Bayesian Computation Methods Research Articles

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.

A real-time regional model for COVID-19: Probabilistic situational awareness and forecasting.

The COVID-19 pandemic is challenging nations with devastating health and economic consequences. The spread of the disease has revealed major geographical heterogeneity because of regionally varying individual behaviour and mobility patterns, unequal meteorological conditions, diverse viral variants, and locally implemented non-pharmaceutical interventions and vaccination roll-out. To support national and regional authorities in surveilling and controlling the pandemic in real-time as it unfolds, we here develop a new regional mathematical and statistical model. The model, which has been in use in Norway during the first two years of the pandemic, is informed by real-time mobility estimates from mobile phone data and laboratory-confirmed case and hospitalisation incidence. To estimate regional and time-varying transmissibility, case detection probabilities, and missed imported cases, we developed a novel sequential Approximate Bayesian Computation method allowing inference in useful time, despite the high parametric dimension. We test our approach on Norway and find that three-week-ahead predictions are precise and well-calibrated, enabling policy-relevant situational awareness at a local scale. By comparing the reproduction numbers before and after lockdowns, we identify spatially heterogeneous patterns in their effect on the transmissibility, with a stronger effect in the most populated regions compared to the national reduction estimated to be 85% (95% CI 78%-89%). Our approach is the first regional changepoint stochastic metapopulation model capable of real time spatially refined surveillance and forecasting during emergencies.

Stochastic model calibration using the Bray-Curtis distance-based uncertainty quantification metric

In the practical engineering, it is usually unaffordable to conduct multiple full-scale physical experiments due to the budget limit. In such scenario, it is challenging to estimate the key parameters of imprecise probability models given insufficient test data. To address this issue, a stochastic model calibration method is developed in this paper. In the proposed framework, the approximate Bayesian computation method is employed as an efficient tool in which the Bray-Curtis distance is embedded as a novel uncertainty quantification metric. We validate the proposed method via a dynamic numerical case study of three-degree spring-mass system.

The stochasticity in adherence to nonpharmaceutical interventions and booster doses and the mitigation of COVID-19

Facing the more contagious COVID-19 variant, Omicron, nonpharmaceutical interventions (NPIs) were still in place and booster doses were proposed to mitigate the epidemic. However, the uncertainty and stochasticity in individuals' behaviours toward the NPIs and booster dose increase, and how this randomness affects the transmission remains poorly understood. We present a model framework to incorporate demographic stochasticity and two kinds of environmental stochasticity (notably variations in adherence to NPIs and booster dose acceptance) to analyze the effects of different forms of stochasticity on transmission. The model is calibrated using the data from December 31, 2021, to March 8, 2022, on daily reported cases and hospitalizations, cumulative cases, deaths and vaccinations for booster doses in Toronto, Canada. An approximate Bayesian computational (ABC) method is used for calibration. We observe that demographic stochasticity could dramatically worsen the outbreak with more incidence compared with the results of the corresponding deterministic model. We found that large variations in adherence to NPIs increase infections. The randomness in booster dose acceptance will not affect the number of reported cases significantly and it is acceptable in the mitigation of COVID-19. The stochasticity in adherence to NPIs needs more attention compared to booster dose hesitancy.

Modeling the Natural History and Screening Effects of Colorectal Cancer Using Both Adenoma and Serrated Neoplasia Pathways: The Development, Calibration, and Validation of a Discrete Event Simulation Model.

This article presents a new discrete event simulation model, DECAS, which models both adenoma-carcinoma and serrated neoplasia pathways for colorectal cancer (CRC) development and CRC screening effects.DECAS is calibrated based on a Bayesian inference method using the data from German screening colonoscopy program, which consists of more than 5 million first-time average-risk participants aged 55 years and older in 2003 to 2014.DECAS is flexible for evaluating various CRC screening strategies and can differentiate screening effects in different parts of the colon.DECAS is validated with large screening sigmoidoscopy and colonoscopy clinical study data and can be further used to evaluate the (cost-)effectiveness of German colorectal cancer screening strategies.

