Bayesian Inference Approach Research Articles

Quantum-assisted Monte Carlo algorithms for fermions

Quantum computing is a promising way to systematically solve the longstanding computational problem, the ground state of a many-body fermion system. Many efforts have been made to realise certain forms of quantum advantage in this problem, for instance, the development of variational quantum algorithms. A recent work by Huggins et al. [1] reports a novel candidate, i.e. a quantum-classical hybrid Monte Carlo algorithm with a reduced bias in comparison to its fully-classical counterpart. In this paper, we propose a family of scalable quantum-assisted Monte Carlo algorithms where the quantum computer is used at its minimal cost and still can reduce the bias. By incorporating a Bayesian inference approach, we can achieve this quantum-facilitated bias reduction with a much smaller quantum-computing cost than taking empirical mean in amplitude estimation. Besides, we show that the hybrid Monte Carlo framework is a general way to suppress errors in the ground state obtained from classical algorithms. Our work provides a Monte Carlo toolkit for achieving quantum-enhanced calculation of fermion systems on near-term quantum devices.

A Bayesian estimation of the Milky Way’s circular velocity curve using Gaia DR3

Aims. Our goal is to calculate the circular velocity curve of the Milky Way, along with corresponding uncertainties that quantify various sources of systematic uncertainty in a self-consistent manner. Methods. The observed rotational velocities are described as circular velocities minus the asymmetric drift. The latter is described by the radial axisymmetric Jeans equation. We thus reconstruct the circular velocity curve between Galactocentric distances from 5 kpc to 14 kpc using a Bayesian inference approach. The estimated error bars quantify uncertainties in the Sun’s Galactocentric distance and the spatial-kinematic morphology of the tracer stars. As tracers, we used a sample of roughly 0.6 million stars on the red giant branch stars with six-dimensional phase-space coordinates from Gaia Data Release 3 (DR3). More than 99% of the sample is confined to a quarter of the stellar disc with mean radial, rotational, and vertical velocity dispersions of (35 ± 18) km s−1, (25 ± 13) km s−1, and (19 ± 9) km s−1, respectively. Results. We find a circular velocity curve with a slope of 0.4 ± 0.6 km s−1 kpc−1, which is consistent with a flat curve within the uncertainties. We further estimate a circular velocity at the Sun’s position of vc(R0) = 233 ± 7 km s−1 and that a region in the Sun’s vicinity, characterised by a physical length scale of ∼1 kpc, moves with a bulk motion of VLSR = 7 ± 7 km s−1. Finally, we estimate that the dark matter (DM) mass within 14 kpc is log10 MDM(R < 14kpc)/ M⊙ =(11.2+2.0-2.3) and the local spherically averaged DM density is ρDM(RO)=(0.41+0.10-0.09) GeV cm-3 = (0.011+0.003-0.002) M⊙pc-3. In addition, the effect of biased distance estimates on our results is assessed.

Evaluating predictors' relative importance using Bayes factors in regression models.

This study presents a Bayesian inference approach to evaluate the relative importance of predictors in regression models. Depending on the interpretation of importance, a number of indices are introduced, such as the standardized regression coefficient, the average squared semipartial correlation, and the dominance analysis measure. Researchers' theories about relative importance are represented by order constrained hypotheses. Support for or against the hypothesis is quantified by the Bayes factor, which can be computed from the prior and posterior distributions of the importance index. As the distributions of the indices are often unknown, we specify prior and posterior distributions for the covariance matrix of all variables in the regression model. The prior and posterior distributions of each importance index can be obtained from the prior and posterior samples of the covariance matrix. Simulation studies are conducted to show different inferences resulting from various importance indices and to investigate the performance of the proposed Bayesian testing approach. The procedure of evaluating relative importance using Bayes factors is illustrated using two real data examples. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

