Bayesian Formalism Research Articles

Improving Error Estimates for Evaluating Satellite-Based Atmospheric CO2 Measurement Concepts through Numerical Simulations

To assess the accuracy of satellite monitoring of anthropogenic CO2 emissions, inversions of satellite data in SWIR are usually combined with the assimilation of the total CO2 column into a Kalman filter that reconstructs the sources and sinks of atmospheric CO2. To provide error estimates of the total CO2 column for multi-month assimilation experiments of simulated satellite data, we parametrise these errors using linear regressions. These regression are obtained from a database that links meteorological situations, albedos, and aerosols to the errors in the inversion of the total CO2 column based on simulated satellite data for those conditions. The errors in this database are explicitly computed using the Bayesian estimation formalism, and the linear regressions are optimised by selecting appropriate predictors and predictants. For different levels of measurement noise, error simulations are performed over a period of several months using the albedo and aerosol data from MODIS.

Bayesian analysis of 1D [formula omitted]H-NMR spectra

Extracting spin system parameters from 1D high resolution 1H-NMR spectra can be an intricate task requiring sophisticate methods. With a few exceptions methods to perform such a total line shape analysis commonly rely on local optimization techniques which for increasing complexity of the underlying spin system tend to reveal local solutions. In this work we propose a full Bayesian modeling approach based on a quantum mechanical model of the spin system. The Bayesian formalism provides a global optimization strategy which allows to efficiently include prior knowledge about the spin system or to incorporate additional constraints concerning the parameters of interest. The proposed algorithm has been tested on synthetic and real 1D 1H-NMR data for various spin systems with increasing complexity. The results show that the Bayesian algorithm provides accurate estimates even for complex spectra with many overlapping regions, and that it can cope with symmetry induced local minima. By providing an unbiased estimate of the model evidence the proposed algorithm furthermore offers a way to discriminate between different spin system candidates.

Extending the quantum tomography of a quasi-photon-number-resolving detector

The ability to discriminate the number of photons in a radiation field has a critical role in the implementation of quantum optical technologies. True photon-number-resolving detectors are rare and complex devices, while a quasi-photon-number-resolving detector (qPNRD) is a practical alternative for real-world applications. Our qPNRD is composed of a fiber demultiplexer and individual non-photon-number-resolving detectors. We perform quantum tomography on our qPNRD based on the positive operator-valued measure and extend the analysis using the Bayesian formalism to uncover how the measurement influences knowledge of the measured photon probability distribution.

Optimizing one-axis twists for variational Bayesian quantum metrology

Quantum metrology and sensing seek advantages in estimating an unknown parameter of some quantum state or channel, using entanglement such as spin squeezing produced by one-axis twists or other quantum resources. In particular, qubit phase estimation, or rotation sensing, appears as a ubiquitous problem with applications to electric field sensing, magnetometry, atomic clocks, and gyroscopes. By adopting the Bayesian formalism to the phase estimation problem to account for limited initial knowledge about the value of the phase, we formulate variational metrology and treat the state preparation (or encoding) and measurement (or decoding) procedures as parameterized quantum circuits. It is important to understand how effective various parametrized protocols are as well as how robust they are to the effects of complex noise such as spatially correlated noise. First, we propose a family of parametrized encoding and decoding protocols called arbitrary-axis twist ansatzes, and show that it can lead to a substantial reduction in the number of one-axis twists needed to achieve a target estimation error. Furthermore, we demonstrate that the estimation error associated with these strategies decreases with system size in a faster manner than classical (or no-twist) protocols, even in the less-explored regimes where the prior information is limited. Last, using a polynomial-sized tensor network algorithm, we numerically analyze practical variational metrology beyond the symmetric subspace of a collective spin and find that quantum advantage persists for the arbitrary-axis twist ansatzes with a few one-axis twists and smaller total twisting angles for practically relevant noise levels. Published by the American Physical Society 2024

Efficient real-time positioning using Bayesian analysis and magnetic anomaly field

Despite the prevalence of well-established and explored navigation systems, alternative localization methods are currently the focus of intensive research. This interest is driven by geopolitical challenges and increasingly sophisticated applications of mobile robots and uncrewed aerial vehicles. This study investigates the problem of real-time positioning in GPS-denied environments. Based on the mapped magnetic anomaly field and using Bayesian formalism for data fusion, the localization obtained from embedded sensors is corrected to reduce cumulative errors. The proposed method has minimal computational cost and a minimal number of tunable parameters. The paper introduces it and demonstrates its effectiveness in a laboratory study. Experimental tests, using a system equipped with an Inertial Measurement Unit, demonstrated a significant reduction in localization uncertainty. The improvement was especially notable in areas with large, smooth variations in the magnetic field. Finally, the accuracy of the method is analyzed, and its performance is compared to a particle filter.