Inferring linguistic transmission between generations at the scale of individuals

Abstract Historical linguistics strongly benefited from recent methodological advances inspired by phylogenetics. Nevertheless, no available method uses contemporaneous within-population linguistic diversity to reconstruct the history of human populations. Here, we developed an approach inspired from population genetics to perform historical linguistic inferences from linguistic data sampled at the individual scale, within a population. We built four within-population demographic models of linguistic transmission over generations, each differing by the number of teachers involved during the language acquisition and the relative roles of the teachers. We then compared the simulated data obtained with these models with real contemporaneous linguistic data sampled from Tajik speakers from Central Asia, an area known for its large within-population linguistic diversity, using approximate Bayesian computation methods. Under this statistical framework, we were able to select the models that best explained the data, and infer the best-fitting parameters under the selected models. The selected model assumes that the lexicon of individuals is the result of a vertical transmission by two teachers, with a specific lexicon for each teacher. This demonstrates the feasibility of using contemporaneous within-population linguistic diversity to infer historical features of human cultural evolution.

Survivors and colonizers: Contrasting biogeographic histories reconciled in the Antarctic freshwater copepod Boeckella poppei

Two main hypotheses have been proposed to explain the contemporary distribution of Antarctic terrestrial biota. We assess whether the current distribution of maritime Antarctic populations of the freshwater copepod Boeckella poppei is the result of (1) a post-Last Glacial Maximum (LGM) colonization, or whether (2) the species survived in regional glacial refugia throughout the LGM and earlier glaciations. Using 438 specimens from 34 different sampling sites across Southern South America, South Georgia, South Orkney Islands, South Shetland Islands, and the Antarctic Peninsula, we analyzed mitochondrial and nuclear sequences to uncover patterns of genetic diversity and population structure. We also performed median-joining haplotype network, phylogenetic reconstruction, and divergence time analyses. Finally, we evaluated past demographic changes and historical scenarios using the Approximate Bayesian Computation (ABC) method. Our data support the existence of two clades with different and contrasting biogeographic histories. The first clade has been present in maritime Antarctica since at least the mid-Pleistocene, with the South Orkney Islands the most likely refugial area. The second clade has a broader distribution including southern South America, South Georgia, South Shetland Islands, and the Antarctic Peninsula. The ABC method identified long-distance dispersal (LDD) colonization event(s) from southern South America to South Georgia and the maritime Antarctic after the LGM deglaciation, supporting more recent colonization of Antarctic locations. The current Antarctic and sub-Antarctic distribution of B. poppei is likely derived from two independent biogeographic events. The combination of both (1) post-LGM colonization from southern South America and (2) longer-term persistence in in situ regional refugia throughout glacial periods challenges current understanding of the biogeographic history of Antarctic freshwater biota. Re-colonization of ice-impacted Antarctic areas would have occurred following a LDD and Establishment model, pointing to the existence of possible post-dispersal barriers, despite widely assumed high passive dispersal capacity in freshwater invertebrates.

Data-Driven Model Falsification and Uncertainty Quantification for Fractured Reservoirs

Many properties of natural fractures are uncertain, such as their spatial distribution, petrophysical properties, and fluid flow performance. Bayes’ theorem provides a framework to quantify the uncertainty in geological modeling and flow simulation, and hence to support reservoir performance predictions. The application of Bayesian methods to fractured reservoirs has mostly been limited to synthetic cases. In field applications, however, one of the main problems is that the Bayesian prior is falsified, because it fails to predict past reservoir production data. In this paper, we show how a global sensitivity analysis (GSA) can be used to identify why the prior is falsified. We then employ an approximate Bayesian computation (ABC) method combined with a tree-based surrogate model to match the production history. We apply these two approaches to a complex fractured oil and gas reservoir where all uncertainties are jointly considered, including the petrophysical properties, rock physics properties, fluid properties, discrete fracture parameters, and dynamics of pressure and transmissibility. We successfully identify several reasons for the falsification. The results show that the methods we propose are effective in quantifying uncertainty in the modeling and flow simulation of a fractured reservoir. The uncertainties of key parameters, such as fracture aperture and fault conductivity, are reduced.