The Mantle Viscosity Structure of Venus

AbstractThe long‐wavelength gravity and topography of Venus are dominated by mantle convective flows, and are hence sensitive to the planet's viscosity structure and mantle density anomalies. By modeling the dynamic gravity and topography signatures and by making use of a Bayesian inference approach, we investigate the viscosity structure of the Venusian mantle by constraining radial viscosity variations. We performed inversions under a wide range of model assumptions that consistently predicted the existence of a thin low‐viscosity zone in the uppermost mantle. The zone is about 235 km thick and has a viscosity reduction of 5–15 times with respect to the underlying mantle. Drawing a parallel with the Earth, the reduced viscosity could be a result of partial melting as suggested for the origin of the asthenosphere. These results support the interpretation that Venus is a geologically active world predominantly governed by ongoing magmatic processes.

The Point Nuisance Method as a Decision-Support System Based on Bayesian Inference Approach

The Point Nuisance Method as a Decision-Support System Based on Bayesian Inference Approach

Generalized Linear Models in Determining Factors Affecting the Number of Community Visits to Health Service with Bayesian Inference Approach

Public health plays an important role in achieving the Sustainable Development Goals (SDGs) set by the United Nations. The SDGs are a series of global targets and commitments aimed at addressing various challenges facing the world today, such as poverty, hunger, gender inequality, climate change, and others. Public health, as one of the important aspects of the SDGs, is closely linked to several sustainable development goals. Efforts made to achieve the SDGs in the health sector are to improve health services. The objective of this study was to identify factors that influence the number of community visits to health services. The data used is a small sample size as one hundred community respondents in Padang City, West Sumatra Province. In this study, the number of respondents' visits to health service was the measured variable, while the predictor variables consisted of five variables, namely the status of the implementation of clean and healthy living behavior, health history, distance to health services, type of insurance owned, and consumption patterns. The generalized linear models is used to identify predictor variables that have significance using the Bayesian inference approach. It was found that there are two predictor variables that are significant in influencing the number of community visits to health services, namely the consumption patterns of respondents and the health history of respondents. These two variables have a very dominant effect on the number of visits to health service facilities in Padang City. This result indicates the community has to pay attention to their consumption patterns and living behavior to prevent periodic disease outbreaks and take care of their health history factors.

Bayesian Inference for State-Space Models With Student-t Mixture Distributions.

This article proposes a robust Bayesian inference approach for linear state-space models with nonstationary and heavy-tailed noise for robust state estimation. The predicted distribution is modeled as the hierarchical Student- t distribution, while the likelihood function is modified to the Student- t mixture distribution. By learning the corresponding parameters online, informative components of the Student- t mixture distribution are adapted to approximate the statistics of potential uncertainties. Then, the obstacle caused by the coupling of the updated parameters is eliminated by the variational Bayesian (VB) technique and fixed-point iterations. Discussions are provided to show the reasons for the achieved advantages analytically. Using the Newtonian tracking example and a three degree-of-freedom (DOF) hover system, we show that the proposed inference approach exhibits better performance compared with the existing method in the presence of modeling uncertainties and measurement outliers.

Iterative optimal sensor placement for adaptive structural identification using mobile sensors: Numerical application to a footbridge

This paper proposes an iterative optimal sensor placement (OSP) framework for structural identification and model updating of structural systems using a small number of mobile sensors. The model updating is performed through a Bayesian inference approach which is solved through asymptotic approximation for computational efficiency. In an iterative manner, the OSP is performed to minimize the information entropy in estimating the updating parameters of the model. Each OSP iteration is performed to find the next location of mobile sensors, where the prior probability distribution of updating parameters is assumed as the posterior probability distribution obtained from the previous iteration. This process is repeated until the uncertainties of updating parameters fall below a predetermined threshold. A forward sequential sensor placement algorithm is used to solve the OSP problem at each iteration. This algorithm provides a nearly-optimal solution and is much more efficient compared to an exhaustive search. This proposed framework is applied to a numerical case study, namely the Dowling Hall Footbridge located at Tufts University campus. Updating parameters used in this study are the added mass at different segments of the bridge deck. The purpose of using added mass is to create a realistic pseudo damage on a specific portion of the bridge. The proposed iterative system identification approach is applied for estimation of updating parameters considering different number of available sensors. This study shows that the iterative OSP approach using a small number of mobile sensors placed iteratively provides better model updating results compared to the case of using an optimal static sensor configuration involving larger number of sensors.

