Bayesian Computation Research Articles

Same principle, but different computations in representing time and space

Time and space are two intertwined contexts that frame our cognition of the world and have shared mechanisms. A well-known theory on this case is “A Theory of Magnitude (ATOM)” which states that the perception of these two domains shares common mechanisms. However, evidence regarding shared computations of time and space is intermixed. To investigate this issue, we asked human subjects to reproduce time and distance intervals with saccadic eye movements in similarly designed tasks. We applied an observer model to both modalities and found underlying differences in the processing of time and space. While time and space computations are both probabilistic, adding priors to space perception minimally improved model performance, as opposed to time perception which was consistently better explained by Bayesian computations. We also showed that while both measurement and motor variability were smaller in distance than time reproduction, only the motor variability was correlated between them, as both tasks used saccadic eye movements for response. Our results suggest that time and space perception abide by the same algorithm but have different computational properties.

Dissecting Bayes: Using influence measures to test normative use of probability density information derived from a sample test.

Bayesian decision theory (BDT) is frequently used to model normative performance in perceptual, motor, and cognitive decision tasks where the possible outcomes of actions are associated with rewards or penalties. The resulting normative models specify how decision makers should encode and combine information about uncertainty and value-step by step-in order to maximize their expected reward. When prior, likelihood, and posterior are probabilities, the Bayesian computation requires only simple arithmetic operations: addition, etc. We focus on visual cognitive tasks where Bayesian computations are carried out not on probabilities but on (1) probability density functions and (2) these probability density functions are derived from samples. We break the BDT model into a series of computations and test human ability to carry out each of these computations in isolation. We test three necessary properties of normative use of pdf information derived from a sample-accuracy, additivity and influence. Influence measures allow us to assess how much weight each point in the sample is assigned in making decisions and allow us to compare normative use (weighting) of samples to actual, point by point. We find that human decision makers violate accuracy and additivity systematically but that the cost of failure in accuracy or additivity would be minor in common decision tasks. However, a comparison of measured influence for each sample point with normative influence measures demonstrates that the individual's use of sample information is markedly different from the predictions of BDT. We will show that the normative BDT model takes into account the geometric symmetries of the pdf while the human decision maker does not. An alternative model basing decisions on a single extreme sample point provided a better account for participants' data than the normative BDT model.

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.

Data-driven Stochastic Model for Quantifying the Interplay Between Amyloid-beta and Calcium Levels in Alzheimer's Disease.

The abnormal aggregation of extracellular amyloid- in senile plaques resulting in calcium dyshomeostasis is one of the primary symptoms of Alzheimer's disease (AD). Significant research efforts have been devoted in the past to better understand the underlying molecular mechanisms driving deposition and dysregulation. Importantly, synaptic impairments, neuronal loss, and cognitive failure in AD patients are all related to the buildup of intraneuronal accumulation. Moreover, increasing evidence show a feed-forward loop between and levels, i.e. disrupts neuronal levels, which in turn affects the formation of . To better understand this interaction, we report a novel stochastic model where we analyze the positive feedback loop between and using ADNI data. A good therapeutic treatment plan for AD requires precise predictions. Stochastic models offer an appropriate framework for modelling AD since AD studies are observational in nature and involve regular patient visits. The etiology of AD may be described as a multi-state disease process using the approximate Bayesian computation method. So, utilizing ADNI data from 2-year visits for AD patients, we employ this method to investigate the interplay between and levels at various disease development phases. Incorporating the ADNI data in our physics-based Bayesian model, we discovered that a sufficiently large disruption in either metabolism or intracellular homeostasis causes the relative growth rate in both and , which corresponds to the development of AD. The imbalance of ions causes disorders by directly or indirectly affecting a variety of cellular and subcellular processes, and the altered homeostasis may worsen the abnormalities of ion transportation and deposition. This suggests that altering the balance or the balance between and by chelating them may be able to reduce disorders associated with AD and open up new research possibilities for AD therapy.

A metapopulation framework integrating landscape heterogeneity to model an airborne plant pathogen: The case of brown rot of peach in France

Plant disease dynamics are driven by the concurrent interplay of host susceptibility, pathogen presence, and environmental conditions. While host susceptibility and environmental conditions can readily be characterized, the transmission of an airborne pathogen depends on the biotic and abiotic conditions of the surrounding environment. We propose an original metapopulation framework integrating landscape heterogeneity, in terms of climate and host density, where populations of plant hosts are connected via air-masses which allow pathogen dispersal. We explicitly account for climatic drivers affecting pathogen transport while modelling aerial dispersal using Lagrangian simulations, as well as host phenology and infection. We calibrate the model parameters according to the literature and using Approximate Bayesian Computation against observations of brown rot incidence in French peach orchards from 2001 to 2020 across an area of 50,000 km2. We use the model to produce maps of risk, distinguishing site dangerousness (risk of causing secondary infection in other sites) and vulnerability (risk of becoming infected) across the our study area. We demonstrate that airborne transport of Monilinia spores is essential in describing the spread of brown rot in French orchards in the considered period. We find that most dangerous and vulnerable sites are located along the Rhône Valley, due to the concurrence of high density of peach cultivation, a suitable climate and persistent airborne connections. Our work represents a first step to integrate metapopulation theory, epidemiology and air-mass movements to inform plant protection strategies at the national level. Furthermore, it could be adapted to optimize crop protection under future climate projections.