A Bayesian Monte Carlo assessment of orbital stability in the late stages of planetary system formation

ABSTRACT The final orbital configuration of a planetary system is shaped by both its early star–disc environment and late-stage gravitational interactions. Assessing the relative importance of each of these factors is not straightforward due to the observed diversity of planetary systems compounded by observational biases. Our goal is to understand how a planetary system may change when planetesimal accretion and planet migrations stop and secular gravitational effects take over. Our approach starts with a novel classification of planetary systems based on their orbital architecture, validated using Approximate Bayesian Computation methods. We apply this scheme to observed planetary systems and also to ∼400 synthetic systems hosting ∼5000 planets, synthesized from a Monte Carlo planet population model. Our classification scheme robustly yields four system classes according to their planet masses and semimajor axes, for both observed and synthetic systems. We then estimate the orbital distribution density of each of the synthetic systems before and after dynamically evolving for 0.1–1 Myr using a gravitational + collisional N-body code. Using the Kullback–Leibler divergence to statistically measure orbital configuration changes, we find that ≲10 per cent of synthetic planetary systems experience such changes. We also find that this fraction belongs to a class of systems for which their centre of mass is very close to their host star. Although changes in the orbital configuration of planetary systems may not be very common, they are more likely to happen in systems with close-in, massive planets, with F- and G-type host-stars and stellar metallicities [Fe/H] >0.2.

Improved calibration of building models using approximate Bayesian calibration and neural networks

Deep energy retrofits of buildings are crucial to meeting climate targets and depend on calibrated energy models for investor confidence. Bayesian inference can improve the rigour in standard practice and improve confidence in calibrated energy models. Approximate Bayesian computation (ABC) methods using neural networks present an opportunity to calibrate energy models while inherently accounting for parameter uncertainty, and face less computational burden than the current standard process for Bayesian calibration. A case study for a large, complex building is presented to demonstrate the applicability of ABC and parameter sensitivity screening is found to result in over-confidence in the resulting inference by between 14% and 85%. Finally, the presentation of posterior distributions as independent distributions may be misleading, which can misattribute the true likelihood of parameters. Highlights Implementation of an Approximate Bayesian Computation method incorporating the Sequential Monte Carlo algorithm with a neural network surrogate model. A comparison of Bayesian inference with standard practice. An investigation of sensitivity screening for parameter selection on the inference results. Application to a complex multi-zone dynamic energy model of a large retail building.

Likelihood-free Hamiltonian Monte Carlo for modeling piping degradation and remaining useful life prediction using the mixed gamma process

The gamma process is a popular model to characterize the temporal uncertainty in degradation processes. According to this model, degradation occurs in tiny independent increments creating a monotonic non-decreasing trend. Mechanical components or units are often repetitively observed over time for measuring the extent of degradation; apparently, they degrade at different rates although operating in the same environment. The mixed gamma degradation process is suitable for capturing these unexplained differences. However, statistical estimation of its parameters and subsequent prediction of remaining useful life (RUL) turn challenging with limited and noisy measurements.While limited observations bring uncertainties to the model parameters, noisy data turns the likelihood function intractable. In such cases, approximate Bayesian computation (ABC) methods are widely applicable for their ability to bypass the likelihood evaluation and generate samples from an approximate target posterior distribution. The currently available Markov chain Monte Carlo (MCMC) based ABC method shows promising results, although it requires significant thinning due to poor mixing of samples. A new ABC method is derived in this paper which imitates the sampling process of the Hamiltonian Monte Carlo (HMC) method. The proposed ABC-HMC algorithm explores a target probability space more effectively — generating better mixing of samples and requiring less thinning than the MCMC based ABC method. Proof of convergence of ABC-HMC is shown by fulfilling the detailed balance condition. The application of the method is shown using real degradation data of piping components of the heat transport system of a nuclear reactor.

