Bayesian Inference Framework Research Articles

PC-Kriging-powered parallelizing Bayesian updating for stochastic vehicle-track dynamical system with contact force measurements and Gaussian process discrepancy model

High-precision vehicle-track coupled dynamical models play a vital role in assessing the running safety of the vehicle, tracking fatigue behavior, and establishing a digital twin for high-speed railways. This study established a high-fidelity vehicle-track coupled dynamical model as a forward solver, which was then updated in a Bayesian inference framework based on the field tests of rail irregularities and wheel/rail normal contact forces. The prediction errors corresponding to different time steps were represented through a Gaussian process (GP) model characterized by a covariance function with the Gaussian kernel to incorporate the correlation between different time steps. To cope with the considerable expense of the likelihood function calculations with large-scale loop operations and the computational burden due to the large batch of repetitive evaluations of the high-fidelity forward model involved in the stochastic sampling from the posterior probability distribution, a metamodel-powered parallelizing stochastic sampling scheme was adopted. The posterior distribution could be formulated by replacing the expensive explicit model evaluation involved in the likelihood function with a Polynomial-Chaos-Kriging (PC-Kriging) predictor providing a surrogate mapping between the wheel/rail normal contact forces and physical parameters. Finally, a parallelizing computing scheme running across multiple CPU cores on high-performance computers was realized to sample from the vectorized formula of the emulator-powered posterior distribution. Field test data from a high-speed railway in China was adopted to demonstrate that the Bayesian inference scheme can quantify the uncertainties of the core physical parameters of the high-fidelity vehicle-track coupled dynamical system by efficiently trading off accuracy and computational efficiency.

Lessons from Hubble and Spitzer: 1D Self-consistent Model Grids for 19 Hot Jupiter Emission Spectra

We present a population-level analysis of the dayside thermal emission spectra of 19 planets observed with Hubble WFC3 and Spitzer IRAC 3.6 and 4.5 μm, spanning equilibrium temperatures 1200–2700 K and 0.7–10.5 Jupiter masses. We use grids of planet-specific 1D, cloud-free, radiative–convective–thermochemical equilibrium models (1D-RCTE) combined with a Bayesian inference framework to estimate atmospheric metallicity, the carbon-to-oxygen ratio, and day-to-night heat redistribution. In general, we find that the secondary eclipse data cannot reject the physics encapsulated within the 1D-RCTE assumption parameterized with these three variables. We find a large degree of scatter in atmospheric metallicities, with no apparent trend, and carbon-to-oxygen ratios that are mainly consistent with solar or subsolar values but do not exhibit population agreement. Together, these indicate either (1) formation pathways vary over the hot and ultra-hot Jupiter population and/or (2) more accurate composition measurements are needed to identify trends. We also find a broad scatter in derived dayside temperatures that do not demonstrate a trend with equilibrium temperature. Like with composition estimates, this suggests either significant variability in climate drivers over the population and/or more precise dayside temperature measurements are needed to identify a trend. We anticipate that 1D-RCTE models will continue to provide valuable insights into the nature of exoplanet atmospheres in the era of JWST.

RadioSED I: Bayesian inference of radio SEDs from inhomogeneous surveys

Abstract We present here RadioSED, a Bayesian inference framework tailored to modelling and classifying broadband radio spectral energy distributions (SEDs) using only data from publicly-released, large-area surveys. We outline the functionality of RadioSED, with its focus on broadband radio emissions which can trace kiloparsec-scale absorption within both the radio jets and the circumgalactic medium of Active Galactic Nuclei (AGN). In particular, we discuss the capability of RadioSED to advance our understanding of AGN physics and composition within youngest and most compact sources, for which high resolution imaging is often unavailable. These young radio AGN typically manifest as peaked spectrum (PS) sources which, before RadioSED, were difficult to identify owing to the large, broadband frequency coverage typically required, and yet they provide an invaluable environment for understanding AGN evolution and feedback. We discuss the implementation details of RadioSED, and we validate our approach against both synthetic and observational data. Since the surveys used are drawn from multiple epochs of observation, we also consider the output from RadioSED in the context of AGN variability. Finally, we show that RadioSED recovers the expected SED shapes for a selection of well-characterised radio sources from the literature, and we discuss avenues for further study of these and other sources using radio SED fitting as a starting point. The scalability and modularity of this framework make it an exciting tool for multiwavelength astronomers as next-generation telescopes begin several all-sky surveys. Accordingly, we make the code for RadioSED, which is written in python, available on Github.

