Bayesian Inference Model Research Articles

Sustained EEG responses to rapidly unfolding stochastic sounds reflect Bayesian inferred reliability tracking.

How does the brain track and process rapidly changing sensory information? Current computational accounts suggest that our sensations and decisions arise from the intricate interplay between bottom-up sensory signals and constantly changing expectations regarding the statistics of the surrounding world. A significant focus of recent research is determining which statistical properties are tracked by the brain as it monitors the rapid progression of sensory information. Here, by combining EEG (three experiments N ≥ 22 each) and computational modelling, we examined how the brain processes rapid and stochastic sound sequences that simulate key aspects of dynamic sensory environments. Passively listening participants were exposed to structured tone-pip arrangements that contained transitions between a range of stochastic patterns. Predictions were guided by a Bayesian predictive inference model. We demonstrate that listeners automatically track the statistics of unfolding sounds, even when these are irrelevant to behaviour. Transitions between sequence patterns drove a shift in the sustained EEG response. This was observed to a range of distributional statistics, and even in situations where behavioural detection of these transitions was at floor. These observations suggest that the modulation of the EEG sustained response reflects a process of belief updating within the brain. By establishing a connection between the outputs of the computational model and the observed brain responses, we demonstrate that the dynamics of these transition-related responses align with the tracking of "precision" - the confidence or reliability assigned to a predicted sensory signal - shedding light on the intricate interplay between the brain's statistical tracking mechanisms and its response dynamics.

Impact-force identification using deep learning and Bayesian inference with application on pipeline structures

Structures like bridges and pipelines are vulnerable to impacts from various sources, such as falling debris, over-height vehicles, or floating objects, which can compromise their integrity. Traditional inspection methods are costly and complex and can lead to economic losses due to shutdowns. This research introduces a probabilistic and more efficient approach by combining deep learning and Bayesian inference techniques to accurately measure and analyze these impacts, aiming to enhance the longevity and safety of these structures while mitigating potential critical failures. In this methodology, a novel two-stage approach is implemented to resolve the inverse problem of identifying impact forces on structures. Initially, a convolutional neural network (CNN) classifier for each of the four sensors is employed to determine the impacting material (aluminum, rubber, plastic). This classification stage utilizes ground truth data to identify the nature of the impact accurately. Following this, the preclassified data, categorized by the actual impacting materials, is directed into one of three 5-layer artificial neural networks (ANNs), each designated for a different impacting material. The ANNs act as surrogate models for Bayesian inference to determine impact force and position, resulting in 12 specialized models, each corresponding to a specific combination of sensor and tip type. The ANNs were evaluated using mean squared error, showing precise predictions of the pipeline’s acceleration frequency signals, while the CNN classifier achieved over 99% F1 scores. Using ANN and CNN results, the approximate Bayesian computation with subset simulation technique showed over 90% precision with 7% uncertainty in inferring impact force and 92% precision with 2% uncertainty in determining the impact position along the pipe. Data fusion, combining sensor responses, further improved precision and reduced uncertainty, achieving over 92% precision with 8% uncertainty for impact force and over 98% precision with 1.8% uncertainty for depth. These results demonstrate the method’s reliability and effectiveness in accurately identifying impact forces and locations, even with a single distant sensor.

Digital Thread-Based Optimisation Framework for Aeronautical Structures: A Vertical Tail Plane Use Case

In this modern era, the constant increase in computational and sensing power has lead to the development of multiple data-driven concepts. Amongst these, the ‘digital thread’ is an architecture that aims at optimising the knowledge of a system by merging prior knowledge of the product with information from multiple stages of its lifecycle in order to improve the performance of new products to be designed, thanks to the increased accuracy of this updated knowledge. Even though the use of these data-driven architectures is becoming increasingly widespread, most of the corresponding developments remain currently limited to the component level. In this respect, this article extends the application of the digital thread from the component level to the structural assembly level and enriches it with additional multi-physics considerations and non-linear failure constraints. To this end, it details the development of a digital thread dedicated to an aircraft vertical tail plane structure made of carbon fibre reinforced polymer, as well as the tools and models required to implement such an approach using Bayesian inference, multi-physics simulations, and empirical models.