Bayesian computational methods for state-space models with application to SIR model

The state-space model is a powerful statistical tool to estimate linear or non-linear discrete-time dynamic systems. This model naturally leads to the estimation problem of the time-varying parameters of the discovery-time demographic version of the susceptible-infected-recovered (SIR) model that we consider. In this paper, we consider computational methods to perform Bayesian inference on state-space models for analysing time-series data. We compare the three popular Bayesian computational methods for state-space models: the adaptive Metropolis-within-Gibbs algorithm, Liu and West's algorithm and variational approximation method based on Gaussian distributions. The performances of the three methods are compared based on synthetic datasets. Furthermore, we analyse the trend of the spread of COVID-19 in South Korea to point out the limitations of existing methods and derive meaningful results.

Estimation of the bio-accessibility of methylmercury from aquatic foods using a PBTK model with an approximate Bayesian computation method in Chinese pregnant women.

Fish are the primary source of protein and docosahexaenoic acid (DHA) for pregnant women and children, but methylmercury (MeHg) pollution is the potential hazard of fish consumption. In risk assessments, the bio-accessibility of MeHg is usually assumed to be 100%, which could lead to overestimation of dietary exposure. An existing PBTK model was adapted to estimate parameters of the bio-accessibility based on MeHg exposure data from a cohort of 397 Chinese pregnant women. The posterior distributions of parameters were determined by using the ABC - MCMC. RMSEP and Spearman's rank correlation coefficients (Rho) were calculated to determine the goodness of model fitting. The Monte Carlo analysis was performed for the parameter distributions to estimate the model variability. The median of daily MeHg intake and maternal MeHg levels were 0.018μg/kg bw and 3.01μg/kg in the early and middle terms of pregnancy. The estimated bio-accessibility of freshwater fish, marine fish and others were 46.1, 17.3 and 58.2%, separately. The RMSEP improved from 11.18 to 2.54 and the Rho improved from 0.19 to 0.22 after bio-accessibility optimization. The model variability was estimated to be 2.6. The bio-accessibility estimated in this study was comparable to that determined in previous in vitro studies. The optimized model could improve the prediction performance on the MeHg body burden by dietary exposure.

A new extension of the two-parameter bathtub hazard shaped distribution

The need of new life time distributions that can be used to fit real data sets is crucial in lifetime data analysis. This article uses the two parameter bathtub (TPBT) and the generalized exponential (GE) distributions to propose a new family of lifetime distributions, named the odd generalized exponential two-parameter bathtub shaped distribution (OGE-TPBT). Statistical properties of the proposed distribution are discussed. The maximum likelihood and Bayesian procedures are used to estimate the model’s parameters and some of its reliability measures. For Bayes method, we use three approaches of the approximate Bayesian computation (ABC) method. Simulation study is provided to investigate the properties of the methods applied. Based on some well know diagnostic tests, we find out that the simulation data provided in this paper is appropriate. To discuss the possible improvements of the new distribution compared to the original two distributions (GE and TPBT) and its applicability, a real-life data set is analyzed. Based on the comparison results, we found out that the OGE-TPBT fits the data better than both the GE and TPBT distributions. Also, we used the same real data set to compare the three approaches of the ABC. Based on the comparisons results of these three approaches, we recommend the naive ABC to approximate Bayes estimations in the situation for which there is no analytic solution.

