Prior Information Research Articles

G-Loc: Tightly-Coupled Graph Localization With Prior Topo-Metric Information

G-Loc: Tightly-Coupled Graph Localization With Prior Topo-Metric Information

Just-in-time framework for robust soft sensing based on robust variational autoencoder

Modeling with high-dimensional data subject to abnormal observations have always been a practical interest. In this paper, under the just-in-time learning (JITL) framework, a robust soft sensor modeling approach is developed based on robust Variational Autoencoder (VAE). Unlike the vanilla VAE that extracts features from the given dataset under the Gaussian prior assumption, robust VAE employs Student’s t-distribution as prior distribution to handle abnormal data. Under assumption of the Student’s t-prior, the proposed robust VAE model is capable of describing collected data contaminated with outliers. Once the robust VAE model is trained, each robust feature variable in the latent space can be determined. Subsequently, similarity measure is calculated using robust Kullback-Leibler divergence between two Student’s t-distributions, that is, the distribution of a new data sample and that of each historical data sample. After completing similarity measurement for a query sample, the weights for input-output historical data can be determined. Based on these weighted historical data samples, a robust probabilistic principal component regression (PPCR) is utilized to perform local modeling for prediction. Numerical simulations, including the Tennessee Eastman and Penicillin fermentation benchmark processes, are utilized to validate the proposed JITL-based robust soft sensor modeling method.

Deep learning-based acoustic emission source localization in heterogeneous rock media without prior wave velocity information

Abstract Acoustic emission (AE) source localization is crucial for monitoring but often relies on prior information, such as wave velocity and arrival time. This study introduces a novel method for locating AE sources in rocks without such information, addressing challenges posed by heterogeneous sensor arrays. Experiments involving pencil led break (PLB) tests on sandstone cubes collected AE waveforms and their coordinates. A ResNet-50 based deep learning model was developed to correlate the time-frequency spectra of AE with PLB locations, expressed as spatial Gaussian distributions. The model, achieved a 79% prediction accuracy for AE localization in complex environments. While there is room for improvement in training data quantity and diversity, the results validate the model’s effectiveness, particularly in coal mines and tunnel engineering.

How Long Does a Memory Last? Bayesian Chronological Modelling and the Temporal Scope of Commemorative Practices at Aeneolithic Monjukli Depe, Turkmenistan

In this paper the history of one house and a human burial in the prehistoric settlement of Monjukli Depe, Turkmenistan, serves as a case study for the use of Bayesian chronological modelling to approach the reach of past memories. The method combines relative and absolute chronological data and aims not only at a more precise and robust chronology of past events, but also allows estimations of duration of particular processes. However, chronological models must be constructed with care, since the prior archaeological information significantly affects the output. The comparison of three alternative models for the Aeneolithic settlement of Monjukli Depe shows that prior information in modelling has a considerable impact on duration estimates for periods of the settlement history. The modelling chronology for Monjukli Depe allows the tracing of commemorative practices at a generational scale—the memory of Monjukli Depe House 14 was transmitted over several generations of inhabitants long after the house destruction. It is clear that houses possessed a great value in the social life of the settlement since local building histories were remembered over a long time.

Awareness Revision and Belief Extension

ABSTRACT What norm governs how an agent should change their beliefs when they encounter a completely new possibility? Orthodox Bayesianism has no answer, as it takes all learning to involve updating prior beliefs. A partial proposal is Reverse Bayesianism, which mandates the preservation of ratios of prior probabilities, but it faces counterexamples introduced by Mahtani (2021). I propose to separate awareness growth into two stages: awareness revision and belief extension. I argue that Mahtani’s cases highlight that we need to theorize awareness revision before we can define a proposal for belief extension, such as Reverse Bayesianism. I provide a formal model of awareness revision which makes explicit how propositions are distinguished within awareness states and identified across them. Reformulating Reverse Bayesianism to take input from my model allows it to navigate Mahtani-style cases. My model leaves open how agents choose to identify propositions across awareness states, and I propose that they ought to do so conservatively: preserving undisturbed prior reasoning about the structure of their awareness. I then spell out this proposal in a special case. This is a partial proposal, and I close with a discussion of how to elaborate on it and how to advance research into awareness revision.

