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This paper applies Bayesian inference with normal-normal conjugate to forecast renewable energy generation. The generation forecasts a probability distribution rather than a quantitative value. An assumed normal distribution is initialized for renewable energy generation. This assumed normal distribution's parameters, the mean μ, and the standard deviation σ, are inferred by Bayesian inference afterward. However, applying Bayesian inference barely shall encounter an intractable integral. To circumvent the intractable integral, this paper considers the normal-normal conjugate method. This method fixes the assumed normal distribution's σ and characterizes μ as another normal distribution and then infers the latter normal distribution parameters. A case study of waste-to-energy generation forecast in Taiwan is investigated in this paper. It has been found from the investigation that the Bayesian inferred probability distribution outperforms the assumed one. [ABSTRACT FROM AUTHOR]

Relay protection rejection and misoperation exist in the existing distribution network, which will affect the fault diagnosis results. To diagnose faults in distribution networks, this paper presents a fault diagnosis method for the distribution network based on the D-S evidence theory Bayesian network. First, the collected relay protection information is divided into two categories, protection information and circuit breaker information; the corresponding Bayesian network model is established based on their respective action logic, and the corresponding component failure probability is obtained by Bayesian backward inference. Second, the fault probabilities obtained from the two Bayesian networks are fused by the D-S evidence theory, and the obtained fault probabilities are used to diagnose the faulty component. Then, using the Bayesian network corresponding to the faulty component to perform Bayesian forward inference, the protection devices and circuit breakers are identified for misoperation or rejection to achieve the fault diagnosis of the distribution network. Finally, the correctness and reliability of the proposed diagnosis method are verified through the analysis of arithmetic cases. [ABSTRACT FROM AUTHOR]

Understanding the emergence of symbol systems, especially language, requires the construction of a computational model that reproduces both the developmental learning process in everyday life and the evolutionary dynamics of symbol emergence throughout history. This study introduces the collective predictive coding (CPC) hypothesis, which emphasizes and models the interdependence between forming internal representations through physical interactions with the environment and sharing and utilizing meanings through social semiotic interactions within a symbol emergence system. The total system dynamics is theorized from the perspective of predictive coding. The hypothesis draws inspiration from computational studies grounded in probabilistic generative models and language games, including the Metropolis-Hastings naming game. Thus, playing such games among agents in a distributed manner can be interpreted as a decentralized Bayesian inference of representations shared by a multi-agent system. Moreover, this study explores the potential link between the CPC hypothesis and the free-energy principle, positing that symbol emergence adheres to the society-wide free-energy principle. Furthermore, this paper provides a new explanation for why large language models appear to possess knowledge about the world based on experience, even though they have neither sensory organs nor bodies. This paper reviews past approaches to symbol emergence systems, offers a comprehensive survey of related prior studies, and presents a discussion on CPC-based generalizations. Future challenges and potential cross-disciplinary research avenues are highlighted. [ABSTRACT FROM AUTHOR]

This paper explores the fact that linear opinion pooling can be represented as a Bayesian update on the opinions of others. It uses this fact to propose a new interpretation of the pooling weights. Relative to certain modelling assumptions the weights can be equated with the so-called truth-conduciveness known from the context of Condorcet's jury theorem. This suggests a novel way to elicit the weights. [ABSTRACT FROM AUTHOR]

Tool wear prediction is of great significance in industrial production. Current tool wear prediction methods mainly rely on the indirect estimation of machine learning, which focuses more on estimating the current tool wear state and lacks effective quantification of random uncertainty factors. To overcome these shortcomings, this paper proposes a novel method for predicting cutting tool wear. In the offline phase, the multiple degradation features were modeled using the Brownian motion stochastic process and a SVR model was trained for mapping the features and the tool wear values. In the online phase, the Bayesian inference was used to update the random parameters of the feature degradation model, and the future trend of the features was estimated using simulation samples. The estimation results were input into the SVR model to achieve in-advance prediction of the cutting tool wear in the form of distribution densities. An experimental tool wear dataset was used to verify the effectiveness of the proposed method. The results demonstrate that the method shows superiority in prediction accuracy and stability. [ABSTRACT FROM AUTHOR]

This paper discusses experimental validations of multilayer microslit panels (MSPs) designed via Bayesian inference to obtain both high sound absorption and wide bandwidth simultaneously. Microslit perforation in thin panels is similar to microperforated panels [Xiang, Fackler, Hou, and Schmitt (2022). J. Acoust. Soc. Am. 151(5), 3094–3103]. MSP absorbers in single-layer configurations are functioning in a limited frequency range. By stacking the MSPs in multiple layered structures, absorbing performance may be widened in frequency ranges while retaining high absorption coefficients. Besides design challenges of multiple MSPs in layered structures to fulfill a practical requirement and minimize fabrication complexity, this paper further discusses challenges in experimental validations when experimental results undesirably deviate from the initial Bayesian design. Causation analysis is applied to the validation efforts where a causal model-based inference effectively provides causal reasoning of fabrication inaccuracies. Along with the causal inference, a causal reasoning conducted in this work can guide corrections due to fabrication inaccuracies during the iterative validation process. [ABSTRACT FROM AUTHOR]

In recent years, various forms of progressive hybrid censoring schemes (PHCS) have gained significant traction in survival and reliability analysis studies due to their versatility. However, these PHCS variants are often characterized by complexity stemming from the multitude of parameters involved in their specification. Consequently, the primary objective of this paper is to propose a unified approach termed combined type II progressive hybrid censoring scheme ( ComT 2 PHCS) capable of encompassing several existing PHCS variations. Our analysis focuses specifically on the exponential distribution (ExDist). Bayesian inference techniques are employed to estimate the parameters of the ExDist under the ComT 2 PHCS. Additionally, we conduct fundamental distributional analyses and likelihood inference procedures. We derive the conditional moment-generating function (CondMGF) of maximum likelihood estimator (MLE) for parameters of the ExDist under ComT 2 PHCS. Further, we use CondMGF for the distribution of MLE for parameters of ExDist under ComT 2 PHCS. Finally, we provide an illustrative example to elucidate the inference methods derived in this paper. [ABSTRACT FROM AUTHOR]