A hierarchical Bayesian network-based semi-mechanistic model for handling data variabilities in dynamical process systems

This work presents a hierarchical Bayesian network-based model for handling dynamic nature, data variabilities, and information fusion in a dynamical process system. The overall dynamics has been captured by physics-based models while uncertainty and local variabilities in the model parameters have been accounted for by using a hierarchical Bayesian network formalism. The resulting semi-mechanistic model has been investigated in two cases, a simulated case of an enzymatic reaction system and a real-world scenario of pandemic risk forecasting. The first case study on the enzymatic reaction system shows effectiveness of the proposed semi-mechanistic framework in a closed system with limited data from different sources. The second case illustrates scope of the proposed semi-mechanistic framework to open systems by investigating transmission of disease under evolving conditions of the advent of multiple waves of a pandemic outbreak. The findings have been presented in terms of the most probable values and credible intervals that account for data variabilities in different scenarios. The model is benchmarked and validated for the fatality forecast of the Coronavirus Disease of 2019 by the observed data and benchmark models reported by the Center for Disease Prevention and Control of the United States [https://covid.cdc.gov/covid-data-tracker/#datatracker-home].

Measurements-based constrained control optimization in presence of uncertainties with application to the driver commands for high-speed trains

The railway world is undergoing major changes. The advent of new technologies allows us to rethink the train system and face new challenges, but one must not forget all the ecological constraints that are now accentuated by the increase in energy costs. This paper focuses on the optimization of the driver commands to limit the energy consumption of the trains under punctuality and security constraints. This problem falls within the framework of control optimization problems for nonlinear dynamic mechanical systems in the presence of constraints and uncertainties. A four-step approach is then proposed in this paper to solve this problem: (1) the introduction of simplified and fast-to-evaluate models to model the nonlinear dynamic behavior of the train and its energy consumption; (2) the identification in a Bayesian formalism of the parameters on which these models depend from on-track measurements on commercial trains; (3) the reformulation of the optimization problem so that it integrates the uncertainties related to an imperfect knowledge of these estimated parameters; (4) the resolution of the optimization problem using evolutionary algorithms. The main specificity of this work lies in the fact that not only the objective function to be minimized, here the energy consumed by the train, is impacted by the uncertainties, but also the admissibility constraints of the solution, here punctuality and operating safety. The integration of the uncertainties in the search for the control function is thus not trivial and requires several original adaptations in order to make the final optimization problem well posed.

Probabilistic Logic Programming Semantics For Procedural Content Generation

Research in procedural content generation (PCG) has recently heralded two major methodologies: machine learning (PCGML) and declarative programming. The former shows promise by automating the specification of quality criteria through latent patterns in data, while the latter offers significant advantages for authorial control. In this paper we propose the use of probabilistic logic as a unifying framework that combines the benefits of both methodologies. We propose a Bayesian formalization of content generators as probability distributions and show how common PCG tasks map naturally to operations on the distribution. Further, through a series of experiments with maze generation, we demonstrate how probabilistic logic semantics allows us to leverage the authorial control of declarative programming and the flexibility of learning from data.