INLA$$^+$$: approximate Bayesian inference for non-sparse models using HPC

INLA$$^+$$: approximate Bayesian inference for non-sparse models using HPC

Probabilistic modeling of ballistic penetration in reinforced concrete panels

AbstractStudying ballistic impact on reinforced concrete (RC) structures is essential for enhancing the safety and cost‐effectiveness of these structures. The depth of penetration (DOP) and residual velocity (RV) of projectiles are critical design parameters requiring precise quantification to improve the ballistic‐resistant design. Traditional empirical models are available for quantifying these parameters but are deterministic and often yield inaccurate results due to the inherent uncertainties in ballistic impacts. This paper introduces a probabilistic approach to quantify DOP and RV accurately. Bayesian inference models are developed using dimensionless explanatory functions to estimate these parameters in RC panels under hard projectile impacts, accounting for associated uncertainties. Numerical modeling is performed using LS‐Dyna, and the model is validated against experimental data from past studies. Data from refined numerical simulations, along with available experiments from the literature, are utilized to develop the probabilistic models. The findings reveal the significant influence of projectile and concrete properties, as well as the projectile's incidence angle, on DOP and RV. The probabilistic models developed are validated with previous experimental results, demonstrating their reliability and accuracy. Consequently, robust design formulae are proposed for estimating DOP and RV for RC panels under hard projectile impacts, providing a valuable tool for precise impact assessments in engineering applications.

Assessment of time-series-derived no-flood references for sar-based Bayesian flood mapping

ABSTRACT The systematic mapping of flood events with Synthetic Aperture Radar (SAR) data is an area of growing importance. One global flood mapping algorithm utilized within the Copernicus Emergency Management Service is based upon a Bayesian Inference model that compares a SAR image to a simulated reference image representing no-flood conditions. This no-flood reference image is at present generated using a harmonic model trained using historic time series, thereby producing a backscatter image representing mean seasonal conditions. One known weakness of this approach is that it cannot account for changing environmental conditions from year to year, potentially causing an overestimation of flood extent during dry periods, snow and frost, or other effects causing lower-than normal backscatter. To minimize this detrimental effect, we introduce an exponential filter to estimate the no-flood reference image by weighting the most recent backscatter observations according to their time difference to the current SAR acquisition. We compare the performance of the new exponential filter model against the harmonic model using a novel time-series flood mapping assessment approach. First, we assess their predictions against the actual SAR image time series for the year 2023. Then, we analyze the false positive rate of the corresponding flood maps generated to ensure the robustness of the automated algorithm outside of flood events. Furthermore, we perform qualitative and quantitative analyses of flood maps matching with semi-automatic results from Copernicus Emergency Management Services and Sentinel Asia as a reference. Our time-series analysis confirms increased false positive rates due to well-known environmental drivers and highlights issues with agricultural overestimation. In this regard, the time-series comparisons of the no-flood reference models show a clear improvement in the TU Wien algorithm with the exponential filter, effectively reducing false positive rates on non-flooded scenes in most study sites. The exponential filter performed better than the harmonic model in most flooded scenes, where sites show generally improved Critical Success Index and User’s accuracy. However, the exponential filter model has difficulties with sites with prolonged floods in the time series, requiring further development. Overall, the exponential filter no-flood reference model shows great promise for improved global near-real-time flood mapping.

Optimizing Large-Scale Educational Assessment with a "Divide-and-Conquer" Strategy: Fast and Efficient Distributed Bayesian Inference in IRT Models.

With the growing attention on large-scale educational testing and assessment, the ability to process substantial volumes of response data becomes crucial. Current estimation methods within item response theory (IRT), despite their high precision, often pose considerable computational burdens with large-scale data, leading to reduced computational speed. This study introduces a novel "divide- and-conquer" parallel algorithm built on the Wasserstein posterior approximation concept, aiming to enhance computational speed while maintaining accurate parameter estimation. This algorithm enables drawing parameters from segmented data subsets in parallel, followed by an amalgamation of these parameters via Wasserstein posterior approximation. Theoretical support for the algorithm is established through asymptotic optimality under certain regularity assumptions. Practical validation is demonstrated using real-world data from the Programme for International Student Assessment. Ultimately, this research proposes a transformative approach to managing educational big data, offering a scalable, efficient, and precise alternative that promises to redefine traditional practices in educational assessments.