Determining the prior mean in Bayesian logistic regression with sparse data: a nonarbitrary approach

Abstract Logistic regression models lead to a bias of the odds ratio (OR) as estimated using the maximum-likelihood (ML) method, when there are few study participants at the binary outcome and factor levels. Although Bayesian methods are frequently applied to reduce this sparse data bias, the specification of the prior distribution for regression coefficients is the most controversial feature. We propose a nonarbitrary and empirical method to determine the prior mean for regression coefficients in Bayesian logistic regression analysis for sparse data. The proposed prior mean is calculated as the difference between the observed log OR and the quasi-expectation of log OR, and is interpreted as a shrinkage statistic of the ML estimate. Further, for easy and fast inference, the proposed method applies to Bayesian logistic regression with the normal prior and the log-F prior via data augmentation. Simulation results indicate that the OR bias based on the proposed method is consistently smaller than that based on the ML method. The OR bias estimated using the proposed method is generally smaller than that based on the mean prior of zero for the regression coefficient. We apply the proposed methods to 2 real data sets.

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 quantum phase estimation with fixed photon states

We consider a two-mode bosonic state with fixed photon number n∈N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n \\in \\mathbb {N}$$\\end{document}, whose upper and lower modes pick up a phase ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} and -ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\\phi $$\\end{document}, respectively. We compute the optimal Fock coefficients of the input state, such that the mean square error (MSE) for estimating ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} is minimized, while the minimum MSE is always attainable by a measurement. Our setting is Bayesian, i.e., we consider ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} to be a random variable that follows a prior probability distribution function (PDF). Initially, we consider the flat prior PDF and we discuss the well-known fact that the MSE is not an informative tool for estimating a phase when the variance of the prior PDF is large. Therefore, we move on to study truncated versions of the flat prior in both single-shot and adaptive approaches. For our adaptive technique, we consider n=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=1$$\\end{document} and truncated prior PDFs. Each subsequent step utilizes as prior PDF the posterior probability of the previous step, and at the same time we update the optimal state and optimal measurement.

The Advance and Spot Selling Strategy Under Quality Information Asymmetry

ABSTRACTWe study firms' optimal pricing and quality selection in the advance period and the spot period under the information asymmetry. Our study theoretically demonstrates that the advance price as a signal of quality information can affect the separating and pooling equilibrium. Importantly, we find that separating equilibrium is more favorable for high cost‐efficiency if consumers have low prior probability that the firm is high cost‐efficiency. For the firm with low cost‐efficiency, the benefit of the separating equilibrium is the same as information is common sense. But no matter which equilibrium firms choose, they will target all consumers during the spot period.

Hardness results for decoding the surface code with Pauli noise

Real quantum computers will be subject to complicated, qubit-dependent noise, instead of simple noise such as depolarizing noise with the same strength for all qubits. We can do quantum error correction more effectively if our decoding algorithms take into account this prior information about the specific noise present. This motivates us to consider the complexity of surface code decoding where the input to the decoding problem is not only the syndrome-measurement results, but also a noise model in the form of probabilities of single-qubit Pauli errors for every qubit.In this setting, we show that quantum maximum likelihood decoding (QMLD) and degenerate quantum maximum likelihood decoding (DQMLD) for the surface code are NP-hard and #P-hard, respectively. We reduce directly from SAT for QMLD, and from #SAT for DQMLD, by showing how to transform a boolean formula into a qubit-dependent Pauli noise model and set of syndromes that encode the satisfiability properties of the formula. We also give hardness of approximation results for QMLD and DQMLD. These are worst-case hardness results that do not contradict the empirical fact that many efficient surface code decoders are correct in the average case (i.e., for most sets of syndromes and for most reasonable noise models). These hardness results are nicely analogous with the known hardness results for QMLD and DQMLD for arbitrary stabilizer codes with independent X and Z noise.