Graphical posterior predictive classification: Bayesian model averaging with particle Gibbs

In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed features is represented by a set of decomposable Gaussian graphical models. Emphasis is then placed on the Bayesian model averaging which takes full account of the class-specific model uncertainty by averaging over the posterior graph model probabilities. An explicit evaluation of the model probabilities is well known to be infeasible. To address this issue, we consider the particle Gibbs strategy of J. Olsson, T. Pavlenko, and F. L. Rios [Electron. J. Statist. 13 (2019), no. 2, 2865–2897] for posterior sampling from decomposable graphical models which utilizes the so-called Christmas tree algorithm of J. Olsson, T. Pavlenko, and F. L. Rios [Stat. Comput. 32 (2022), no. 5, Paper No. 80, 18] as proposal kernel. We also derive a strong hyper Markov law which we call the hyper normal Wishart law that allows to perform the resultant Bayesian calculations locally. The proposed predictive graphical classifier reveals superior performance compared to the ordinary Bayesian predictive rule that does not account for the model uncertainty, as well as to a number of out-of-the-box classifiers.

Constraining Nuclear Parameters Using Gravitational Waves from f-mode Oscillations in Neutron Stars

Gravitational waves (GWs) emanating from unstable quasi-normal modes in neutron stars (NSs) could be accessible with the improved sensitivity of the current GW detectors or with the next-generation GW detectors and, therefore, can be employed to study the NS interior. Assuming f-mode excitation in isolated pulsars with typical energy of pulsar glitches and considering potential f-mode GW candidates for A+ (upgraded LIGO detectors operating at fifth observing run design sensitivity) and Einstein Telescope (ET), we demonstrate the inverse problem of NS asteroseismology within a Bayesian formalism to constrain the nuclear parameters and NS equation of state (EOS). We describe the NS interior within relativistic mean-field formalism. Taking the example of glitching pulsars, we find that for a single event in A+ and ET, among the nuclear parameters, the nucleon effective mass (m*) within 90% credible interval can be restricted within 10% and 5%, respectively. At the same time, the incompressibility (K) and the slope of the symmetry energy (L) are only loosely constrained. Considering multiple (10) events in A+ and ET, all the nuclear parameters are well constrained, especially m*, which can be constrained to 3% and 2% in A+ and ET, respectively. Uncertainty in the observables of a 1.4 M ⊙ NS such as radius (), f-mode frequency (), damping time (), and a few EOS properties including squared speed of sound (c s 2) are also estimated.

Single-cell Bayesian deconvolution

Individual cells exhibit substantial heterogeneity in protein abundance and activity, which is frequently reflected in broad distributions of fluorescently labeled reporters. Since all cellular components are intrinsically fluorescent to some extent, the observed distributions contain background noise that masks the natural heterogeneity of cellular populations. This limits our ability to characterize cell-fate decision processes that are key for development, immune response, tissue homeostasis, and many other biological functions. It is therefore important to separate the contributions from signal and noise in single-cell measurements. Addressing this issue rigorously requires deconvolving the noise distribution from the signal, but approaches in that direction are still limited. Here, we present a non-parametric Bayesian formalism that performs such a deconvolution efficiently on multidimensional measurements, providing unbiased estimates of the resulting confidence intervals. We use this approach to study the expression of the mesodermal transcription factor Brachyury in mouse embryonic stem cells undergoing differentiation.

Robust sequential online prediction with dynamic ensemble of multiple models: A review

The use of time series for sequential online prediction (SOP) has long been a research topic, but achieving robust and computationally efficient SOP with non-stationary time series remains a challenge. This paper reviews a framework, called Bayesian Dynamic Ensemble of Multiple Models (BDEMM), which addresses SOP in a theoretically elegant way, and have found widespread use in various fields. BDEMM utilizes a model pool of weighted candidate models, adapted online using Bayesian formalism to capture possible temporal evolutions of the data. This review comprehensively describes BDEMM from five perspectives: its theoretical foundations, algorithms, practical applications, connections to other research, and strengths, limitations, and potential future directions.

Physical Properties of the Asteroid Belts from Brightness-limited Surveys

We introduce a general debiasing Bayesian formalism to brightness-limited surveys of solar system objects that constrains the statistical distribution of a population’s physical characteristics such as size, albedo, heliocentric distance, or others to account for the survey detections and measured properties such as brightness. We reanalyze the Dark Energy Camera search for main-belt asteroids of Peña et al. and fit a smooth double power-law size to its size distribution. Using only detections with reliable distances and accurate orbital information, we find no evidence for a significant difference in size distribution between the inner, middle, and outer belts for objects between 0.1 and 1 km in diameter, with q 2 = 2.27 ± 0.05 a good fit for the small-end slope. We show that the intrinsic number density of objects is consistent between these populations and is compatible with observational biases. As spectral classes are distributed unevenly throughout the main belt, these results support the ongoing collisional reprocessing of the asteroid belt for objects smaller than 5 km.