The role of explicit knowledge in compensating for a visuo-proprioceptive cue conflict.

It is unclear how explicit knowledge of an externally imposed mismatch between visual and proprioceptive cues of hand position affects perceptual recalibration. The Bayesian causal inference framework might suggest such knowledge should abolish the visual and proprioceptive recalibration that occurs when individuals perceive these cues as coming from the same source (their hand), while the visuomotor adaptation literature suggests explicit knowledge of a cue conflict does not eliminate implicit compensatory processes. Here we compared visual and proprioceptive recalibration in three groups with varying levels of knowledge about the visuo-proprioceptive cue conflict. All participants estimated the position of visual, proprioceptive, or combined targets related to their left index fingertip, with a 70mm visuo-proprioceptive offset gradually imposed. Groups 1, 2, and 3 received no information, medium information, and high information, respectively, about the offset. Information was manipulated using instructional and visual cues. All groups performed the task similarly at baseline in terms of variance, weighting, and integration. Results suggest the three groups recalibrated vision and proprioception differently, but there was no difference in variance or weighting. Participants who received only instructional cues about the mismatch (Group 2) did not recalibrate less, on average, than participants provided no information about the mismatch (Group 1). However, participants provided instructional cues and extra visual cues of their hands during the perturbation (Group 3) demonstrated significantly less recalibration than other groups. These findings are consistent with the idea that instructional cues alone are insufficient to override participants' intrinsic belief in common cause and reduce recalibration.

Impurity transport study based on measurement of visible wavelength high-n charge exchange transitions at W7-X

A recently installed high-speed charge exchange diagnostic at the W7-X stellarator has been used to identify several high-n Rydberg emission lines near 500 nm following impurity injections. The wavelengths of observed high-n Rydberg transitions are independent of the impurity species and originate from ions with ionization states ranging from 14+ to 45+ suggesting that this approach can be applied to a variety of heavy impurities. Moreover, little to no passive signal is observed since the high-n energy levels are unlikely to be populated by electron impact excitation. The combination of the newly developed diagnostic and the observation of high-n Rydberg states provides spatially resolved, high-speed measurements of multiple charge states which are analyzed in a Bayesian inference framework to determine both impurity diffusion and convection profiles. Measurements from the 2023 experimental campaign conclusively show high diffusion and an inward pinch in the core, well above predictions by neoclassical theory.

Element-wise parallel deep learning for structural distributed damage diagnosis by leveraging physical properties of long-gauge static strain transmissibility under moving loads

The Transmissibility Function (TF) has gained considerable interest in structural damage detection because of its relatively high sensitivity to damage and robustness to excitation. This study proposed a distributed damage diagnosis method for beam-like structures based on a long-gauge static strain TF defined as the ratio of the Fourier transform of static strain response under moving loads from a target long-gauge sensor to that from the reference sensor. It has been discovered that each long-gauge static strain TF is independent of moving loads, making it an ideal damage indicator. It exhibits direct proportionality to the ratio of bending stiffness between the two measured zones covered by the target and reference long-gauge strain sensors while being unaffected by the stiffness of any other zones not covered by these two sensors. Moreover, the TF at zero frequency was proved to be equivalent to the ratio of static strain time history areas, relying solely on the stiffness of the covered zones. Leveraged by the physical properties of long-gauge static strain TF, an element-wise parallel deep neural network architecture was developed to decompose damage diagnosis into independent sub-tasks on the element level, utilizing a variational autoencoder (VAE) in the Bayesian inference framework for extracting features from the long-gauge strain TF and a regressor for mapping the features to elemental stiffness reduction. The divide-and-conquer strategy and element-wise parallel learning architecture allow for a significant reduction in the number of labeled training samples generated based on the updated numerical baseline model as it only requires simulated scenarios involving a single damage element. The efficiency and robustness of the proposed method were demonstrated through a numerical simply supported beam and a laboratory experiment on a two-span bridge.