A MCMC method based on surrogate model and Gaussian process parameterization for infinite Bayesian PDE inversion

This work focuses on an inversion problem derived from parametric partial differential equations (PDEs) with an infinite-dimensional parameter, represented as a coefficient function. The objective is to estimate this coefficient function accurately despite having only noisy measurements of the PDE solution at sparse input points. Conventional methods for inversion require numerous calls to a refined PDE solver, resulting in significant computational complexity, especially for challenging PDE problems, making the inference of the coefficient function practically infeasible. To address this issue, we propose a MCMC method that combines an deep learning-based surrogate and Gaussian process parameterization to efficiently infer the posterior of the coefficient function. The surrogate model is a combination of a cost-effective coarse PDE solver and a neural network-based transformation which provides an approximate solution derived from the refined PDE solver but based on the coarse PDE solution. The coefficient function is represented by Gaussian process with finite number of spatially dependent parameters and this parametric representation will be beneficial for the preconditioned Crank-Nicolson (pCN) Markov chain Monte Carlo method to sample efficiently from the posterior distribution. Approximate Bayesian computation method is used for constructing an informative dataset for the transformation learning. Our numerical examples demonstrate the effectiveness of this approach in accurately estimating the coefficient function while significantly reducing the computational burden associated with traditional inversion techniques.

Probabilistic Offline Policy Ranking with Approximate Bayesian Computation

In practice, it is essential to compare and rank candidate policies offline before real-world deployment for safety and reliability. Prior work seeks to solve this offline policy ranking (OPR) problem through value-based methods, such as Off-policy evaluation (OPE). However, they fail to analyze special case performance (e.g., worst or best cases), due to the lack of holistic characterization of policies’ performance. It is even more difficult to estimate precise policy values when the reward is not fully accessible under sparse settings. In this paper, we present Probabilistic Offline Policy Ranking (POPR), a framework to address OPR problems by leveraging expert data to characterize the probability of a candidate policy behaving like experts, and approximating its entire performance posterior distribution to help with ranking. POPR does not rely on value estimation, and the derived performance posterior can be used to distinguish candidates in worst-, best-, and average-cases. To estimate the posterior, we propose POPR-EABC, an Energy-based Approximate Bayesian Computation (ABC) method conducting likelihood-free inference. POPR-EABC reduces the heuristic nature of ABC by a smooth energy function, and improves the sampling efficiency by a pseudo-likelihood. We empirically demonstrate that POPR-EABC is adequate for evaluating policies in both discrete and continuous action spaces across various experiment environments, and facilitates probabilistic comparisons of candidate policies before deployment.

Estimating actual SARS-CoV-2 infections from secondary data

Eminent in pandemic management is accurate information on infection dynamics to plan for timely installation of control measures and vaccination campaigns. Despite huge efforts in diagnostic testing of individuals, the underestimation of the actual number of SARS-CoV-2 infections remains significant due to the large number of undocumented cases. In this paper we demonstrate and compare three methods to estimate the dynamics of true infections based on secondary data i.e., (a) test positivity, (b) infection fatality and (c) wastewater monitoring. The concept is tested with Austrian data on a national basis for the period of April 2020 to December 2022. Further, we use the results of prevalence studies from the same period to generate (upper and lower bounds of) credible intervals for true infections for four data points. Model parameters are subsequently estimated by applying Approximate Bayesian Computation—rejection sampling and Genetic Algorithms. The method is then validated for the case study Vienna. We find that all three methods yield fairly similar results for estimating the true number of infections, which supports the idea that all three datasets contain similar baseline information. None of them is considered superior, as their advantages and shortcomings depend on the specific case study at hand.

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.

Structured Variational Approximations with Skew Normal Decomposable Graphical Models and Implicit Copulas

Although there is much recent work developing flexible variational methods for Bayesian computation, Gaussian approximations with structured covariance matrices are often preferred computationally in high-dimensional settings. This article considers approximate inference methods for complex latent variable models where the posterior is close to Gaussian, but with some skewness in the posterior marginals. We consider skew decomposable graphical models (SDGMs), which are based on the closed skew normal family of distributions, as variational approximations. These approximations can reflect the true posterior conditional independence structure and capture posterior skewness. To increase flexibility, implicit copula SDGM approximations are also developed, where elementwise transformations of an approximately standardized SDGM random vector are considered. This implicit copula extension is an important contribution of our work, and improves the accuracy of SDGM approximations for only a modest increase in computational cost. Our parameterization of the copula approximation is novel, even in the Gaussian case. Performance of the methods is examined in a number of real examples involving generalized linear mixed models and state space models. Supplemental materials including code and appendix are available online.

A Sequential Sampling Approach to the Integration of Habits and Goals

AbstractHabits often conflict with goal-directed behaviors and this phenomenon continues to attract interests from neuroscientists, experimental psychologists, and applied health psychologists. Recent computational models explain habit-goal conflicts as the competitions between two learning systems, arbitrated by a central unit. Based on recent research that combined reinforcement learning and sequential sampling, we show that habit-goal conflicts can be more parsimoniously explained by a dynamic integration of habit and goal values in a sequential sampling model, without any arbitration. A computational model was developed by extending the multialternative decision field theory with the assumptions that habits bias starting points of preference accumulation, and that goal importance and goal relevance determine sampling probabilities of goal-related attributes. Simulation studies demonstrated our approach’s ability to qualitatively reproduce important empirical findings from three paradigms – classic devaluation, devaluation with a concurrent schedule, and reversal learning, and to predict gradual changes in decision times. In addition, a parameter recovery exercise using approximate Bayesian computation showcased the possibility of fitting the model to empirical data in future research. Implications of our work for habit theories and applications are discussed.