A novel online time calibration framework via double-stage EKF for visual-inertial odometry

Abstract There is an unavoidable time offset between the camera stream and the inertial measurement unit (IMU) data due to the sensor triggering and transmission delays, which will seriously affect the accuracy of visual-inertial odometry (VIO). A novel online time calibration framework via double-stage EKF for VIO is proposed in this paper. First, the first-stage complementary Kalman filter is constructed by adapting the complementary characteristics between the accelerometer and the gyroscope in the IMU, where the rotation result predicted by the gyroscope is corrected through the measurement of the accelerometer so that the IMU can output a more accurate initial pose. Second, the unknown time offset is added to the state vector of the VIO system. The estimated pose of IMU is used as the prediction information, and the reprojection error of multiple cameras on the same feature point is used as the constraint information. During the operation of the VIO system, the time offset is continuously calculated and superimposed on the IMU timestamp to obtain the data synchronized by the IMU and the camera. The Schur complement model is used to marginalize the camera state that carries less information in the system state, avoiding the loss of prior information between images, and improving the accuracy of camera pose estimation. Finally, the effectiveness of proposed algorithm is verified using the EuRoC dataset and the real experimental data.

Two-Step Iterative Medical Microwave Tomography

In the field of medical imaging, microwave tomography (MWT) is based on the scattering and absorption characteristics of different tissues to microwaves and can reconstruct the electromagnetic property distribution of biological tissues non-invasively and without ionizing radiation. However, due to the inherently nonlinear and ill-posed characteristics of MWT calculations, actual imaging is prone to overfitting or artifacts. To address this, this paper proposes a two-step iterative imaging approach for rapid medical microwave tomography. This method establishes corresponding objective functions for microwave imaging across multiple frequencies and conducts iterative calculations on images at varying resolutions. This effectively enhances image clarity and accuracy while alleviating the issue of prolonged computational time associated with imaging complex structures at high resolution due to insufficient prior information during iterative processes. In the electromagnetic simulation section, we simulated a three-layer brain model and conducted imaging experiments. The results demonstrate that the algorithm significantly enhances imaging resolution, accurately pinpointing cerebral hemorrhages at different locations using an eight-antenna array and successfully reconstructs tomography images with a hemorrhage area radius of 1 cm. Lastly, experiments were conducted using a medical microwave tomography platform and four simplified human brain models, achieving millimeter-level accuracy in MWT.

Conditional sufficient variable selection with prior information

AbstractDimension reduction and variable selection play crucial roles in high-dimensional data analysis. Numerous existing methods have been demonstrated to attain either or both of these goals. The Minimum Average Variance Estimation (MAVE) method and its variants are effective approaches to estimate directions on the Central Mean Subspace (CMS). The Sparse Minimum Average Variance Estimation (SMAVE) combines the concepts of sufficient dimension reduction and variable selection and has been demonstrated to exhaustively estimate CMS while simultaneously selecting informative variables using LASSO without assuming any specific model or distribution on the predictor variables. In many applications, however, researchers typically possess prior knowledge for a set of predictors that is associated with response. In the presence of a known set of variables, the conditional contribution of additional predictors provides a natural evaluation of the relative importance. Based on this concept, we propose the Conditional Sparse Minimum Average Variance Estimation (CSMAVE) method. By utilizing prior information and creating a meaningful conditioning set for SMAVE, we intend to select variables that will result in a more parsimonious model and a more accurate interpretation than SMAVE. We evaluate our strategy by analyzing simulation examples and comparing them to the SMAVE method. And a real-world dataset validates the applicability and efficiency of our method.

Investigating the role of keratin proteins and microbial associations in hereditary and pathogenic alopecia.