Bayesian inference typically focuses upon two issues. The first is estimating the parameters of some model from data, and the second is quantifying the evidence for alternative hypotheses—formulated as alternative models. This paper focuses upon a third issue. Our interest is in the selection of data—either through sampling subsets of data from a large dataset or through optimising experimental design—based upon the models we have of how those data are generated. Optimising data-selection ensures we can achieve good inference with fewer data, saving on computational and experimental costs. This paper aims to unpack the principles of active sampling of data by drawing from neurobiological research on animal exploration and from the theory of optimal experimental design. We offer an overview of the salient points from these fields and illustrate their application in simple toy examples, ranging from function approximation with basis sets to inference about processes that evolve over time. Finally, we consider how this approach to data selection could be applied to the design of (Bayes-adaptive) clinical trials. [ABSTRACT FROM AUTHOR]

We consider a problem of inferring contact network from nodal states observed during an epidemiological process. In a black-box Bayesian optimisation framework this problem reduces to a discrete likelihood optimisation over the set of possible networks. The cardinality of this set grows combinatorially with the number of network nodes, which makes this optimisation computationally challenging. For each network, its likelihood is the probability for the observed data to appear during the evolution of the epidemiological process on this network. This probability can be very small, particularly if the network is significantly different from the ground truth network, from which the observed data actually appear. A commonly used stochastic simulation algorithm struggles to recover rare events and hence to estimate small probabilities and likelihoods. In this paper we replace the stochastic simulation with solving the chemical master equation for the probabilities of all network states. Since this equation also suffers from the curse of dimensionality, we apply tensor train approximations to overcome it and enable fast and accurate computations. Numerical simulations demonstrate efficient black-box Bayesian inference of the network. [ABSTRACT FROM AUTHOR]

Accurate deflection prediction of in-service bridges can be used to assess the overall structural stiffness and detect abnormal states in advance. The bridge structures, especially long-span bridges, experience varying environmental and operational conditions, including temperature, humidity, wind excitation, and traffic loads, as well as long-term material deterioration and stiffness degradation mechanisms, and therefore, their deformation behavior shows complex variation phenomena, which pose challenges to many current deflection prediction methods. To address this subject, a Bayesian dynamic difference model (BDDM) to predict bridge deflection behavior online is proposed in this paper, explicitly considering the effect of the nonstationarity of time series data under varying environmental and operational conditions. A novel dynamic difference model is first proposed to include the nonstationary residual term and provide a linear approximation of a complex nonlinear process. Then, the formulas for recursively updating the dynamic difference model based on Bayesian inference are proposed. The proposed method is first validated through a numerical application using simulated nonstationary time series data with a nonlinear trend, indicating that it can adaptively capture nonstationary variations, update noise variance estimations, and improve prediction accuracy. To further demonstrate its performance, the BDDM is employed to predict the daily maximum deflection of a real-world cable-stayed bridge using measured data, and its performance is compared with several existing methods. The findings reveal that the proposed method outperforms other methods in terms of prediction accuracy, and can be potentially implemented for an online monitoring and early warning system. [ABSTRACT FROM AUTHOR]

This paper responds to Professor Paolo Giudici's call for papers in ‘Safe Machine Learning’ and explores the application of Bayesian inference within the SAFE model framework, aiming to enhance the accuracy and reliability of environmental, social, and governance (ESG) factor analysis in the financial sector. The paper begins by introducing the basic concept of the SAFE model, which integrates ESG factors into the assessment of corporate credit ratings to promote sustainable development in the financial field. Furthermore, this paper discusses forecast estimation, uncertainty quantification, Gaussian processes, iterative optimization, and model robustness within the SAFE model framework. It is important to note that the SAFE model is not limited to the aforementioned applications; it also has the capacity to understand the model's extensive utility in other financial sectors, which can reflect the model's comprehensive scope. [ABSTRACT FROM AUTHOR]

In the literature, modifying the baseline distributions and proposing novel approach of the existing probability models play an important role in the analysis of real-world phenomena as well as the development of new distributions essentially stems from the need to adequately characterize environmental and lifetime events. In this paper, we introduce a new model by applying maximum compound technique to the baseline distributions for modeling more types data used in different case of studies including symmetric, asymmetric, skewed and complex data sets. The proposed model called univariate maximum Harris extended Rayleigh distribution and three parameters characterize it, and it is regarded as strong competitor for widely applied symmetrical and non symmetrical models. The paper offers varied fundamental distributional and mathematical properties of the suggested distribution, such as conditional probability and its expectation, as well as quantile and moment-generating functions. The model's parameters are estimated by applying numerous procedures including maximum likelihood estimation, Expectation–Maximization iterative method and Bayesian approach. Bayesian estimation is performed via various loss functions such as square error, Linex and general entropy functions. As well as, approximate and Bootstrap methods are used to construct the confidence interval for the unknown parameters of the proposed model. Additionally, we illustrated different extensive simulation experiments to see the potential of the suggested estimation methods which give satisfactory performance results. In the end, we applied two real data sets for illustrative purposes. In our illustration, we have compared the practicality of the recommended model with several well-known competing distributions. [ABSTRACT FROM AUTHOR]

Particle-based Variational Inference (ParVI) methods have been widely adopted in deep Bayesian inference tasks such as Bayesian neural networks or Gaussian Processes, owing to their efficiency in generating high-quality samples given the score of the target distribution. Typically, ParVI methods evolve a weighted-particle system by approximating the first-order Wasserstein gradient flow to reduce the dissimilarity between the particle system's empirical distribution and the target distribution. Recent advancements in ParVI have explored sophisticated gradient flows to obtain refined particle systems with either accelerated position updates or dynamic weight adjustments. In this paper, we introduce the semi-Hamiltonian gradient flow on a novel Information–Fisher–Rao space, known as the SHIFR flow, and propose the first ParVI framework that possesses both accelerated position update and dynamical weight adjustment simultaneously, named the General Accelerated Dynamic-Weight Particle-based Variational Inference (GAD-PVI) framework. GAD-PVI is compatible with different dissimilarities between the empirical distribution and the target distribution, as well as different approximation approaches to gradient flow. Moreover, when the appropriate dissimilarity is selected, GAD-PVI is also suitable for obtaining high-quality samples even when analytical scores cannot be obtained. Experiments conducted under both the score-based tasks and sample-based tasks demonstrate the faster convergence and reduced approximation error of GAD-PVI methods over the state-of-the-art. [ABSTRACT FROM AUTHOR]