UAV autonomous source seeking with cumulative exposure minimization in complex hazardous environments

Considering autonomous searching for an unknown source in complex hazardous environments while balancing search efficiency and flight safety, this paper proposes a framework called source seeking with cumulative exposure minimization (SSCEM) for an unmanned aerial vehicle (UAV) equipped with gas sensors. First, the hazardous substance dispersion is formulated by using an isotropic plume model, and the stochastic sensor measurement in turbulent environments is modeled as a Poisson distribution. Second, the source term including the source location and release rate, is estimated by using a Bayesian inference framework. A particle filter is adopted to reduce the computational burden. Third, as cumulative exposure to hazardous fields can lead to airborne device failures and endanger flight safety, to achieve a reasonable trade-off among exploitation, exploration and flight safety, SSCEM for UAVs is proposed based on information theory and an interfered fluid dynamical system (IFDS), where heuristic action candidates in a continuous domain and a cost function considering cumulative exposure collectively drive the UAV to approach the unknown source location while reducing cumulative exposure, and no-fly zone avoidance is realized using the IFDS. Eventually, source seeking is efficiently performed by the UAV with no-fly zone avoidance and kinematic requirements being met, and comparative simulation results demonstrate the performance of SSCEM.

A Bayesian Spatiotemporal Modeling Approach to the Inverse Heat Conduction Problem

Abstract This study introduces a Bayesian spatiotemporal modeling approach to solve inverse heat conduction problems (IHCPs), employing penalized splines within a spatiotemporal forward model. The complexity and ill-posed nature of IHCPs, characterized by potential nonexistence, nonuniqueness, or instability of solutions, pose significant challenges for traditional methods. Addressing this, our study presents a spatiotemporal forward model that incorporates spatial, temporal, and interaction terms, accurately capturing the intricate dynamics inherent in IHCPs and using this information as a leverage to solve the inverse problem. We adopted a Bayesian inference framework for the subsequent parameter estimation problem and developed a Gibbs sampling algorithm to sample from the posterior distribution of the model's parameters, enhancing the estimation process. Through case studies on a one-dimensional (1D) heat simulation and a pool boiling experiment using multisensor thermocouple data for heat flux reconstruction, we demonstrate the model's superiority over traditional methods. The inclusion of the spatiotemporal interaction term significantly enhances model performance, indicating its potential for broader application in solving IHCPs. The application of this method in both simulated and real-world scenarios highlights its effectiveness in capturing the spatiotemporal complexities of IHCPs. This work contributes to the field by offering a robust methodology for addressing the spatial and temporal complexities inherent in IHCPs, supported by a comprehensive Bayesian inference framework and the use of a Gibbs sampling algorithm for parameter estimation.

Opponent Exploitation Based on Bayesian Strategy Inference and Policy Tracking

In a multi-agent competitive environment, it is important for an agent to detect the opponent's policy and adopt a suitable policy to exploit the opponent. Conventionally, most methods, e.g., Bayesian Policy Reuse (BPR) variants, assume the opponent adopts a fixed policy or a randomly changing policy. In this paper, we make a more realistic and reasonable assumption that the opponent may select its policy based on the previous observation. Here, we define the term “strategy” as the mapping from the previous observation to the opponent's selected policy, and we propose the Bayesian Strategy Inference (BSI) framework to infer the opponent's strategy. Furthermore, to deal with opponents who may randomly select their policies, the BSI framework is combined with an intra-episode policy tracking mechanism to construct the Bayesian Strategy Inference plus Policy Tracking (BSI-PT) algorithm. In our experiments, we design an extended batter vs. pitcher game (EBvPG) for the evaluation of the proposed BSI-PT framework. The experimental results demonstrate that BSI-PT obtains higher policy prediction accuracy and winning percentage than three other BPR variants against the opponents with a specific policy selection strategy, with a random selection strategy, or with a partially random strategy.

Bayesian model class selection of nonlinear constitutive relationships for piezoelectric energy harvesters with small set of observations

The demand for efficient energy harvesting from vibratory environments has notably increased with the proliferation of piezoelectric devices. However, mismatches between model predictions and experimental observations underpin a critical challenge: accurately modeling piezoelectric energy harvesters (PEHs) while accounting for the inherent uncertainties in their electromechanical properties. A comprehensive Bayesian inference framework is posited for identifying electromechanical properties and facilitating model class selection of nonlinear PEHs. This approach addresses uncertainties by integrating prior knowledge and experimental data to update model parameters, offering the potential to balance model complexity and predictive precision systematically. The influence of different excitation amplitudes and the number of observations employed in the framework is studied. The results demonstrated the ability to capture both linear and nonlinear behaviors, while the model class selection effectively determined the simplest constitutive models sufficient for accurate predictions, validated against varying excitation intensities. By elucidating the trade-off between model simplicity and accuracy, this method not only refines the understanding of PEH behavior under diverse operating conditions but also equips designers with a robust predictive tool. Consequently, this methodology serves to optimize the deployment of PEHs in real-world applications, such as structural health monitoring, ensuring reliable energy supply with quantifiable confidence levels.