Evaluating the predictive power of combined gene expression dynamics from single cells on antibiotic survival.

Heteroresistance can allow otherwise drug-susceptible bacteria to survive and resume growth after antibiotic exposure. This temporary form of antibiotic tolerance can be caused by the upregulation of stress response genes or a decrease in cell growth rate. However, it is not clear how expression of multiple genes contributes to the tolerance phenotype. By using fluorescent reporters for stress related genes, we conducted real time measurements of expression prior to, during, and after antibiotic exposure. We first identified relationships between growth rate and reporter levels based on auto and cross correlation analysis, revealing consistent patterns where changes in growth rate were anticorrelated with fluorescence following a delay. We then used pairs of stress gene reporters and time lapse fluorescence microcopy to measure the growth rate and reporter levels in cells that survived or died following antibiotic exposure. Using these data, we asked whether combined information about reporter expression and growth rate could improve our ability to predict whether a cell would survive or die following antibiotic exposure. We developed a Bayesian inference model to predict how the combination of dual reporter expression levels and growth rate impact ciprofloxacin survival in Escherichia coli . We found clear evidence of the impact of growth rate and the gadX promoter activity on survival. Unexpectedly, our results also revealed examples where additional information from multiple genes decreased prediction accuracy, highlighting an important and underappreciated effect that can occur when integrating data from multiple simultaneous measurements.

Bad Local Minima Exist in the Stochastic Block Model

We study the disassortative stochastic block model with three communities, a well-studied model of graph partitioning and Bayesian inference for which detailed predictions based on the cavity method exist (Decelle et al. in Phys Rev E 84:066106, 2011). We provide strong evidence that for a part of the phase where efficient algorithms exist that approximately reconstruct the communities, inference based on maximum a posteriori (MAP) fails. In other words, we show that there exist modes of the posterior distribution that have a vanishing agreement with the ground truth. The proof is based on the analysis of a graph colouring algorithm from Achlioptas and Moore (J Comput Syst Sci 67:441–471, 2003).

SpatialGEV: Fast Bayesian inference for spatial extreme value models in R

SpatialGEV: Fast Bayesian inference for spatial extreme value models in R

A general Bayesian algorithm for the autonomous alignment of beamlines.

Autonomous methods to align beamlines can decrease the amount of time spent on diagnostics, and also uncover better global optima leading to better beam quality. The alignment of these beamlines is a high-dimensional expensive-to-sample optimization problem involving the simultaneous treatment of many optical elements with correlated and nonlinear dynamics. Bayesian optimization is a strategy of efficient global optimization that has proved successful in similar regimes in a wide variety of beamline alignment applications, though it has typically been implemented for particular beamlines and optimization tasks. In this paper, we present a basic formulation of Bayesian inference and Gaussian process models as they relate to multi-objective Bayesian optimization, as well as the practical challenges presented by beamline alignment. We show that the same general implementation of Bayesian optimization with special consideration for beamline alignment can quickly learn the dynamics of particular beamlines in an online fashion through hyperparameter fitting with no prior information. We present the implementation of a concise software framework for beamline alignment and test it on four different optimization problems for experiments on X-ray beamlines at the National Synchrotron Light Source II and the Advanced Light Source, and an electron beam at the Accelerator Test Facility, along with benchmarking on a simulated digital twin. We discuss new applications of the framework, and the potential for a unified approach to beamline alignment at synchrotron facilities.

Bayesian blockwise inference for joint models of longitudinal and multistate data with application to longitudinal multimorbidity analysis.