Increasing demand for railway transportation combined with more severe climate events, such as extreme heat, leads to an increased risk of degradation of track support and failure due to rail buckling. In this paper, distributed fiber optic sensing (DFOS) was used, for the first time, to assess track support degradation and the likelihood of rail dynamic buckling of curved rail sections. A monitoring campaign was conducted to measure the dynamic distributed strain response of a 9-m-long section of curved track during the passage of a passenger train. The distributed strain data were used to assess the axial strain and vertical bending curvature response during the passage of the train, and the distributed vertical curvature profile was then used to evaluate the wheel forces and track modulus of the monitored site using the Bayesian inference approach. The estimated wheel forces showed good agreement with the expected values, and the estimated track modulus was comparable to that measured using conventional techniques at other similar rail sites. With the estimated wheel forces and track modulus as inputs, a finite-element model developed in a commercial software package (i.e., ABAQUS) was used to assess the dynamic buckling capacity of the rail by considering the reduced rail lateral resistance due to the passing train. The results indicate that for this site, the passage of locomotives reduces the thermal buckling capacity by several degrees Celsius depending on the initial geometric imperfections in the rail, whereas passenger cars have negligible impact on the capacity. [ABSTRACT FROM AUTHOR]

Background: Skin diseases are severe diseases. Identification of these severe diseases depends upon the abstraction of atypical skin regions. The segmentation of these skin diseases is essential to rheumatologists in risk impost and for valuable and vital decision‐making. Skin lesion segmentation from images is a crucial step toward achieving this goal—timely exposure of malignancy in psoriasis expressively intensifies the persistence ratio. Defies occur when people presume skin diseases they have without accurately and precisely incepted. However, analyzing malignancy at runtime is a big challenge due to the truncated distinction of the visual similarity between malignance and non‐malignance lesions. However, images' different shapes, contrast, and vibrations make skin lesion segmentation challenging. Recently, various researchers have explored the applicability of deep learning models to skin lesion segmentation. Materials and methods: This paper introduces a skin lesions segmentation model that integrates two intelligent methodologies: Bayesian inference and edge intelligence. In the segmentation model, we deal with edge intelligence to utilize the texture features for the segmentation of skin lesions. In contrast, Bayesian inference enhances skin lesion segmentation's accuracy and efficiency. Results: We analyze our work along several dimensions, including input data (datasets, preprocessing, and synthetic data generation), model design (architecture, modules), and evaluation aspects (data annotation requirements and segmentation performance). We discuss these dimensions from seminal works and a systematic viewpoint and examine how these dimensions have influenced current trends. Conclusion: We summarize our work with previously used techniques in a comprehensive table to facilitate comparisons. Our experimental results show that Bayesian‐Edge networks can boost the diagnostic performance of skin lesions by up to 87.80% without incurring additional parameters of heavy computation. [ABSTRACT FROM AUTHOR]

This paper presents a novel adaptation of the conventional approximate Bayesian computation sequential Monte Carlo (ABC-SMC) sampling algorithm for parameter estimation in the presence of uncertainties, coined combinatorial ABC-SMC. Inference of this type is used in situations where there does not exist a closed form of the associated likelihood function, which is replaced by a simulating model capable of producing artificial data. In the literature, conventional ABC-SMC is utilised to perform inference on continuous parameters. The novel scheme presented here has been developed to perform inference on parameters that are high-dimensional binary, rather than continuous. By altering the form of the proposal distribution from which to sample candidates in subsequent iterations (referred to as waves), high-dimensional binary variables may be targeted and inferred by the scheme. The efficacy of the proposed scheme is demonstrated through application to vibration data obtained in a structural dynamics experiment on a fibre-optic sensor simulated as a finite plate with uncertain boundary conditions at its edges. Results indicate that the method provides sound inference on the plate boundary conditions, which is validated through subsequent application of the method to multiple vibration datasets. Comparisons between appropriate forms of the metric function used in the scheme are also developed to highlight the effect of this element in the schemes convergence. [ABSTRACT FROM AUTHOR]

Flow has been described as a state of optimal performance, experienced universally across a broad range of domains: from art to athletics, gaming to writing. However, its phenomenal characteristics can, at first glance, be puzzling. Firstly, individuals in flow supposedly report a loss of self-awareness, even though they perform in a manner which seems to evince their agency and skill. Secondly, flow states are felt to be effortless, despite the prerequisite complexity of the tasks that engender them. In this paper, we unpick these features of flow, as well as others, through the active inference framework, which posits that action and perception are forms of active Bayesian inference directed at sustained self-organisation; i.e., the minimisation of variational free energy. We propose that the phenomenology of flow is rooted in the deployment of high precision weight over (i) the expected sensory consequences of action and (ii) beliefs about how action will sequentially unfold. This computational mechanism thus draws the embodied cognitive system to minimise the ensuing (i.e., expected) free energy through the exploitation of the pragmatic affordances at hand. Furthermore, given the challenging dynamics the flowinducing situation presents, attention must be wholly focussed on the unfolding task whilst counterfactual planning is restricted, leading to the attested loss of the sense of self-as-object. This involves the inhibition of both the sense of self as a temporally extended object and higher-order, meta-cognitive forms of self-conceptualisation. Nevertheless, we stress that self-awareness is not entirely lost in flow. Rather, it is pre-reflective and bodily. Our approach to bodily-action-centred phenomenology can be applied to similar facets of seemingly agentive experience beyond canonical flow states, providing insights into the mechanisms of so-called selfless experiences, embodied expertise and wellbeing. [ABSTRACT FROM AUTHOR]