Data-Fusion-Based Quality Enhancement for HR Measurements Collected by Wearable Sensors.

The advancements of Internet of Things (IoT) technologies have enabled the implementation of smart and wearable sensors, which can be employed to provide older adults with affordable and accessible continuous biophysiological status monitoring. The quality of such monitoring data, however, is unsatisfactory due to excessive noise induced by various disturbances, such as motion artifacts. Existing methods take advantage of summary statistics, such as mean or median values, for denoising, without taking into account the biophysiological patterns embedded in data. In this research, a functional data analysis modeling method was proposed to enhance the data quality by learning individual subjects' diurnal heart rate (HR) patterns from historical data, which were further improved by fusing newly collected data. This proposed data-fusion approach was developed based on a Bayesian inference framework. Its effectiveness was demonstrated in an HR analysis from a prospective study involving older adults residing in assisted living or home settings. The results indicate that it is imperative to conduct personalized healthcare by estimating individualized HR patterns. Furthermore, the proposed calibration method provides a more accurate (smaller mean errors) and more precise (smaller error standard deviations) HR estimation than raw HR and conventional methods, such as the mean.

Projections of Single-level and Multilevel Spinal Instrumentation Procedure Volume and Associated Costs for Medicare Patients to 2050.

Instrumented spinal fusions can be used in the treatment of vertebral fractures, spinal instability, and scoliosis or kyphosis. Construct-level selection has notable implications on postoperative recovery, alignment, and mobility. This study sought to project future trends in the implementation rates and associated costs of single-level versus multilevel instrumentation procedures in US Medicare patients aged older than 65 years in the United States. Data were acquired from the Centers for Medicare & Medicaid Services from January 1, 2000, to December 31, 2019. Procedure costs and counts were abstracted using Current Procedural Terminology codes to identify spinal level involvement. The Prophet machine learning algorithm was used, using a Bayesian Inference framework, to generate point forecasts for 2020 to 2050 and 95% forecast intervals (FIs). Sensitivity analyses were done by comparing projections from linear, log-linear, Poisson and negative-binomial, and autoregressive integrated moving average models. Costs were adjusted for inflation using the 2019 US Bureau of Labor Statistics' Consumer Price Index. Between 2000 and 2019, the annual spinal instrumentation volume increased by 776% (from 7,342 to 64,350 cases) for single level, by 329% (from 20,319 to 87,253 cases) for two-four levels, by 1049% (from 1,218 to 14,000 cases) for five-seven levels, and by 739% (from 193 to 1,620 cases) for eight-twelve levels (P < 0.0001). The inflation-adjusted reimbursement for single-level instrumentation procedures decreased 45.6% from $1,148.15 to $788.62 between 2000 and 2019, which is markedly lower than for other prevalent orthopaedic procedures: total shoulder arthroplasty (-23.1%), total hip arthroplasty (-39.2%), and total knee arthroplasty (-42.4%). By 2050, the number of single-level spinal instrumentation procedures performed yearly is projected to be 124,061 (95% FI, 87,027 to 142,907), with associated costs of $93,900,672 (95% FI, $80,281,788 to $108,220,932). The number of single-level instrumentation procedures is projected to double by 2050, while the number of two-four level procedures will double by 2040. These projections offer a measurable basis for resource allocation and procedural distribution.

Lyα Emission at z = 7–13: Clear Evolution of Lyα Equivalent Width Indicating a Late Cosmic Reionization History