An early warning method for tunneling-induced ground surface settlement considering accident precursors and consequences

Ground surface settlement is a key indicator of the environmental safety of tunneling. Traditional early warning methods for tunneling-induced ground surface settlement are mainly based on the comparison results of the accumulated settlement and the control threshold in the standard, which may omit precursor information and delay the timing of warnings. In actual tunneling projects, the occurrence of most accidents is not in isolation, but is the cumulative result of a sequence of accident precursors. Therefore, this paper presents an early warning method for tunneling-induced ground surface settlement, with the aim of comprehensively considering accident precursors and consequences in early warning. By applying the proposed early warning method, accident precursors of excessive ground settlement can be identified as early warning signals, and damage consequences of tunneling to the surrounding environment can be utilized for the classification of warning levels. Safety principles provide guidelines for the modeling of accident scenarios and the implement of targeted safety interventions. The complete accident scenario of excessive surface settlement is characterized by the bow-tie. Relevant data are obtained from expert knowledge, and fuzzy set theory is employed to cope with the uncertainty of expert knowledge. Then, the bow-tie is mapped into the Bayesian network formalism. Within the Bayesian network, the consequence can be updated according to the accident precursor observed in tunneling, and the dynamic early warning can be issued accordingly. Moreover, the truncated accident sequence can be extracted from the accident scenario to help provide targeted safety interventions. Finally, a case study demonstrates that the proposed early warning method can effectively reduce the frequency and consequences of tunneling-induced excessive ground surface settlement.

Integrate inter–well connectivity data with static reservoir models based on Bayesian formalism

The inter-well connectivity calculated from reservoir dynamic production data reflects formation heterogeneity quantitatively. Currently, the calculated inter-well connectivity between pair wells is mainly used as a tool for water flood management but not for quantitative reservoir characterization. This study proposes an innovative, dynamic data integration workflow that can integrate inter-well connectivity with a static reservoir model. In the workflow, the first step is calculating the inter-well connectivity vectors from the reservoir pairwise injector and producer wells. The second step covers interpolation in the domain of interest. The third step is to update the permeability model based on the Bayesian updating method. The result of this study shows that integrating the calculated inter-well connectivity with the static models enhances model reliability and it also provides an insight to deeper geological understanding reflected from dynamic data integration in reservoir modeling.

Learning quantum systems

The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient control, calibration and validation of quantum states and their dynamics. Although the full simulation of large-scale quantum systems may only be possible on a quantum computer, classical characterization and optimization methods still play an important role. Here, we review different approaches that use classical post-processing techniques, possibly combined with adaptive optimization, to learn quantum systems, their correlation properties, dynamics and interaction with the environment. We discuss theoretical proposals and successful implementations across different multiple-qubit architectures such as spin qubits, trapped ions, photonic and atomic systems, and superconducting circuits. This Review provides a brief background of key concepts recurring across many of these approaches with special emphasis on the Bayesian formalism and neural networks.

From integrative atomic-resolution ensembles of disordered proteins to simulations of phase-separated condensates.

Dysregulation of biomolecular condensates of disordered proteins such as tau and TDP-43 is a driver of neurodegenerative diseases. A detailed understanding of the structure and dynamics of disordered proteins in dilute and condensed states will help to elucidate their roles in health and disease. However, the inherent flexibility of disordered proteins and their condensates makes structural studies and their interpretation challenging. Atomistic molecular dynamics simulations could help to address this challenge, but the need for long simulations has stymied progress. To overcome this limitation, we adopt a hierarchical approach, combining a highly accurate description of local structures with efficient sampling of possible global structures. We show how to make use of experimental data in the modeling of disordered proteins with a Bayesian formalism, overcoming the problem of exponentially varying weights in the ensemble refinement of long-chain polymeric molecules with importance sampling. Our atomic-resolution ensembles of dilute α-synuclein and tau agree well with small-angle X-ray scattering and NMR data, which were not used to generate the ensembles. For tau we find that pathogenic P301 mutations shift the ensemble towards locally more extended structures, which may be more aggregation prone. Using the same framework we simulate phase-separated condensates not just of tau but also of the neurodegeneration-linked protein TDP-43. Our atomistic simulations of TDP-43 complement coarse-grained simulations of its phase behavior which together demonstrate how phosphorylation of TDP-43 gives rise to an anti-aggregation effect. Thus TDP-43 phosphorylation may help to counteract progression of neurodegenerative diseases such as amyotrophic lateral sclerosis and frontotemporal dementia.