The traditional sparse recovery (SR) space-time adaptive processing (STAP) algorithms are greatly affected by grid mismatch, leading to poor performance in airborne bistatic radar clutter suppression. In order to address this issue, this paper proposes an SR STAP algorithm for airborne bistatic radars based on atomic selection under the Bayesian framework. This method adopts the idea of atomic selection for the process of Bayesian inference, continuously evaluating the contribution of atoms to the likelihood function to add or remove atoms, and then using the selected atoms to estimate the clutter support subspace and perform sparse recovery in the clutter support subspace. Due to the inherent sparsity of clutter signals, performing sparse recovery in the clutter support subspace avoids using a massive number of atoms from an overcomplete space-time dictionary, thereby greatly improving computational efficiency. In airborne bistatic radar scenarios where significant grid mismatch exists, this method can mitigate the performance degradation caused by grid mismatch by encrypting grid points. Since the sparse recovery is performed in the clutter support subspace, encrypting grid points does not lead to excessive computational burden. Additionally, this method integrates out the noise term under a new hierarchical Bayesian model, preventing the adverse effects caused by inaccurate noise power estimation during iterations in the traditional SR STAP algorithms, further enhancing its performance. Our simulation results demonstrate the high efficiency and superior clutter suppression performance and target detection performance of this method. [ABSTRACT FROM AUTHOR]

Clustered data are a complex and frequently used type of data. Traditional factor analysis methods are effective for non-clustered data, but they do not adequately capture correlations between multiple observed individuals or variables in clustered data. This paper proposes a Bayesian approach utilizing MCMC and Gibbs sampling algorithms to accurately estimate parameters of interest within the clustered factor analysis model. The mean traversal graph of parameters ensures that the Markov chain converges, and the Bayesian case-deletion model is used to analyze the model's impact and identify outliers in clustered data using Cook's posterior mean distance. The applicability and validity of the principal-component-method-based factor analysis model for clustered data are demonstrated by comparing the parameter estimation of this method with the principal component method, the clustered data with and without internal relationships are compared by example analysis, and the anomalous groups are identified by the Cook's posterior mean distance. [ABSTRACT FROM AUTHOR]

This paper presents a learning- and scenario-based model predictive control (MPC) design approach for systems modelled in the linear parameter-varying (LPV) framework. Using input-output data collected from the system, a state-space LPV model with uncertainty quantification is first learned through the variational Bayesian inference Neural Network (BNN) approach. The learned probabilistic model is assumed to contain the true dynamics of the system with a high probability and is used to generate scenarios that ensure safety for a scenario-based MPC. Moreover, to guarantee stability and enhance the performance of the closed-loop system, a parameter-dependent terminal cost and controller, as well as a terminal robust positive invariant set are designed. Numerical examples will be used to demonstrate that the proposed control design approach can ensure safety and achieve desired control performance. [ABSTRACT FROM AUTHOR]

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Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the ensemble Kalman sampler (EKS) or the affine invariant Langevin dynamics (ALDI) rely on successive evaluations of the forward model or its gradient. A main drawback of these methods hence is their vast number of required forward calls as well as their possible lack of convergence in the case of more involved posterior measures such as multimodal distributions. The goal of this paper is to address these challenges to some extent. First, several possible adaptive ensemble enrichment strategies that successively enlarge the number of particles in the underlying Langevin dynamics are discussed that in turn lead to a significant reduction of the total number of forward calls. Second, analytical consistency guarantees of the ensemble enrichment method are provided for linear forward models. Third, to address more involved target distributions, the method is extended by applying adapted Langevin dynamics based on a homotopy formalism for which convergence is proved. Finally, numerical investigations of several benchmark problems illustrate the possible gain of the proposed method, comparing it to state-of-the-art Langevin samplers. [ABSTRACT FROM AUTHOR]

A broad range of different of Bayesian cloud detection schemes is applied to measurements from the Medium Resolution Imaging Spectrometer (MERIS), the Advanced Along-Track Scanning Radiometer (AATSR), and their combination. The cloud masks were designed to be numerically efficient and suited for the processing of large amounts of data. Results from the classical and naive approach to Bayesian cloud masking are discussed for MERIS and AATSR as well as for their combination. A sensitivity study on the resolution of multidimensional histograms, which were postprocessed by Gaussian smoothing, shows how theoretically insufficient amounts of truth data can be used to set up accurate classical Bayesian cloud masks. Sets of exploited features from single and derived channels are numerically optimized and results for naive and classical Bayesian cloud masks are presented. The application of the Bayesian approach is discussed in terms of reproducing existing algorithms, enhancing existing algorithms, increasing the robustness of existing algorithms, and on setting up new classification schemes based on manually classified scenes. [ABSTRACT FROM AUTHOR]

To address the problem that traditional spectral clustering algorithms cannot obtain the complete structural information of networks, this paper proposes a spectral clustering community detection algorithm, PMIK-SC, based on the point-wise mutual information (PMI) graph kernel. The kernel is constructed according to the point-wise mutual information between nodes, which is then used as a proximity matrix to reconstruct the network and obtain the symmetric normalized Laplacian matrix. Finally, the network is partitioned by the eigendecomposition and eigenvector clustering of the Laplacian matrix. In addition, to determine the number of clusters during spectral clustering, this paper proposes a fast algorithm, BI-CNE, for estimating the number of communities. For a specific network, the algorithm first reconstructs the original network and then runs Monte Carlo sampling to estimate the number of communities by Bayesian inference. Experimental results show that the detection speed and accuracy of the algorithm are superior to other existing algorithms for estimating the number of communities. On this basis, the spectral clustering community detection algorithm PMIK-SC also has high accuracy and stability compared with other community detection algorithms and spectral clustering algorithms. [ABSTRACT FROM AUTHOR]

Mapping of underwater objects is usually conducted with autonomous underwater vehicles (AUVs).A standard approach in mine countermeasure (MCM) operations is to perform a two-phase reconnaissance: in the first phase, a survey mission is carried out to detect and classify the objects; in the second phase, objects are reacquired to confirm the actual presence of mines. The data acquired during this multiphase mission greatly depends on the accuracy of theAUV's navigation system. This paper proposes a graph-based mapping algorithm that takes into account the unknown AUV position, as well as the output of the classification process, and uses the sum-product algorithm (SPA) to obtain a principled and intuitive approximation of the Bayesian inference needed for object detection and estimation. The SPA-basedmapping algorithm is derived in detail, and its performance is evaluated in a simulated MCM scenario. [ABSTRACT FROM AUTHOR]