The purpose of this research was to identify the role of keratin proteins in causing inherited as well as pathogenic alopecia, pinpoint deleterious SNPs, and predict structural changes affecting protein-protein interactions in hair disorders. To elucidate the role of keratin proteins and genetic mutations in alopecia by analyzing protein structures through bioinformatics and identifying a mutation in the LPAR6 gene. It sought to identify the microorganisms linked to alopecia and conducted a comprehensive bioinformatics analysis of proteins with unknown experimental structures and molecular simulation analysis. The study identified a genetic mutation (c.188A > T, p.Asp63Val) in the LPAR6 gene associated with hereditary hair loss. Pathogenic alopecia was identified to be associated with S. aureus and two ic keratinophilic fungi namely M. canis, and T. violaceum. Additionally, among 14 proteins lacking prior structural information, four proteins namely Keratin, type II cuticular Hb3 (KR1), Keratin, type II cuticular Hb6 (KR2), Keratin, type II cytoskeletal 74 (KR3) and Keratin, type II cuticular Hb1 (KR4) exhibited common 'K-head' and 'F' domains. Docking analysis revealed five distinct binding sites (C1-C5) for each protein. The 'K-head' displayed the highest predicted binding affinities with Vina scores of -5.6 for KR2 and - 4.7 for KR4 whereas the 'F' domain showed Vina scores of -6.0 for KR3 and - 5.7 for KR2. This research underscores the crucial role of keratin proteins in both hereditary and pathogenic alopecia, emphasizing their significance for future investigations.

Statistical inference and data analysis for inverted Kumaraswamy distribution based on maximum ranked set sampling with unequal samples

A very useful modification to ranked set sampling (RSS) that allows a larger set size without significantly increasing ranking errors is the maximum ranked set sampling with unequal samples (MRSSU) approach. This article covers the parameter estimation of the inverted Kumaraswamy distribution using MRSSU and RSS designs. The maximum likelihood and Bayesian estimation techniques are considered. The regarded Bayesian estimation technique is determined in the case of non-informative and informative priors represented by Jeffreys and gamma priors, respectively. Squared error and minimum expected are the two loss functions that are employed. We presented a simulation study to evaluate the performance of the recommended estimations using root mean squared error and relative bias. The Bayes point estimates were computed using the Metropolis–Hastings algorithm. Additional conclusions have been made based on actual geological data regarding the intervals between Kiama Blowhole’s 64 consecutive eruptions. Based on the same number of measured units, the results of simulation and real data analysis showed that MRSSU estimators performed much better than their RSS counterparts.

Simultaneous Fixed and Random Effects Selection in Order-restricted Mixed Effects Models

When dealing with longitudinal data, if we directly select a specific model for modeling without any prior information about the existence of significant random effects before utilizing the mixed model, it may result in the misuse of the model, thereby affecting the final estimation results. This paper investigates a variable selection method that can jointly select both fixed and random effects in Bayesian mixed model under order constraints. This method can effectively prevent model misuse. A computationally feasible Gibbs algorithm is proposed for posterior inference. The performance of our proposal is evaluated by simulated data and two real applications related to Blood lead levels and Ramus bone heights. Results show that the proposed approaches perform very well in various situations.

Estimating the Confidence Intervals for the Coefficients of Variation Delta-Gamma Distributions

A common application of the coefficient of variation (CV), which is the ratio of the population standard deviation to the population mean, is frequently used to assess quality control and economic processes, among others. The fiducial quantity approach, Bayesian confidence intervals (CIs) using the Jeffreys, uniform, or normal-gamma-beta (NGB) priors, and highest posterior density (HPD) intervals using the Jeffreys, uniform, or NGB priors were used to provide estimators for the CI for the ratio of CV of two delta-gamma distributions. An evaluation of their performance in terms of average length and coverage probability was carried out using Monte Carlo simulations. The results of this study indicate that the HPD using the Jeffreys prior and fiducial quantity methods are the best for estimating the CI for the ratio of the CV of two delta-gamma distributions. Rainfall data from Mae Hong Son province in Thailand was used to illustrate their practicability when analyzing real-life processes.