We present the evolution of Lyα emission derived from 53 galaxies at z = 6.6–13.2, which have been identified by multiple JWST/NIRSpec spectroscopy programs of Early Release Science, General Observer, Director's Discretionary Time, and Guaranteed Time Observations. These galaxies fall on the star formation main sequence and are typical star-forming galaxies with UV magnitudes of −22.5 ≤ M UV ≤ −17.0. We find that 15 out of 53 galaxies show Lyα emission at the >3σ level, and we obtain Lyα equivalent width (EW) measurements and stringent 3σ upper limits for the 15 and 38 galaxies, respectively. Confirming that Lyα velocity offsets and line widths of our galaxies are comparable to those of low-redshift Lyα emitters, we investigate the redshift evolution of the Lyα EW. We find that Lyα EWs statistically decrease toward high redshifts on the Lyα EW versus the M UV plane for various probability distributions of the uncertainties. We then evaluate neutral hydrogen fractions x H I with the redshift evolution of the Lyα EW and the cosmic reionization simulation results on the basis of a Bayesian inference framework, and obtain x H I < 0.79, = 0.62 − 0.36 + 0.15 ?> , and 0.93 − 0.07 + 0.04 ?> at z ∼ 7, 8, and 9–13, respectively. These moderately large x H I values are consistent with the Planck cosmic microwave background optical depth measurement and previous x H I constraints from galaxy and QSO Lyα damping wing absorption and strongly indicate a late reionization history. Such a late reionization history suggests that major sources of reionization would emerge late and be hosted by moderately massive halos compared with the widely accepted picture of abundant low-mass objects for the sources of reionization.

Discussion on "Bayesian meta-analysis of penetrance for cancer risk" by Thanthirige Lakshika M. Ruberu, Danielle Braun, Giovanni Parmigiani, and Swati Biswas.

Ruberu etal. (2023) introduce an elegant approach to fit a complicated meta-analysis problem with diverse reporting modalities into the framework of hierarchical Bayesian inference. We discuss issues related to some of the involved parametric model assumptions.

Structural reliability analysis with extremely small failure probabilities: A quasi-Bayesian active learning method

The concept of Bayesian active learning has recently been introduced from machine learning to structural reliability analysis. Although several specific methods have been successfully developed, significant efforts are still needed to fully exploit their potential and to address existing challenges. This work proposes a quasi-Bayesian active learning method, called ‘Quasi-Bayesian Active Learning Cubature’, for structural reliability analysis with extremely small failure probabilities. The method is established based on a cleaver use of the Bayesian failure probability inference framework. To reduce the computational burden associated with the exact posterior variance of the failure probability, we propose a quasi posterior variance instead. Then, two critical elements for Bayesian active learning, namely the stopping criterion and the learning function, are developed subsequently. The stopping criterion is defined based on the quasi posterior coefficient of variation of the failure probability, whose numerical solution scheme is also tailored. The learning function is extracted from the quasi posterior variance, with the introduction of an additional parameter that allows multi-point selection and hence parallel distributed processing. By testing on four numerical examples, it is empirically shown that the proposed method can assess extremely small failure probabilities with desired accuracy and efficiency.

Uncertainty Quantification in Heterogeneous Treatment Effect Estimation with Gaussian-Process-Based Partially Linear Model

Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in treatment effect estimation to support decision-making in a relatively small sample size setting. Our proposed model places Gaussian process priors on the nonparametric components of a semiparametric model called a partially linear model. This model formulation has three advantages. First, we can analytically compute the posterior distribution of a treatment effect without relying on the computationally demanding posterior approximation. Second, we can guarantee that the posterior distribution concentrates around the true one as the sample size goes to infinity. Third, we can incorporate prior knowledge about a treatment effect into the prior distribution, improving the estimation efficiency. Our experimental results show that even in the small sample size setting, our method can accurately estimate the heterogeneous treatment effects and effectively quantify its estimation uncertainty.

Multimorbidity analysis with low condition counts: a robust Bayesian approach for small but important subgroups

BackgroundRobustly examining associations between long-term conditions may be important in identifying opportunities for intervention in multimorbidity but is challenging when evidence is limited. We have developed a Bayesian inference framework that is robust to sparse data and used it to quantify morbidity associations in the oldest old, a population with limited available data. MethodsWe conducted a retrospective cross-sectional study of a representative dataset of primary care patients in Scotland as of March 2007. We included 40 long-term conditions and studied their associations in 12,009 individuals aged 90 and older, stratified by sex (3,039 men, 8,970 women). We analysed associations obtained with Relative Risk (RR), a standard measure in the literature, and compared them with our proposed measure, Associations Beyond Chance (ABC). To enable a broad exploration of interactions between long-term conditions, we built networks of association and assessed differences in their analysis when associations are estimated by RR or ABC. FindingsOur Bayesian framework was appropriately more cautious in attributing association when evidence is lacking, particularly in uncommon conditions. This caution in reporting association was also present in reporting differences in associations between sex and affected the aggregated measures of multimorbidity and network representations. InterpretationIncorporating uncertainty into multimorbidity research is crucial to avoid misleading findings when evidence is limited, a problem that particularly affects small but important subgroups. Our proposed framework improves the reliability of estimations of associations and, more in general, of research into disease mechanisms and multimorbidity. FundingNational Institute for Health and Care Research.