Bayesian inference has gained popularity in the last half of the twentieth century thanks to the wider applications in numerous fields such as economics, finance, physics, engineering, life sciences, environmental studies, and so forth. In this paper, we studied some key benefits of Bayesian inference and how they can be used in predicting loan default in the banking sector. Various traditional classification techniques are also presented to draw comparisons primarily in terms of the ease of interpretability and model performance. This paper includes the use of non-informative priors to attempt to arrive to the convergence of posterior distribution. Finally, with the Bayesian techniques proven to be an alternative to the classical approaches, the paper attempted to demonstrate that Bayesian techniques are indeed powerful in financial data analytics and applications. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to investigate how oil price uncertainty affects real gross domestic product (GDP) and industrial production in eight Central and Eastern European countries (CEEC). Design/methodology/approach: In the research process, the authors use the Bayesian method of inference for the two applied methodologies – Markov switching generalized autoregressive conditional heteroscedasticity (GARCH) model and quantile regression. Findings: The results clearly indicate that oil price uncertainty has a low effect on output in moderate market conditions in the selected countries. On the other hand, in the phases of contraction and expansion, which are portrayed by the tail quantiles, the authors find negative and positive Bayesian quantile parameters, which are relatively high in magnitude. This implies that in periods of deep economic crises, an increase in the oil price uncertainty reduces output, amplifying in this way recession pressures in the economy. Contrary, when the economy is in expansion, oil price uncertainty has no influence on the output. The probable reason lies in the fact that the negative effect of oil volatility is not strong enough in the expansion phase to overpower all other positive developments which characterize a growing economy. Also, evidence suggests that increased oil uncertainty has a more negative effect on industrial production than on real GDP, whereas industrial share in GDP plays an important role in how strong some CEECs are impacted by oil uncertainty. Originality/value: This paper is the first one that investigates the spillover effect from oil uncertainty to output in CEEC. [ABSTRACT FROM AUTHOR]

Bridge cable is an important force transmission component of bridge, but it is easy to be damaged during service, such as fatigue damage and corrosion damage, which seriously threatens the safety of bridge structure. Therefore, it is necessary to identify damage of cable force. Generally, the damage of cable force can be identified by the change of cable frequency. This paper establishes a cable force damage identification model based on Bayesian inference and uses Metropolis‐Hastings (MH) algorithm to solve the posterior probability function of unknown parameter. In the Bayesian inference model, the influence of the priori function of unknown parameters on the posterior probability distribution model is discussed. In the MH algorithm, the influence of different proposed distributions (Normal distribution, Gamma distribution and Weibull distribution) on the sampling results is discussed based on three numerical simulation studies, and the influence of burned sample proportion on the establishment of a posteriori distribution function is analyzed. Furthermore, the influence of monitoring noise data and missing data on cable force damage identification is considered, and the robustness of the proposed method is analyzed. [ABSTRACT FROM AUTHOR]

An investigation into oomycete diversity in rice paddies of Fars Province in Iran led to the identification of two new Pythium sensu lato (s.l.) species as Globisporangium izadpanahii sp. nov. and Pythium banihashemianum sp. nov. The identification was based on morphological and physiological features as well as on the phylogenetic analysis of nuclear (ITS and βtub) and mitochondrial (cox1 and cox2) loci using Bayesian inference and Maximum Likelihood. The present paper formally describes these two new species and defines their phylogenetic relationships with other congeneric species. According to multiple gene genealogy analysis, G. izadpanahii sp. nov. was grouped with other species of Globisporangium (formerly, clade G of Pythium s.l.) and was closely related to both G. nagaii and the recently described G. coniferarum. The second species, designated P. banihashemianum sp. nov., was grouped with other species of Pythium sensu stricto (formerly, clade B of Pythium s.l.) and, according to the phylogenetic analysis, shared an ancestor with P. plurisporium. The production of globose hyphal swellings was a major characteristic of G. izadpanahii sp. nov., which did not produce vesicles and zoospores. In pathogenicity tests on rice seedlings, P. banihashemianum sp. nov. isolates were highly pathogenic and caused severe root and crown rot, while G. izadpanahii sp. nov. isolates were not pathogenic. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel approach to state estimation in dynamic systems by combining Physics-Informed Neural Networks (PINNs) with an adaptive Unscented Kalman Filter (UKF). Recognizing the limitations of traditional state estimation methods, we refine the PINN architecture with hybrid loss functions and Monte Carlo Dropout for enhanced uncertainty estimation. The Unscented Kalman Filter is augmented with an adaptive noise covariance mechanism and incorporates model parameters into the state vector to improve adaptability. We further validate this hybrid framework by integrating the enhanced PINN with the UKF for a seamless state prediction pipeline, demonstrating significant improvements in accuracy and robustness. Our experimental results show a marked enhancement in state estimation fidelity for both position and velocity tracking, supported by uncertainty quantification via Bayesian inference and Monte Carlo Dropout. We further extend the simulation and present evaluations on a double pendulum system and state estimation on a quadcopter drone. This comprehensive solution is poised to advance the state-of-the-art in dynamic system estimation, providing unparalleled performance across control theory, machine learning, and numerical optimization domains. [ABSTRACT FROM AUTHOR]

In this paper, we are proposing extensions to the multinomial principal component analysis (MPCA) framework, which is a Dirichlet (Dir)-based model widely used in text document analysis. The MPCA is a discrete analogue to the standard PCA (it operates on continuous data using Gaussian distributions). With the extensive use of count data in modeling nowadays, the current limitations of the Dir prior (independent assumption within its components and very restricted covariance structure) tend to prevent efficient processing. As a result, we are proposing some alternatives with flexible priors such as generalized Dirichlet (GD) and Beta-Liouville (BL), leading to GDMPCA and BLMPCA models, respectively. Besides using these priors as they generalize the Dir, importantly, we also implement a deterministic method that uses variational Bayesian inference for the fast convergence of the proposed algorithms. Additionally, we use collapsed Gibbs sampling to estimate the model parameters, providing a computationally efficient method for inference. These two variational models offer higher flexibility while assigning each observation to a distinct cluster. We create several multitopic models and evaluate their strengths and weaknesses using real-world applications such as text classification and sentiment analysis. [ABSTRACT FROM AUTHOR]