Simulation-based decision support system for earthmoving operations using computer vision

A reliable Decision Support System (DSS), particularly in the construction domain, can be driven by quality input information. Although vision-based methods have been widely utilized to retrieve contextual information, their potential is not fully leveraged in construction simulation yet. This study introduces an automated framework that utilizes multi-view video footage for vision-based input modeling within simulation domains. The proposed framework addresses project uncertainties (e.g., equipment performance, operators’ skills, road network, and weather status) using a proactive approach where project task durations are modeled as probabilistic distributions. The modeled distributions are continuously calibrated using the Markov Chain Monte Carlo Bayesian Inference (MCMCBI) approach. A simulation-based Simulated Annealing (SA) optimization is also employed to provide an efficient resource assignment. The extracted vision-based data is validated statistically against actual and spatiotemporal data. The results demonstrate that the suggested vision-based approach can provide qualified DSS input. Statistical analysis also confirms that vision-based data is more consistent with actual data than spatiotemporal data. The presented approach is successfully applied to an actual case study of a large-scale earthmoving project.

Topology identification of sparse network: A stochastic variational Bayesian approach

The topology identification of sparse networks is crucial for network modeling in many fields. The variational Bayesian inference has been proved to be effective for solving this issue. However, since all the observed data are used to compute the posterior distributions of the global variables at each iteration of the classical variational inference, the computation complexity is too high to be suitable for large data sets, especially for large-scale networks, where more data is needed for the inference. In this paper, we derive an efficient algorithm to maximize a lower bound function in the Bayesian inference based on stochastic optimization, where only a part of data is used at each iteration. Compared with the traditional variational Bayesian inference approach, the proposed method can significantly decrease the computation so that it is more suitable for the network identification with large data sets. Several typical sparse networks are used to test the performance of the proposed method, and the results demonstrate its merits.

Underreporting of SARS-CoV-2 infections during the first wave of the 2020 COVID-19 epidemic in Finland-Bayesian inference based on a series of serological surveys.

In Finland, the first wave of the COVID-19 epidemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) took place from March to June 2020, with the majority of COVID-19 cases diagnosed in the Helsinki-Uusimaa region. The magnitude and trend in the incidence of COVID-19 is one way to monitor the course of the epidemic. The diagnosed COVID-19 cases are a subset of the infections and therefore the COVID-19 incidence underestimates the SARS-CoV-2 incidence. The likelihood that an individual with SARS-CoV-2 infection is diagnosed with COVID-19 depends on the clinical manifestation as well as the infection testing policy and capacity. These factors may fluctuate over time and the underreporting of infections changes accordingly. Quantifying the extent of underreporting allows the assessment of the true incidence of infection. To obtain information on the incidence of SARS-CoV-2 infection in Finland, a series of serological surveys was initiated in April 2020. We develop a Bayesian inference approach and apply it to data from the serological surveys, registered COVID-19 cases, and external data on antibody development, to estimate the time-dependent underreporting of SARS-Cov-2 infections during the first wave of the COVID-19 epidemic in Finland. During the entire first wave, there were 1 to 5 (95% probability) SARS-CoV-2 infections for every COVID-19 case. The underreporting was highest before April when there were 4 to 17 (95% probability) infections for every COVID-19 case. It is likely that between 0.5%-1.0% (50% probability) and no more than 1.5% (95% probability) of the adult population in the Helsinki-Uusimaa region were infected with SARS-CoV-2 by the beginning of July 2020.