Multistate models provide a useful framework for modelling complex event history data in clinical settings and have recently been extended to the joint modelling framework to appropriately handle endogenous longitudinal covariates, such as repeatedly measured biomarkers, which are informative about health status and disease progression. However, the practical application of such joint models faces considerable computational challenges. Motivated by a longitudinal multimorbidity analysis of large-scale UK health records, we introduce novel Bayesian inference approaches for these models that are capable of handling complex multistate processes and large datasets with straightforward implementation. These approaches decompose the original estimation task into smaller inference blocks, leveraging parallel computing and facilitating flexible model specification and comparison. Using extensive simulation studies, we show that the proposed approaches achieve satisfactory estimation accuracy, with notable gains in computational efficiency compared to the standard Bayesian estimation strategy. We illustrate our approaches by analysing the coevolution of routinely measured systolic blood pressure and the progression of three important chronic conditions, using a large dataset from the Clinical Practice Research Datalink Aurum database. Our analysis reveals distinct and previously lesser-known association structures between systolic blood pressure and different disease transitions.

A Comprehensive Review of Statistical Methods in Microbiology and epidemiology: A Data-Driven Approach

The rapid growth of computational power and big data analytics has transformed the landscape of statistical methods in microbiology and epidemiology. Advanced techniques such as machine learning, Bayesian inference, and network modeling are now being used alongside traditional statistical approaches. These methods offer unprecedented precision in identifying microbial patterns, tracking infectious diseases, and predicting outbreaks. This review highlights recent advances in statistical tools used in microbiology and epidemiology, particularly in analyzing antibiotic resistance, viral mutation rates, and epidemiological forecasting models for global pandemics such as COVID-19. The integration of novel statistical methodologies has improved our understanding of complex microbial interactions, resistance evolution, and the dynamics of infectious disease spread, enabling more informed public health interventions.

Herd behavior in public goods games.

The problem of free-riding arises when individuals benefit from a shared resource, service, or public good without contributing proportionately to its provision. This conduct often leads to a collective action problem, as individuals pursue personal gains while relying on the contributions of others. In this study, we present a Bayesian inference model to elucidate the behavior of participants in a public goods game, a conceptual framework that captures the essence of the free-riding problem. Here, individuals possess information on the distribution of group donations to the public good. Our model is grounded in the premise that individuals strive to harmonise their actions with the group's donation patterns. Our model is able to replicate behavioral patterns that resemble those observed in experiments with midsized groups (100 people), but fails to replicate those for larger scales (1000 people). Our results suggest that, in these scenarios, humans prefer imitation and convergence behaviors over profit optimization. These insights contribute to understanding how cooperation is achieved through alignment with group behavior.

Imprecise probabilistic inference from sequential data.

Although the Bayesian paradigm is an important benchmark in studies of human inference, the extent to which it provides a useful framework to account for human behavior remains debated. We document systematic departures from Bayesian inference under correct beliefs, even on average, in the estimates by experimental subjects of the probability of a binary event following observations of successive realizations of the event. In particular, we find underreaction of subjects' estimates to the evidence ("conservatism") after only a few observations and at the same time overreaction after longer sequences of observations. This is not explained by an incorrect prior nor by many common models of Bayesian inference. We uncover the autocorrelation in estimates, which suggests that subjects carry imprecise representations of the decision situations, with noise in beliefs propagating over successive trials. But even taking into account these internal imprecisions and assuming various incorrect beliefs, we find that subjects' updates are inconsistent with the rules of Bayesian inference. We show how subjects instead considerably economize on the attention that they pay to the information relevant to the decision, and on the degree of control that they exert over their precise response, while giving responses fairly adapted to the task. A "noisy-counting" model of probability estimation reproduces the several patterns we exhibit in subjects' behavior. In sum, human subjects in our task perform reasonably well while greatly minimizing the amount of information that they pay attention to. Our results emphasize that investigating this economy of attention is crucial in understanding human decisions. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Parallel Sampling of Decomposable Graphs Using Markov Chains on Junction Trees

Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is straightforward in this setup, inferring the underlying graph is a challenge driven by the computational difficulty in exploring the space of decomposable graphs. This work makes two contributions to address this problem. First, we provide sufficient and necessary conditions for when multi-edge perturbations maintain decomposability of the graph. Using these, we characterize a simple class of partitions that efficiently classify all edge perturbations by whether they maintain decomposability. Second, we propose a novel parallel nonreversible Markov chain Monte Carlo sampler for distributions over junction tree representations of the graph. At every step, the parallel sampler executes simultaneously all edge perturbations within a partition. Through simulations, we demonstrate the efficiency of our new edge perturbation conditions and class of partitions. We find that our parallel sampler yields improved mixing properties in comparison to the single-move variate, and outperforms current state-of-the-art methods in terms of accuracy and computational efficiency. The implementation of our work is available in the Python package parallelDG. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

New Analytical Paradigm to Determine Concentration of Brown Carbon and Its Sample-by-Sample Mass Absorption Efficiency.

