ch/research/software-lab/ufig.html.

Approximate inference for longitudinal mechanistic HIV contact network

Network models are increasingly used to study infectious disease spread. Exponential Random Graph models have a history in this area, with scalable inference methods now available. An alternative approach uses mechanistic network models. Mechanistic network models directly capture individual behaviors, making them suitable for studying sexually transmitted diseases. Combining mechanistic models with Approximate Bayesian Computation allows flexible modeling using domain-specific interaction rules among agents, avoiding network model oversimplifications. These models are ideal for longitudinal settings as they explicitly incorporate network evolution over time. We implemented a discrete-time version of a previously published continuous-time model of evolving contact networks for men who have sex with men and proposed an ABC-based approximate inference scheme for it. As expected, we found that a two-wave longitudinal study design improves the accuracy of inference compared to a cross-sectional design. However, the gains in precision in collecting data twice, up to 18%, depend on the spacing of the two waves and are sensitive to the choice of summary statistics. In addition to methodological developments, our results inform the design of future longitudinal network studies in sexually transmitted diseases, specifically in terms of what data to collect from participants and when to do so.

The genetic diversity of Nipah virus across spatial scales.

Nipah virus (NiV), a highly lethal virus in humans, circulates in Pteropus bats throughout South and Southeast Asia. Difficulty in obtaining viral genomes from bats means we have a poor understanding of NiV diversity. We develop phylogenetic approaches applied to the most comprehensive collection of genomes to date (N=257, 175 from bats, 73 from humans) from six countries over 22 years (1999-2020). We divide the four major NiV sublineages into 15 genetic clusters. Using Approximate Bayesian Computation fit to a spatial signature of viral diversity, we estimate the presence and the average size of genetic clusters per area. We find that, within any bat roost, there are an average of 2.4 co-circulating genetic clusters, rising to 5.5 clusters at areas of 1500-2000km2. We estimate that each genetic cluster occupies an average area of 1.3million km2 (95%CI: 0.6-2.3 million), with 14 clusters in an area of 100,000km2 (95%CI: 6-24). In the few sites in Bangladesh and Cambodia where genomic surveillance has been concentrated, we estimate that most clusters have been identified, but only ∼15% of overall NiV diversity has been uncovered. Our findings are consistent with entrenched co-circulation of distinct lineages, even within roosts, coupled with slow migration over larger spatial scales.

Evolution of homologous recombination rates across bacteria

Bacteria are nonsexual organisms but are capable of exchanging DNA at diverse degrees through homologous recombination. Intriguingly, the rates of recombination vary immensely across lineages where some species have been described as purely clonal and others as "quasi-sexual." However, estimating recombination rates has proven a difficult endeavor and estimates often vary substantially across studies. It is unclear whether these variations reflect natural variations across populations or are due to differences in methodologies. Consequently, the impact of recombination on bacterial evolution has not been extensively evaluated and the evolution of recombination rate-as a trait-remains to be accurately described. Here, we developed an approach based on Approximate Bayesian Computation that integrates multiple signals of recombination to estimate recombination rates. We inferred the rate of recombination of 162 bacterial species and one archaeon and tested the robustness of our approach. Our results confirm that recombination rates vary drastically across bacteria; however, we found that recombination rate-as a trait-is conserved in several lineages but evolves rapidly in others. Although some traits are thought to be associated with recombination rate (e.g., GC-content), we found no clear association between genomic or phenotypic traits and recombination rate. Overall, our results provide an overview of recombination rate, its evolution, and its impact on bacterial evolution.

Bayesian estimation of large-scale simulation models with Gaussian process regression surrogates

Large scale, computationally expensive simulation models pose a particular challenge when it comes to estimating their parameters from empirical data. Most simulation models do not possess closed-form expressions for their likelihood function, requiring the use of simulation-based inference, such as simulated method of moments, indirect inference, likelihood-free inference or approximate Bayesian computation. However, given the high computational requirements of large-scale models, it is often difficult to run these estimation methods, as they require more simulated runs that can feasibly be carried out. The aim is to address the problem by providing a full Bayesian estimation framework where the true but intractable likelihood function of the simulation model is replaced by one generated by a surrogate model trained on the limited simulated data. This is provided by a Linear Model of Coregionalization, where each latent variable is a sparse variational Gaussian process, chosen for its desirable convergence and consistency properties. The effectiveness of the approach is tested using both a simulated Bayesian computing analysis on a known data generating process, and an empirical application in which the free parameters of a computationally demanding agent-based model are estimated on US macroeconomic data.

A historical stepping-stone path for an island-colonizing cactus across a submerged "bridge" archipelago.

Here we use population genomic data (ddRAD-Seq) and ecological niche modeling to test biogeographic hypotheses for the divergence of the island-endemic cactus species Cereus insularis Hemsl. (Cereeae; Cactaceae) from its sister species C. fernambucensis Lem. The Cereus insularis grows in the Fernando de Noronha Islands (FNI), a Neotropical archipelago located 350 km off the Brazilian Atlantic Forest (BAF) coast. Phylogeographic reconstructions support a northward expansion by the common ancestor of C. insularis and C. fernambucensis along the mainland BAF coast, with C. insularis diverging from the widespread mainland taxon C. fernambucensis after colonizing FNI in the late Pleistocene. The morphologically distinct C. insularis is monophyletic and nested within C. fernambucensis, as expected from a progenitor-derivative speciation model. We tested alternative biogeographic and demographic hypotheses for the colonization of the FNI using Approximate Bayesian Computation. We found the greatest support for a stepping-stone path that emerged during periods of decreased sea level (the "bridge" hypothesis), in congruence with historical ecological niche modeling that shows highly suitable habitats on stepping-stone islands during glacial periods. The outlier analyses reveal signatures of selection in C. insularis, suggesting a putative role of adaptation driving rapid anagenic differentiation of this species in FNI.