Selection of relevant fixed and random effects without prior choices made from possibly insufficient theory is important in mixed models. Inference with current boosting techniques suffers from biased estimates of random effects and the inflexibility of random effects selection. This paper proposes a new inference method "BayesBoost" that integrates a Bayesian learner into gradient boosting with simultaneous estimation and selection of fixed and random effects in linear mixed models. The method introduces a novel selection strategy for random effects, which allows for computationally fast selection of random slopes even in high-dimensional data structures. Additionally, the new method not only overcomes the shortcomings of Bayesian inference in giving precise and unambiguous guidelines for the selection of covariates by benefiting from boosting techniques, but also provides Bayesian ways to construct estimators for the precision of parameters such as variance components or credible intervals, which are not available in conventional boosting frameworks. The effectiveness of the new approach can be observed via simulation and in a real-world application. [ABSTRACT FROM AUTHOR]

Model updating procedures based on experimental data are commonly used in case of historic buildings to identify numerical models that are subsequently employed to assess their structural behaviour. The reliability of these models is closely related to their ability to account for all the uncertainties that are involved in the knowledge process. In this regard, to handle these uncertainties and quantify their propagation, Bayesian inference is frequently employed being able to deal with the effects of parameter uncertainty, observation errors and model inadequacy. The computation of the posterior distribution through Bayesian inference needs–however–the evaluation of the likelihood function, which requires solving complex multi-dimensional integration problems. To bridge this shortcoming, the paper compares two Bayesian inference approaches to show how different approximations affect the results of simulated inference: a discrete approach for the likelihood computation in the Bayesian Model Updating (BMU) and a Monte Carlo likelihood-free method known as Approximate Bayesian Computation (ABC) are reported. As reference, the typology of historic masonry towers was considered by using their natural frequencies as experimental data for model updating. The two procedures provide very similar results supporting the validity of both methods despite ABC turns out to be a more flexible approach. [ABSTRACT FROM AUTHOR]

In this paper, we have considered the classical and Bayesian inference of the unknown parameters of the lifetime distribution based on the observations obtained from a simple step‐stress life‐testing (SSLT) experiment and when more than one cause of failures are observed. We have used the Tampered Random Variable (TRV) approach. The main advantage of the TRV approach is that it can be easily extended to a multiple step‐stress model as well as for different lifetime distributions. In this paper, it is assumed that the lifetime of the experimental units at each stress level follows Weibull distribution with the same shape parameter and different scale parameters. Further, we have introduced different tempering co‐efficient for different causes of failures. The maximum likelihood estimators and the associated asymptotic confidence intervals are obtained based on Type‐II censored observations. Further, we have considered the Bayesian inference of the unknown model parameters based on a fairly general class prior distributions. An extensive simulation study is performed to examine the performances of the proposed method, and the analysis of a real data set has been provided to show how the method can be used in practice. We have compared the TRV model with some of the other existing models, and the TRV model provides a better fit in terms of information theoretic criteria. We have also provided some optimality criteria, to determine the optimal stress change time and some sensitivity analyses have been performed. Most of the methods can be extended for other lifetime distributions also. [ABSTRACT FROM AUTHOR]

This paper discusses the challenging issues that reliability practitioners face in conducting destructive tests that lead to completely censored lifetimes, especially in estimating the defect rate of products. Manufacturers need to measure the defect rate for quality control purposes, but obtaining enough defective devices for accurate estimation is not easy when the defect rate is relatively low. To address the issues, a Bayesian approach for estimating the defect rate is proposed in this paper. The proposed method is devised to make up for the heavy computational burdens of the Metropolis-Hastings algorithm. To quantify the uncertainty in the Bayesian estimation, a nonparametric bootstrap technique is employed to construct a credible interval for the defect rate. The performance of the proposed method is evaluated through a variety of Monte Carlo simulation studies. The efficiency of the proposed Bayesian estimation procedure is validated using a real-world dataset of return-springs in DC motor systems under an accelerated destructive degradation test. • Estimate the defect rate of products in conducting destructive tests with completely censored lifetime data. • Propose a computationally efficient Bayesian estimator of an analytical form for the defect rate with masking. • Propose a nonparametric bootstrap technique to construct a credible interval for the defect rate. • The proposed method is validated using accelerated destructive degradation testing data of return-springs. [ABSTRACT FROM AUTHOR]

The basic Markov-switching model has been extended in various ways ever since the seminal work of Hamilton (1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle." Econometrica 57: 357–84). However, the estimation of Markov-switching models in the literature has relied upon parametric assumptions on the distribution of the error term. In this paper, we present a Bayesian approach for estimating Markov-switching models with unknown and potentially non-normal error distributions. We approximate the unknown distribution of the error term by the Dirichlet process mixture of normals, in which the number of mixtures is treated as a parameter to estimate. In doing so, we pay special attention to the identification of the model. We then apply the proposed model and MCMC procedure to the growth of the postwar U.S. industrial production index. Our model can effectively control for irregular components that are not related to business conditions. This leads to sharp and accurate inferences on recession probabilities. [ABSTRACT FROM AUTHOR]

Increases in the use of Bayesian inference in applied analysis, the complexity of estimated models, and the popularity of efficient Markov chain Monte Carlo (MCMC) inference under conjugate priors have led to more scrutiny regarding the specification of the parameters in prior distributions. Impact of prior parameter assumptions on posterior statistics is commonly investigated in terms of local or pointwise assessments, in the form of derivatives or more often multiple evaluations under a set of alternative prior parameter specifications. This paper expands upon these localized strategies and introduces a new approach based on the graph of posterior statistics over prior parameter regions (sensitivity manifolds) that offers additional measures and graphical assessments of prior parameter dependence. Estimation is based on multiple point evaluations with Gaussian processes, with efficient selection of evaluation points via active learning, and is further complemented with derivative information. The application introduces a strategy to assess prior parameter dependence in a multivariate demand model with a high dimensional prior parameter space, where complex prior-posterior dependence arises from model parameter constraints. The new measures uncover a considerable prior dependence beyond parameters suggested by theory, and reveal novel interactions between the prior parameters and the elasticities. [ABSTRACT FROM AUTHOR]