Brown carbon (BrC) has a substantial direct radiative effect, but current estimates of its impact on radiative balance are highly uncertain due to a lack of measurements of its light-absorbing properties, such as mass absorption efficiency (MAE). Here, we present a new analytical paradigm based on a Bayesian inference (BI) model that takes multiwavelength aethalometer measurements and total carbon data to resolve the concentrations of black carbon and BrC, and MAEs of BrC on a sample-by-sample basis. Hourly MAEs, unattainable in previous studies, can now be calculated, enabling the first-time observation of the darkening-bleaching dynamics of BrC in response to photochemical transformation. We demonstrate the application of this BI model to analyze measurements collected over one year (2021-2022) in Hong Kong. Diel variations in MAE370nm of BrC reveal a darkening-to-bleaching transition occurring between 8 and 10 O'clock when the solar irradiance ranges from 30 to 400 W m-2. Furthermore, we consistently observe an increase in MAE370nm of BrC with nitrogen oxide concentrations, suggesting the enhanced formation of nitrogenous organics. This BI model-based data analysis would bring forth a breakthrough in amassing observation data of BrC and its MAEs in diverse ambient environments and with high time resolution.

Bayesian Inference for SIS Type Epidemic Model by Skellam’s Distribution with Real Application to COVID-19

Bayesian Inference for SIS Type Epidemic Model by Skellam’s Distribution with Real Application to COVID-19

A Bayesian inference model can predict the effects of attention on the serial dependence in heading estimation from optic flow.

It has been demonstrated that observers can accurately estimate their self-motion direction (i.e., heading) from optic flow, which can be affected by attention. However, it remains unclear how attention affects the serial dependence in the estimation. In the current study, participants conducted two experiments. The results showed that the estimation accuracy decreased when attentional resources allocated to the heading estimation task were reduced. Additionally, the estimates of currently presented headings were biased toward the headings of previously seen headings, showing serial dependence. Especially, this effect decreased (increased) when the attentional resources allocated to the previously (currently) seen headings were reduced. Furthermore, importantly, we developed a Bayesian inference model, which incorporated attention-modulated likelihoods and qualitatively predicted changes in the estimation accuracy and serial dependence. In summary, the current study shows that attention affects the serial dependence in heading estimation from optic flow and reveals the Bayesian computational mechanism behind the heading estimation.

A performance-based ballistic design framework for RC panels and a probabilistic model for crater quantification

Ballistic design is crucial for widely utilised concrete structures in today’s unpredictable world. In the past, extensive experimental and numerical studies have investigated concrete panels, resulting in design guidelines and empirical formulations for local damage parameters. However, with the advent of performance-based design, notably in seismic design, the ballistic design of concrete structures lacks a comprehensive design philosophy. Additionally, deterministic empirical formulations for local damage parameters, particularly in the case of reinforced concrete (RC) panels’ crater formation, necessitate a probabilistic treatment. Consequently, this paper addresses the need for a well-defined ballistic design philosophy for concrete structures and introduces a probabilistic approach for crater quantification. Firstly, a novel multi-level and multi-parameter performance-based design framework for RC panels is proposed, centred on damage states, namely depth of penetration and crater area. This framework establishes an innovative design philosophy featuring four damage levels for each state. Secondly, using dimensionless explanatory functions, a Bayesian inference model is developed to estimate the crater diameter in RC panels under hard projectile impact, accounting for the associated uncertainties. LS-Dyna is used for numerical modelling of RC panels and rigid projectiles. The numerical models are validated with the experimental data and are utilised to develop the probabilistic model. This study reveals the profound influence of projectile and concrete properties in addition to the incidence angle of the projectile on crater formation. The developed probabilistic model is validated with experimental results demonstrating its reliability and accuracy. Consequently, a reliable design formula for estimating crater diameter for RC panels under hard projectile impact is proposed in addition to the novel ballistic design framework.