209 A CTS Team Approach to Modeling Migration and Suppression of CCR2+/CX3CR1+ Myeloid Cells in Glioblastoma

OBJECTIVES/GOALS: Evaluate the migration and immune suppressive functions of CCR2+/CX3CR1+ myeloid-derived suppressor cells (MDSCs). Integrate experimental data and biologically relevant mathematical models of infiltrating MDSCs in the context of glioblastoma (GBM). METHODS/STUDY POPULATION: CCR2+/CX3CR1+ cells were enriched from bone marrow obtained from CCR2(+/RFP)/CX3CR1(+/GFP) glioma-bearing mice to evaluate their immune-suppressive phenotype and ability to migrate to CCL2 and CCL7. Fluorescent imaging and quantification were performed on a range of tumor sizes to acquire vasculature, tumor, T cell, and MDSC densities. A system of ordinary differential equations was constructed to represent the temporal dynamics of glioma cells, T cells, and MDSCs within the tumor microenvironment. The Approximate Bayesian Computation method was used to determine probability distributions of important parameters, such as the suppression rate of T cells by MDSCs. RESULTS/ANTICIPATED RESULTS: CCR2+/CX3CR1+ M-MDSCs isolated from the bone marrow of tumor-bearing mice suppress CD8+ T cell proliferation and IFNγ production. CCR2+/CX3CR1+ cells migrate to recombinant and KR158B glioma sourced CCL2 and CCL7. Parameter values determined by the Approximate Bayesian Computation method agreed with parameter values from experimental data. This result further validated the structure and results of the mathematical model when performing computer simulations; thus, we can predict CCR2+/CX3CR1+ M-MDSC infiltration over time. DISCUSSION/SIGNIFICANCE: The immune-suppressive microenvironment in GBM contributes to poor outcomes despite standard of care. This study integrates biological and mathematical models to better understand infiltrating immune-suppressive cells, namely CCR2+/CX3CR1+ M-MDSCs. Future directions include modeling immunotherapies.

Retrospective exposure reconstruction using approximate Bayesian computation: A case study on perfluorooctanoic acid and preeclampsia

BackgroundIn environmental epidemiology, measurements of toxicants in biological samples are often used as individual exposure assignments. It is common to obtain only one or a few exposure biomarkers per person and use those measurements to represent each person's relevant toxicant exposure for a given health outcome, even though most exposure biomarkers can fluctuate over time. When the timing of the exposure reflected by the biomarker measurement is misaligned with disease development especially if it occurs after the disease outcome, results could be subject to reverse causality or exposure measurement error. ObjectiveThis study aimed to use an approximate Bayesian computation (ABC) method to improve PFOA exposure estimates and characterize the effects of PFOA on preeclampsia in the C8 Studies. MethodsSerum PFOA concentrations were measured in blood samples collected during 2005–2006 in West Virginia and Ohio (the C8 Studies), and residential and water use histories and pregnancy outcomes were obtained from self-reports. Our previous results may have been influenced by the choice of methods for characterizing PFOA exposures. Here we use an ABC method to combine measured PFOA serum concentrations and environmentally modeled PFOA concentrations to reconstruct historical PFOA exposures. We also expanded our previous work by assuming more realistic lognormal distributions for key input parameters in the exposure and pharmacokinetic models. ResultsCompared to using fixed values of model parameters and Monte Carlo simulations, ABC produced similar Spearman correlations between estimated and measured serum PFOA concentrations, yet substantially reduced the mean squared error by over 50%. Based on ABC, compared to previous studies, we found a similar adjusted odds ratio (AOR) for the association between PFOA and preeclampsia. ConclusionsBayesian combination of modeled exposure and measured biomarker concentrations can reduce exposure measurement error compared to modeled exposure.

Parapatric speciation with recurrent gene flow of two sexual dichromatic pheasants