Exclusive semileptonic Bs→Kℓν decays on the lattice

Semileptonic $B_s \to K \ell \nu$ decays provide an alternative $b$-decay channel to determine the CKM matrix element $|V_{ub}|$, and to obtain a $R$-ratio to investigate lepton-flavor-universality violations. Results for the CKM matrix element may also shed light on the discrepancies seen between analyses of inclusive or exclusive decays. We calculate the decay form factors using lattice QCD with domain-wall light quarks and a relativistic $b$-quark. We analyze data at three lattice spacings with unitary pion masses down to $268\,\mathrm{MeV}$. Our numerical results are interpolated/extrapolated to physical quark masses and to the continuum to obtain the vector and scalar form factors $f_+(q^2)$ and $f_0(q^2)$ with full error budgets at $q^2$ values spanning the range accessible in our simulations. We provide a possible explanation of tensions found between results for the form factor from different lattice collaborations. Model- and truncation-independent $z$-parameterization fits following a recently proposed Bayesian-inference approach extend our results to the entire allowed kinematic range. Our results can be combined with experimental measurements of $B_s \to D_s$ and $B_s\to K$ semileptonic decays to determine $|V_{ub}|=3.8(6)\times 10^{-3}$. The error is currently dominated by experiment. We compute differential branching fractions and two types of $R$ ratios, the one commonly used as well as a variant better suited to test lepton-flavor universality.

Integrative taxonomy provides evidence for a cryptic lineage in the velvet worm Peripatopsis birgeri species complex (Onychophora: Peripatopsidae) in KwaZulu-Natal, South Africa

During the present study, species boundaries in the velvet worm Peripatopsis birgeri species complex in KwaZulu-Natal, South Africa, were examined with the use of DNA sequence data, gross morphology, scanning electron microscopy (SEM) and ecological niche modelling. Mitochondrial CO1 and nuclear 18S rRNA sequence data were used to generate a phylogeny using both a Bayesian inference and maximum likelihood approaches. Both the CO1 sequence data and the combined DNA sequence topology (CO1 + 18S rRNA) revealed the presence of two geographically distinct clades within the P. birgeri species complex. Results from three species delimitation methods (GMYC, PTP and ASAP), were incongruent in determining the number of species within the species complex and generally overestimated the number of operational taxonomic units. The latter result can be attributed to the marked genetic structure within the species complex, a result corroborated by the CO1 haplotype network and statistically significant F ST values. Divergence time estimation suggests that the two clades diverged during the Plio/Pleistocene. Niche modelling revealed that the two clades were differentially impacted by bioclimatic variables and occupied different habitats. Gross morphological characteristics, such as leg pair numbers and colour revealed no fixed differences between the two clades, however, a creamy white headband/collar occurred exclusively in specimens of clade 1 (P. birgeri). In contrast, SEM revealed fixed dorsal and ventral scale rank differences between the two clades. The results corroborate the presence of a novel species within the P. birgeri s.s. species complex. Peripatopsis birgeri s.s. is revised and restricted to the southern Drakensberg and a new species, P. polychroma sp. nov. (clade 2), from the northern Drakensberg and adjacent Afrotemperate forests in the interior of KwaZulu-Natal is described. https://zoobank.org/urn:lsid:zoobank:org:pub:569557AB-8BC8-49B6-B8AA-96507371297B

The impact of Grey Heron (Ardea cinerea L.) colony on soil biogeochemistry and vegetation: a natural long-term in situ experiment in a planted pine forest