Complex Polyploids: Origins, Genomic Composition, and Role of Introgressed Alleles.

Introgression allows polyploid species to acquire new genomic content from diploid progenitors or from other unrelated diploid or polyploid lineages, contributing to genetic diversity and facilitating adaptive allele discovery. In some cases, high levels of introgression elicit the replacement of large numbers of alleles inherited from the polyploid's ancestral species, profoundly reshaping the polyploid's genomic composition. In such complex polyploids it is often difficult to determine which taxa were the progenitor species and which taxa provided additional introgressive blocks through subsequent hybridization. Here, we use population-level genomic data to reconstruct the phylogenetic history of Betula pubescens (downy birch), a tetraploid species often assumed to be of allopolyploid origin and which is known to hybridize with at least four other birch species. This was achieved by modeling of polyploidization and introgression events under the multispecies coalescent and then using an approximate Bayesian computation (ABC) rejection algorithm to evaluate and compare competing polyploidization models. We provide evidence that B. pubescens is the outcome of an autoploid genome doubling event in the common ancestor of B. pendula and its extant sister species, B. platyphylla, that took place approximately 178,000-188,000 generations ago. Extensive hybridization with B. pendula, B. nana, and B. humilis followed in the aftermath of autopolyploidization, with the relative contribution of each of these species to the B. pubescens genome varying markedly across the species' range. Functional analysis of B. pubescens loci containing alleles introgressed from B. nana identified multiple genes involved in climate adaptation, while loci containing alleles derived from B. humilis revealed several genes involved in the regulation of meiotic stability and pollen viability in plant species.

Mathematical Modelling of Parasite Dynamics: A Stochastic Simulation-Based Approach and Parameter Estimation via Modified Sequential-Type Approximate Bayesian Computation

The development of mathematical models for studying newly emerging and re-emerging infectious diseases has gained momentum due to global events. The gyrodactylid-fish system, like many host-parasite systems, serves as a valuable resource for ecological, evolutionary, and epidemiological investigations owing to its ease of experimental manipulation and long-term monitoring. Although this system has an existing individual-based model, it falls short in capturing information about species-specific microhabitat preferences and other biological details for different Gyrodactylus strains across diverse fish populations. This current study introduces a new individual-based stochastic simulation model that uses a hybrid τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}-leaping algorithm to incorporate this essential data, enhancing our understanding of the complexity of the gyrodactylid-fish system. We compare the infection dynamics of three gyrodactylid strains across three host populations. A modified sequential-type approximate Bayesian computation (ABC) method, based on sequential Monte Carlo and sequential importance sampling, is developed. Additionally, we establish two penalised local-linear regression methods (based on L1 and L2 regularisations) for ABC post-processing analysis to fit our model using existing empirical data. With the support of experimental data and the fitted mathematical model, we address open biological questions for the first time and propose directions for future studies on the gyrodactylid-fish system. The adaptability of the mathematical model extends beyond the gyrodactylid-fish system to other host-parasite systems. Furthermore, the modified ABC methodologies provide efficient calibration for other multi-parameter models characterised by a large set of correlated or independent summary statistics.

Impact of time resolution on estimation of energy savings using a copula-based calibration in UBEM

Urban Building Energy modelling (UBEM) has emerged in the last decade as an important tool to accelerate energy transition in the building sector. To fulfil one of its major purposes - forecasting energy savings for potential energy conservation measures at an urban scale, several challenges are still to be addressed. Two key challenges include: 1) the need to calibrate models with a large number of unknown parameters across numerous buildings (either individually or through archetype representation); 2) the limited availability of high-resolution measured data, which raises concerns about calibrated models based solely on yearly values for accurate energy savings forecast. This study addresses these challenges using a case study of 35 buildings in a district in Stockholm, Sweden. Firstly, a new iterative Approximate Bayesian Computation (ABC) method for calibration is proposed, incorporating a copula-based sampling process at each iteration. Secondly, the new calibration process is applied with three different time resolutions to examine the impact of data resolution on forecasted energy usage, particularly when applied to a classical energy conservation measure. Results demonstrate the efficiency of the new method across the 35 buildings, facilitating the rapid population of a final joint distribution for the nine unknown parameters considered in each building. While the marginals may be strongly influenced by the time resolution, the forecasted energy consumption remains identical across the three analysed time resolutions. However, a noticeable difference is observed when the ECM pertains to a formerly unknown or known parameter.

Constraints on the Evolution of the Ionizing Background and Ionizing Photon Mean Free Path at the End of Reionization

The variations in Lyα forest opacity observed at z > 5.3 between lines of sight to different background quasars are too strong to be caused by fluctuations in the density field alone. The leading hypothesis for the cause of this excess variance is a late, ongoing reionization process at redshifts below six. Another model proposes strong ionizing background fluctuations coupled to a short, spatially varying mean free path of ionizing photons, without explicitly invoking incomplete reionization. With recent observations suggesting a short mean free path at z ∼ 6, and a dramatic improvement in z > 5 Lyα forest data quality, we revisit this latter possibility. Here, we apply the likelihood-free inference technique of approximate Bayesian computation (ABC) to jointly constrain the hydrogen photoionization rate ΓHI and the mean free path of ionizing photons λ mfp from the effective optical depth distributions at z = 5.0–6.1 from XQR-30. We find that the observations are well-described by fluctuating mean free path models with average mean free paths that are consistent with the steep trend implied by independent measurements at z ∼ 5–6, with a concomitant rapid evolution of the photoionization rate.