Accurate identification of moving vehicle loads on beam-like bridge structures integrating novel PCA-based dictionary with grouping and weighting strategy

Most moving load identification (MLI) methods incorporate the dictionary theory as a regularization technique to address the ill-posedness of the problem. However, the selection of atoms in the dictionary often inadequately represents the actual vehicle loads in existing methods, and the prior information from these atoms is disregarded in the subsequent MLI computations. Therefore, a novel MLI framework is proposed for beam-like bridge structures based on a novel dictionary derived from principal component analysis (PCA) and newly grouping and weighting strategy in this study. At first, a vehicle-bridge coupling system (VBCS) is established to obtain the interaction forces between the moving vehicles and bridge deck. The system matrices between the interaction forces and structural responses are derived in the time domain. The PCA technique is then employed to extract information from these interaction forces and to subsequently construct a PCA-based dictionary. Based on the eigenvalues of each principal component in the dictionary, a weighted group sparse model, incorporating the newly grouping and weighting strategy, is defined to obtain the coefficients of each atom. The solution to this model is obtained using the alternating direction method (ADM). Finally, the proposed method is validated in numerical simulations comparing with some existing methods. The effects of noise levels, road surface roughness, number of training data, response combinations and the tolerances in ADM were also studied. Similarity law for the VBCS is conducted in experimental verifications to construct the PCA-based dictionary, allowing for a reasonable identification of gross vehicle weights. The results indicate that the MLI accuracy has been enhanced by the proposed method, and the similarity law employed in experiments is reasonable. Settingthe tolerance in ADM as ε = 1 × 10−5 can lead to a higher accuracy and reduce the computation cost in both numerical simulations and experimental verifications.

Ensemble-Enhanced Semi-Supervised Learning with Optimized Graph Construction for High-Dimensional Data.

Graph-based methods have demonstrated exceptional performance in semi-supervised classification. However, existing graph-based methods typically construct either a predefined graph in the original space or an adaptive graph within the output space, which often limits their ability to fully utilize prior information and capture the optimal intrinsic data distribution, particularly in high-dimensional data with abundant redundant and noisy features. This paper introduces a novel approach: Semi-Supervised Classification with Optimized Graph Construction (SSC-OGC). SSC-OGC leverages both predefined and adaptive graphs to explore intrinsic data distribution and effectively employ prior information. Additionally, a graph constraint regularization term (GCR) and a collaborative constraint regularization term (CCR) are incorporated to further enhance the quality of the adaptive graph structure and the learned subspace, respectively. To eliminate the negative effect of constructing a predefined graph in the original data space, we further propose a Hybrid Subspace Ensemble-enhanced framework based on the proposed Optimized Graph Construction method (HSE-OGC). Specifically, we construct multiple hybrid subspaces, which consist of meticulously chosen features from the original data to achieve high-quality and diverse space representations. Then, HSE-OGC constructs multiple predefined graphs within hybrid subspaces and trains multiple SSC-OGC classifiers to complement each other, significantly improving the overall performance. Experimental results conducted on various high-dimensional datasets demonstrate that HSE-OGC exhibits outstanding performance.

Transferability of real-time EVT safety models: an investigation using autonomous vehicles data

Recent research has shown that data from autonomous vehicles (AVs) enables proactive, real-time road safety management. However, with low AV market penetration, it's crucial to assess the transferability of AV-based safety models to other locations. This study transfers real-time safety models from a data-rich to a data-scarce environment using vehicular conflict data collected by AVs. Multi-site Bayesian hierarchical Extreme Value Theory models are developed in two cities, with model transfer evaluated using informative priors and parameter recalibration. Both approaches produce reliable results, though the transferability index favors the informed prior method, while predictive deviance shows similar performance for both. Model sensitivity to temporal data limitations is assessed, revealing that the recalibration approach is more sensitive to block size, whereas the informed prior method remains stable. A novel method mimicking data limitations shows transferred models perform well with data utilizations above 20%, promoting transferability to mitigate data inadequacy.