Increased anthropogenic pressure including intensification of agricultural activities leads to long-term decline of natural biotopes, with planted forests often considered as promising compensatory response, although reduced biodiversity and ecosystem stability represent their common drawbacks. Here we present a complex investigation of the impact of a large Grey Heron (Ardea cinerea L.) colony on soil biogeochemistry and vegetation in a planted Scots pine forest representing a natural in situ experiment on an engineered ecosystem. After settling around 2006, the colony expanded for 15 years, leading to the intensive deposition of nutrients with feces, food remains and feather thereby considerably altering the local soil biogeochemistry. Thus, lower pH levels around 4.5, 10- and 2-fold higher concentrations of phosphorous and nitrogen, as well as 1.2-fold discrepancies in K, Li, Mn, Zn and Co., respectively, compared to the surrounding control forest area could be observed. Unaltered total organic carbon (Corg) suggests repressed vegetation, as also reflected in the vegetation indices obtained by remote sensing. Moreover, reduced soil microbial diversity with considerable alternations in the relative abundance of Proteobacteria, Firmicutes, Acidobacteriota, Actinobacteriota, Verrucomicrobiota, Gemmatimonadota, Chujaibacter, Rhodanobacter, and Bacillus has been detected. The above alterations to the ecosystem also affected climate stress resilience of the trees indicated by their limited recovery from the major 2010 drought stress, in marked contrast to the surrounding forest (p = 3∙10−5). The complex interplay between geographical, geochemical, microbiological and dendrological characteristics, as well as their manifestation in the vegetation indices is explicitly reflected in the Bayesian network model. Using the Bayesian inference approach, we have confirmed the predictability of biodiversity patterns and trees growth dynamics given the concentrations of keynote soil biogeochemical alternations with correlations R > 0.8 between observations and predictions, indicating the capability of risk assessment that could be further employed for an informed forest management.

A discrete-time susceptible-infectious-recovered-susceptible model for the analysis of influenza data.

We develop a discrete time compartmental model to describe the spread of seasonal influenza virus. As time and disease state variables are assumed to be discrete, this model is considered to be a discrete time, stochastic, Susceptible-Infectious-Recovered-Susceptible (DT-SIRS) model, where weekly counts of disease are assumed to follow a Poisson distribution. We allow the disease transmission rate to also vary over time, and the disease can only be reintroduced after extinction if there is a contact with infected individuals from other host populations. To capture the variability of influenza activities from one season to the next, we define the seasonality with a 4-week period effect that may change over years. We examine three different transmission rates and compare their performance to that of existing approaches. Even though there is limited information for susceptible and recovered individuals, we demonstrate that the simple models for transmission rates effectively capture the behaviour of the disease dynamics. We use a Bayesian approach for inference. The framework is applied in an analysis of the temporal spread of influenza in the province of Manitoba, Canada, 2012-2015.

Annual Mean Temperature and Rain Precipitation in North America Using NHPP to Detect Climate Changes

In this study, non-homogeneous Poisson processes (NHPP) are assumed to analyze annual average temperatures and rain precipitations, considering climate data for some regions of North America reported for a long period. A power law process (PLP) is assumed for the intensity function (derivative of the mean value function) or rate \(\lambda\) (t), t \(\ge\) 0 of the NHPP which the Poisson events occur considering data (accumulated number of years in a given time interval [0,t) where the climate measure is above a threshould given by the overal average in the assumed period) in presence or not of a change-point. The parameters of the assumed model are estimated under a Bayesian approach and using MCMC (Markov Chain Monte Carlo) methods. Alternatively to the use of a PLP process, we also assume a polynomial parametrical form for the mean value function of the NHPP process where a simple Bayesian inference approach is proposed to get better fit for the intensity and mean value functions of the NHPP process. From the fitted models it was possible to to detect the years where climate changes occurred.

Identify the Robin coefficient in an inhomogeneous time-fractional diffusion-wave equation

This paper is devoted to identifying the Robin coefficient in a one-dimensional inhomogeneous time-fractional diffusion-wave equation from the viewpoint of Bayesian inference approach. The priori modeling is implemented by a Markov Random Field (MRF). A hierarchical Bayesian model is adopted to select regularization parameters automatically. The Markov chain Monte Carlo (MCMC) algorithms are conducted to explore the posterior state space. Three numerical examples are carried out to demonstrate the performance of the proposed method.