Data-Driven Bayesian Inference for Stochastic Model Identification of Nonlinear Aeroelastic Systems

The objective of this work is to propose a data-driven Bayesian inference framework to efficiently identify parameters and select models of nonlinear aeroelastic systems. The framework consists of the use of Bayesian theory together with advanced kriging surrogate models to effectively represent the limit cycle oscillation response of nonlinear aeroelastic systems. Three types of sampling methods, namely, Markov chain Monte Carlo, transitional Markov chain Monte Carlo, and the sequential Monte Carlo sampler, are implemented into Bayesian model updating. The framework has been demonstrated using a nonlinear wing flutter test rig. It is modeled by a two-degree-of-freedom aeroelastic system and solved by the harmonic balance methods. The experimental data of the flutter wing is obtained using control-based continuation techniques. The proposed methodology provided up to a 20% improvement in accuracy compared to conventional deterministic methods and significantly increased computational efficiency in the updating and uncertainty quantification processes. Transitional Markov chain Monte Carlo was identified as the optimal choice of sampling method for stochastic model identification. In selecting alternative nonlinear models, multimodal solutions were identified that provided a closer representation of the physical behavior of the complex aeroelastic system than a single solution.

Assessing the dynamics and impact of COVID-19 vaccination on disease spread: A data-driven approach

The COVID-19 pandemic has significantly impacted global health, social, and economic situations since its emergence in December 2019. The primary focus of this study is to propose a distinct vaccination policy and assess its impact on controlling COVID-19 transmission in Malaysia using a Bayesian data-driven approach, concentrating on the year 2021. We employ a compartmental Susceptible-Exposed-Infected-Recovered-Vaccinated (SEIRV) model, incorporating a time-varying transmission rate and a data-driven method for its estimation through an Exploratory Data Analysis (EDA) approach. While no vaccine guarantees total immunity against the disease, and vaccine immunity wanes over time, it is critical to include and accurately estimate vaccine efficacy, as well as a constant vaccine immunity decay or wane factor, to better simulate the dynamics of vaccine-induced protection over time. Based on the distribution and effectiveness of vaccines, we integrated a data-driven estimation of vaccine efficacy, calculated at 75% for Malaysia, underscoring the model's realism and relevance to the specific context of the country. The Bayesian inference framework is used to assimilate various data sources and account for underlying uncertainties in model parameters. The model is fitted to real-world data from Malaysia to analyze disease spread trends and evaluate the effectiveness of our proposed vaccination policy. Our findings reveal that this distinct vaccination policy, which emphasizes an accelerated vaccination rate during the initial stages of the program, is highly effective in mitigating the spread of COVID-19 and substantially reducing the pandemic peak and new infections. The study found that vaccinating 57–66% of the population (as opposed to 76% in the real data) with a better vaccination policy such as proposed here is able to significantly reduce the number of new infections and ultimately reduce the costs associated with new infections. The study contributes to the development of a robust and informative representation of COVID-19 transmission and vaccination, offering valuable insights for policymakers on the potential benefits and limitations of different vaccination policies, particularly highlighting the importance of a well-planned and efficient vaccination rollout strategy. While the methodology used in this study is specifically applied to national data from Malaysia, its successful application to local regions within Malaysia, such as Selangor and Johor, indicates its adaptability and potential for broader application. This demonstrates the model's adaptability for policy assessment and improvement across various demographic and epidemiological landscapes, implying its usefulness for similar datasets from various geographical regions.

Inference of the Paramentes of a Bioreactor via Approximate Bayesian Evidence

In the context of the recent water crisis, the development and improvement of technologies for efficiently treating wastewater becomes increasingly necessary. Aligned with this, the activated sludge process is widely used in biological wastewater treatment plants to remove carbon and nutrients from wastewater. Although significant advancements have been achieved in recent years in modelling these processes to improve their performance and energy efficiency, the models are still complex and difficult to calibrate using data from real plants. In this work, we use Bayesian inference frameworks to estimate the parameters of the activated sludge process. We employ Gaussian processes to estimate the solution to the differential equations of the activated sludge process model and we fit this estimation to manufactured data of the observations of the wastewater. We find that the use of the Bayesian inference framework outperforms the classical approach in scenarios where measurements are more strongly affected by noise.