Bayesian parameter estimation for targeted anisotropic gravitational-wave background

Extended sources of the stochastic gravitational backgrounds have been conventionally searched on the spherical harmonics bases. The analysis during the previous observing runs by the ground-based gravitational-wave detectors, such as LIGO and Virgo, have yielded the constraints on the angular power spectrum ${C}_{\ensuremath{\ell}}$, yet it lacks the capability of estimating other parameters such as a spectral index. In this paper, we introduce an alternative Bayesian formalism to search for such stochastic signals with a particular distribution of anisotropies on the sky. This approach provides a Bayesian posterior of model parameters and also enables selection tests among different signal models. While the conventional analysis fixes the highest angular scale a priori, here we show a more systematic and quantitative way to determine the cutoff scale based on a Bayes factor, which depends on the amplitude and the angular scale of observed signals. Also, we analyze the third observing runs of LIGO and Virgo for the population of millisecond pulsars and obtain the 95% constraints of the signal amplitude, $\ensuremath{\epsilon}<2.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$.

The effects of base rate neglect on sequential belief updating and real-world beliefs.

Base-rate neglect is a pervasive bias in judgment that is conceptualized as underweighting of prior information and can have serious consequences in real-world scenarios. This bias is thought to reflect variability in inferential processes but empirical support for a cohesive theory of base-rate neglect with sufficient explanatory power to account for longer-term and real-world beliefs is lacking. A Bayesian formalization of base-rate neglect in the context of sequential belief updating predicts that belief trajectories should exhibit dynamic patterns of dependence on the order in which evidence is presented and its consistency with prior beliefs. To test this, we developed a novel 'urn-and-beads' task that systematically manipulated the order of colored bead sequences and elicited beliefs via an incentive-compatible procedure. Our results in two independent online studies confirmed the predictions of the sequential base-rate neglect model: people exhibited beliefs that are more influenced by recent evidence and by evidence inconsistent with prior beliefs. We further found support for a noisy-sampling inference model whereby base-rate neglect results from rational discounting of noisy internal representations of prior beliefs. Finally, we found that model-derived indices of base-rate neglect-including noisier prior representation-correlated with propensity for unusual beliefs outside the laboratory. Our work supports the relevance of Bayesian accounts of sequential base-rate neglect to real-world beliefs and hints at strategies to minimize deleterious consequences of this pervasive bias.

Fused Microwave and Ultrasonic Breast Imaging Within the Framework of a Joint Variational Bayesian Approximation

Early diagnosis of breast tumors can, in principle, be achieved by jointly running electromagnetic and acoustic probings, more precisely microwave (MW) and ultrasound (US). Indeed, such modalities are noninvasive, nonionizing, and low cost and proceed without registration for free pending breasts, not like other joint modalities that impose compression. Because of the strongly contrasted electromagnetic parameters of breast constituents, MW yields high-contrast images of low resolution and converse with the US when faced with weakly refracting elements. The key benefit is the common breast structure, and fusion should produce images with both high contrast and resolution. A Bayesian formalism is chosen, and an unsupervised joint variational Bayesian approximation (JVBA) is developed. In that, edges’ hidden variables and hyperparameters are automatically tuned along with the optimization. The mathematics is detailed in a general setting of fusion, and then, one proposes imaging of realistic MRI-derived breast slices. A wealth of numerical simulations from noisy single-frequency MW and multiple-frequency US data preserved from inverse crime yields means (i.e., breast maps) and variances of the unknown electromagnetic and acoustic parameter distributions as probabilistic realizations, evolutions of hyperparameters, as well as global indicators of accuracy. Comparisons with a joint contrast-source inversion edge-preserving (JCSI-EP) developed earlier in a deterministic framework illustrate the methodology.