Understanding speciation has long been a fundamental goal of evolutionary biology. It is widely accepted that speciation requires an interruption of gene flow to generate strong reproductive isolation between species. The mechanism of how speciation in sexually dichromatic species operates in the face of gene flow remains an open question. Two species in the genus Chrysolophus, the Golden Pheasant (C. pictus) and Lady Amherst's Pheasant (C. amherstiae), both of which exhibit significant plumage dichromatism, are currently parapatric in southwestern China with several hybrid recordings in field. In this study, we estimated the pattern of gene flow during the speciation of the two pheasants using the Approximate Bayesian Computation (ABC) method based on data from multiple genes. Using a newly assembled de novo genome of Lady Amherst's Pheasant and resequencing of widely distributed individuals, we reconstructed the demographic history of the two pheasants by the PSMC (pairwise sequentially Markovian coalescent) method. The results provide clear evidence that the gene flow between the two pheasants was consistent with the predictions of the isolation with migration model during divergence, indicating that there was long-term gene flow after the initial divergence (ca. 2.2 million years ago). The data further support the occurrence of secondary contact between the parapatric populations since around 30 kya with recurrent gene flow to the present, a pattern that may have been induced by the population expansion of the Golden Pheasant in the late Pleistocene. The results of the study support the scenario of speciation between the Golden Pheasant and Lady Amherst's Pheasant with cycles of mixing-isolation-mixing, possibly due to the dynamics of geographical context in the late Pleistocene. The two species provide a good research system as an evolutionary model for testing reinforcement selection in speciation.

Minimax confidence intervals for the Sliced Wasserstein distance

Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance. Specifically, we construct confidence intervals for the Sliced Wasserstein distance which have finite-sample validity under no assumptions or under mild moment assumptions. These intervals are adaptive in length to the regularity of the underlying distributions. We also bound the minimax risk of estimating the Sliced Wasserstein distance, and as a consequence establish that the lengths of our proposed confidence intervals are minimax optimal over appropriate distribution classes. To motivate the choice of these classes, we also study minimax rates of estimating a distribution under the Sliced Wasserstein distance. These theoretical findings are complemented with a simulation study demonstrating the deficiencies of the classical bootstrap, and the advantages of our proposed methods. We also show strong correspondences between our theoretical predictions and the adaptivity of our confidence interval lengths in simulations. We conclude by demonstrating the use of our confidence intervals in the setting of simulator-based likelihood-free inference. In this setting, contrasting popular approximate Bayesian computation methods, we develop uncertainty quantification methods with rigorous frequentist coverage guarantees.

An inverse transformation algorithm to infer parameter distributions from population snapshot data

Population snapshot data can be used to study heterogeneity in cell populations. Various approaches to integrating such data into computational models have been published, which enable new treatment strategies for cancer therapy, by exploiting the intra-tumor heterogeneity. A precision medicine approach for the cure of cancer could benefit from the combination of single-cell data and respective analytical methods. Here, we introduce the inverse transformation algorithm, which transforms population snapshot data to parameter distributions that are consistent with the underlying data given a dynamic model with distributed parameters. Therefore, it enables the assessment of the heterogeneity in and behavior of the whole underlying cell population. In contrast to the frequently used Approximate Bayesian Computation methods for population matching, our algorithm is a non-parametric likelihood-free approach. It directly computes a density function value for a single parameter based on density transformation methods. If the model can be described as a one-to-one map that invertibly maps parameters to measurable outputs, the inverse transformation algorithm asymptotically returns the true underlying parameter distribution.The inverse transformation algorithm is applied to snapshot data simulated via standard differential equation models for biochemical reaction networks. In particular, we evaluate our algorithm on two small test-bed models and discuss advantages and limitations in comparison to other existing approaches.

Statistical Network Analysis with Bergm

Recent advances in computational methods for intractable models have made network data increasingly amenable to statistical analysis. Exponential random graph models (ERGMs) emerged as one of the main families of models capable of capturing the complex dependence structure of network data in a wide range of applied contexts. The Bergm package for R has become a popular package to carry out Bayesian parameter inference, missing data imputation, model selection and goodness-of-fit diagnostics for ERGMs. Over the last few years, the package has been considerably improved in terms of efficiency by adopting some of the state-of-the-art Bayesian computational methods for doublyintractable distributions. Recently, version 5 of the package has been made available on CRAN having undergone a substantial makeover, which has made it more accessible and easy to use for practitioners. New functions include data augmentation procedures based on the approximate exchange algorithm for dealing with missing data, adjusted pseudolikelihood and pseudo-posterior procedures, which allow for fast approximate inference of the ERGM parameter posterior and model evidence for networks on several thousands nodes.