Deterministic and probabilistic-based model updating of aging steel bridges

Numerical modeling is a very useful tool in different fields of bridge engineering, such as load-carrying capacity assessment or structural health monitoring. Developing a reliable computational model that accurately represents the actual bridge mechanical behavior entails advanced FEM-based modeling complemented by a comprehensive experimental campaign that provides the necessary supporting information and allows validating simulation outcomes. This paper proposes a unified approach aimed at the experimental characterization and FE model updating of aging steel bridges. It first involves the realization of an extensive experimental campaign aimed at the bridge's geometrical, material, and dynamic behavior characterization. Then, a model calibration framework is developed, where deterministic (optimization) and probabilistic (Bayesian inference) approaches are employed, and techniques such as global variance-based sensitivity analysis and Kriging-based surrogate modeling are further implemented in order to enhance the identification process and reduce the overall computational burden. The methodology has been validated in a historical riveted steel bridge in O Barqueiro, north of Galicia, Spain. The results show a good agreement in the identified model parameter values and a noticeable correlation between numerical and experimental modal properties, with an average relative error in frequencies of 0.34% and 0.44% for the deterministic and probabilistic approaches and an average MAC (Modal Assurance Criterion) ratio of 0.96.

Planetary system around LTT 1445A unveiled by ESPRESSO: Multiple planets in a triple M-dwarf system

We present radial velocity follow-up obtained with ESPRESSO of the M-type star LTT 1445A (TOI-455), for which a transiting planet b with an orbital period of 5.4 days was detected by TESS. We report the discovery of a second transiting planet (LTT 1445A c) and a third non-transiting candidate planet (LTT 1445A d) with orbital periods of 3.12 and 24.30 days, respectively. The host star is the main component of a triple M-dwarf system at a distance of 6.9 pc. We used 84 ESPRESSO high-resolution spectra to determine accurate masses of 2.3 ± 0.3M⊕and 1.0 ± 0.2M⊕for planets b and c and a minimum mass of 2.7 ± 0.7M⊕for planet d. Based on its radius of 1.43 ± 0.09R⊕as derived from the TESS observations, LTT 1445A b has a lower density than the Earth and may therefore hold a sizeable atmosphere, which makes it a prime target for theJames WebbSpace Telescope (JWST). We used a Bayesian inference approach with the nested sampling algorithm and a set of models to test the robustness of the retrieved physical values of the system. There is a probability of 85% that the transit of planet c is grazing, which results in a retrieved radius with large uncertainties at 1.60−0.34+0.67R⊕. LTT 1445A d orbits the inner boundary of the habitable zone of its host star and could be a prime target for the JWST.

Bridge weigh-in-motion considering dynamic response in observation noise with application to multiple driving conditions

In addition to causing a static response when traversing a bridge, moving vehicles also produce a dynamic response, which is thought to be one of the factors adversely affecting the accuracy of bridge weigh-in-motion approaches. This paper proposes a novel method for improving the accuracy of such approaches. Rather than modeling the dynamic response directly, the proposed model considers it as noise with autocorrelation. A Bayesian inference approach is considered as it allows a rational way of assimilating data into the model. Here, the dynamic response is considered in the form of a covariance matrix of observation noise, composed of the residuals of the measured and calculated responses, in a Bayesian framework. In a validation study using actual measured data, it was confirmed that the estimation of axle weights in the presence of multiple vehicles was significantly improved. From the result, it can be concluded that proper modeling of the dynamic response in observation data leads to more accurate weigh-in-motion estimates of axle weights and GVW, particularly when complicated vehicle travel is involved. A comparison of static and dynamic influence lines is also discussed using actual measured data. It is shown that the weights estimated by the dynamic influence line are generally more accurate than those by the static influence line when correlation of noise is not considered. The dynamic component in influence line can be interpreted as a regularization term. The proposed method, which uses static influence line and covariance matrix considering correlation of noise, is more accurate than the method with dynamic influence line and also, it does not cause any bias.