The paper examines the question of non-anonymous Growth Incidence Curves (na-GIC) from a Bayesian inferential point of view. Building on the notion of conditional quantiles of Barnett (1976. "The Ordering of Multivariate Data." Journal of the Royal Statistical Society: Series A 139: 318–55), we show that removing the anonymity axiom leads to a complex and shaky curve that has to be smoothed, using a non-parametric approach. We opted for a Bayesian approach using Bernstein polynomials which provides confidence intervals, tests and a simple way to compare two na-GICs. The methodology is applied to examine wage dynamics in a US university with a particular attention devoted to unbundling and anti-discrimination policies. Our findings are the detection of wage scale compression for higher quantiles for all academics and an apparent pro-female wage increase compared to males. But this pro-female policy works only for academics and not for the para-academics categories created by the unbundling policy. [ABSTRACT FROM AUTHOR]

This paper tackles the challenge of time series forecasting in the presence of missing data. Traditional methods often struggle with such data, which leads to inaccurate predictions. We propose a novel framework that combines the strengths of Generative Adversarial Networks (GANs) and Bayesian inference. The framework utilizes a Conditional GAN (C-GAN) to realistically impute missing values in the time series data. Subsequently, Bayesian inference is employed to quantify the uncertainty associated with the forecasts due to the missing data. This combined approach improves the robustness and reliability of forecasting compared to traditional methods. The effectiveness of our proposed method is evaluated on a real-world dataset of air pollution data from Mexico City. The results demonstrate the framework's capability to handle missing data and achieve improved forecasting accuracy. [ABSTRACT FROM AUTHOR]

This paper presents a novel stochastic optimization methodology to perform empirical Bayesian inference in semi-blind image deconvolution problems. Given a blurred image and a parametric class of possible operators, the proposed optimization approach automatically calibrates the parameters of the blur model by maximum marginal likelihood estimation, followed by (non-blind) image deconvolution by maximum a posteriori estimation conditionally to the estimated model parameters. In addition to the blur model, the proposed approach also automatically calibrates the noise level as well as any regularization parameters. The marginal likelihood of the blur, noise, and regularization parameters is generally computationally intractable, as it requires calculating several integrals over the entire solution space. Our approach addresses this difficulty by using a stochastic approximation proximal gradient optimization scheme, which iteratively solves such integrals by using a Moreau- Yosida regularized unadjusted Langevin Markov chain Monte Carlo algorithm. This optimization strategy can be easily and efficiently applied to any model that is log-concave and by using the same gradient and proximal operators that are required to compute the maximum a posteriori solution by convex optimization. We provide convergence guarantees for the proposed optimization scheme under realistic and easily verifiable conditions and subsequently demonstrate the effectiveness of the approach with a series of deconvolution experiments and comparisons with alternative strategies from the state of the art [ABSTRACT FROM AUTHOR]

The modelling of many real-world problems relies on computationally heavy simulations of randomly interacting individuals or agents. However, the values of the parameters that underlie the interactions between agents are typically poorly known, and hence they need to be inferred from macroscopic observations of the system. Since statistical inference rests on repeated simulations to sample the parameter space, the high computational expense of these simulations can become a stumbling block. In this paper, we compare two ways to mitigate this issue in a Bayesian setting through the use of machine learning methods: One approach is to construct lightweight surrogate models to substitute the simulations used in inference. Alternatively, one might altogether circumvent the need for Bayesian sampling schemes and directly estimate the posterior distribution. We focus on stochastic simulations that track autonomous agents and present two case studies: tumour growths and the spread of infectious diseases. We demonstrate that good accuracy in inference can be achieved with a relatively small number of simulations, making our machine learning approaches orders of magnitude faster than classical simulation-based methods that rely on sampling the parameter space. However, we find that while some methods generally produce more robust results than others, no algorithm offers a one-size-fits-all solution when attempting to infer model parameters from observations. Instead, one must choose the inference technique with the specific real-world application in mind. The stochastic nature of the considered real-world phenomena poses an additional challenge that can become insurmountable for some approaches. Overall, we find machine learning approaches that create direct inference machines to be promising for real-world applications. We present our findings as general guidelines for modelling practitioners. Author summary: Computer simulations play a vital role in modern science as they are commonly used to compare theory with observations. One can infer the properties of a system by comparing the data to the predicted behaviour in different scenarios. Each scenario corresponds to a simulation with slightly different settings. However, since real-world problems are highly complex, the simulations often require extensive computational resources, making direct comparisons with data challenging, if not insurmountable. It is, therefore, necessary to resort to inference methods that mitigate this issue, but it is not clear-cut what path to choose for any specific research problem. In this paper, we provide general guidelines for how to make this choice. We do so by studying examples from oncology and epidemiology and by taking advantage of machine learning. More specifically, we focus on simulations that track the behaviour of autonomous agents, such as single cells or individuals. We show that the best way forward is problem-dependent and highlight the methods that yield the most robust results across the different case studies. Rather than relying on a single inference technique, we recommend employing several methods and selecting the most reliable based on predetermined criteria. [ABSTRACT FROM AUTHOR]

The reversible-jump Markov chain Monte Carlo (RJMCMC) algorithm can generate a jump Markov chain in the parameter space of different dimensions, and select a suitable model effectively. In this paper, when the order of the double threshold variables autoregressive (DT-AR) is unknown, the RJMCMC method is designed to identify the order of the DT-AR model in this paper. The simulation experiments and the real example show that the proposed method works well in identifying the order and estimating the parameters of the DT-AR model simultaneously. [ABSTRACT FROM AUTHOR]

The accuracy of single-mode optical imaging systems for vehicle target recognition is limited by external ambient illumination or imaging equipment resolution. In this paper, a vehicle target recognition method based on visible and infrared image fusion using Bayesian inference is proposed. Based on the significance area detection combined with Spectral Residual (SR) and EdgeBox algorithms, the target area is marked on the visible light image, and the maximum between-class variance method and GrabCut algorithm are used to segment vehicle targets in marked images. The open operation filter is employed to extract the vehicle target features in the infrared image, and the fusion result of the visible light image and the infrared image is obtained by introducing the Intersection Over Union (IOU), and as the parameter of Bayesian inference, the class and attribute of the parameter are defined and substituted into the established naive Bayesian classification model, and the probability of the class is calculated to determine whether the vehicle target is recognized. Experiments under different test conditions were carried out, and the experimental results were as follows: the accuracy of image target recognition reached 77% when the vehicle target was not occluded; when the vehicle target was partially occluded, the accuracy of image target recognition reached 74%; the results verified that the proposed method can recognize vehicle targets in different scenarios. [ABSTRACT FROM AUTHOR]

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a Bayesian approach: parameter and prediction uncertainties become easily available, facilitating more rigorous statistical analysis. Furthermore, prior knowledge can be incorporated. However, the construction of scalable techniques that combine both structural and parameter uncertainty remains a challenge. In this paper, we apply the concept of model uncertainty as a framework for structural learning in BNNs and, hence, make inferences in the joint space of structures/models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Experimental results on a range of benchmark datasets show that we obtain comparable accuracy results with the competing models, but based on methods that are much more sparse than ordinary BNNs. [ABSTRACT FROM AUTHOR]

In many real-life scenarios, one variable is observed only if the other concomitant variable or the set of concomitant variables (in the multivariate scenario) is truncated from below, above, or from a two-sided approach. Hidden truncation models have been applied to analyze data when bivariate or multivariate observations are subject to some form of truncation. While the statistical inference for hidden truncation models (truncation from above) under the frequentist and the Bayesian paradigms has been adequately discussed in the literature, the estimation of a two-sided hidden truncation model under the Bayesian framework has not yet been discussed. In this paper, we consider the Bayesian inference for a general two-sided hidden truncation model based on the Arnold–Strauss bivariate exponential distribution. In addition, a Bayesian model selection approach based on the Bayes factor to select between models without truncation, with truncation from below, from above, and two-sided truncation is also explored. An extensive simulation study is carried out for varying parameter choices under the conjugate prior set-up. For illustrative purposes, a real-life dataset is re-analyzed to demonstrate the applicability of the proposed methodology. [ABSTRACT FROM AUTHOR]

Carl Morris 1938–2023 was well-known for his pioneering research in Bayesian multiparameter inference and prediction. Morris was also known for his development of statistical thinking and methodology in sports. This paper provides an overview of Morris' contributions in sports. This includes Morris' experience in sports as a youth, summaries of some of Morris' best-known contributions using sports data, his influence working with students, and some of Morris' thinking about the interplay of statistics and sports. [ABSTRACT FROM AUTHOR]

The spatially misaligned data problem occurs when data at different spatial scales need to be combined. Bayesian hierarchical models such as melding and downscaler approaches are suitable to solve this problem but their application is limited when MCMC is used for inference due to the high computational cost. The use of INLA and SPDE represents an alternative to MCMC for Bayesian inference that enables faster inference for latent Gaussian models. In this paper, we describe how INLA and SPDE can be adapted to fit Bayesian melding and downscaler models to combine spatially misaligned data. We assess the performance of the models using simulated and real data in a range of scenarios and sampling strategies and compare the suitability of the models in each situation. We also show how to obtain fine particulate matter (PM 2.5 ) predictions in the UK at a continuous surface and at policy-relevant spatial scales by combining spatially misaligned monitoring station data, satellite-derived indicators, road information, and environmental factors. [ABSTRACT FROM AUTHOR]

This paper investigates statistical inferences for product lifetimes following the inverted modified Lindley distribution, utilizing progressive Type-II censored data. The estimation of model parameters employs the maximum likelihood method, complemented by the construction of approximate confidence intervals. Bayesian estimates are also explored, incorporating squared error and linear exponential loss functions with noninformative priors. To approximate Bayes estimates, the proposal presents Gibbs sampling based on the MCMC algorithm. This results in the generation of the greatest posterior density credible intervals for the parameters. A real data analysis is conducted to validate the accuracy of all the models and methods discussed. Finally, computational studies using Monte Carlo simulations are presented to compare the suggested estimators. [ABSTRACT FROM AUTHOR]

In this paper, we consider aggregated functional data composed by a linear combination of component curves and the problem of estimating these component curves. We propose the application of a bayesian wavelet shrinkage rule based on a mixture of a point mass function at zero and the logistic distribution as prior to wavelet coefficients to estimate mean curves of components. This procedure has the advantage of estimating component functions with important local characteristics such as discontinuities, spikes and oscillations for example, due the features of wavelet basis expansion of functions. Simulation studies were done to evaluate the performance of the proposed method, and its results are compared with a spline-based method. An application on the so-called Tecator dataset is also provided. [ABSTRACT FROM AUTHOR]

Progressive type-II (Prog-II) censoring schemes are gaining traction in estimating the parameters, and reliability characteristics of lifetime distributions. The focus of this paper is to enhance the accuracy and reliability of such estimations for the inverse power exponentiated Pareto (IPEP) distribution, a flexible extension of the exponentiated Pareto distribution suitable for modeling engineering and medical data. We aim to develop novel statistical inference methods applicable under Prog-II censoring, leading to a deeper understanding of failure time behavior, improved decision-making, and enhanced overall model reliability. Our investigation employs both classical and Bayesian approaches. The classical technique involves constructing maximum likelihood estimators of the model parameters and their bootstrap covariance intervals. Using the Gibbs process constructed by the Metropolis–Hasting sampler technique, the Markov chain Monte Carlo method provides Bayesian estimates of the unknown parameters. In addition, an actual data analysis is carried out to examine the estimation process's performance under this ideal scheme. [ABSTRACT FROM AUTHOR]