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Post-disaster recovery modelling of engineering systems has become an important facet of catastrophe risk modelling and management for natural hazards. The post-disaster recovery trajectory of a civil infrastructure system can be quantified using (a) the initial post-disaster functionality level, Qo; (b) rapidity, h (i.e., the rate of functionality restoration); and (c) recovery time, Rt. This study uses a Bayesian estimation approach to derive a set of probabilistic models to estimate Qo, Rt, and h of electric power networks (EPNs) using post-earthquake recovery data from 16 large earthquakes in Japan between 2003 and 2022. The considered predictor (explanatory) variables include earthquake magnitude, year of occurrence, seismic intensity, and exposed population (PEX). Apart from being a simple and efficient stand-alone tool, the proposed data-driven models can be a useful benchmarking tool for simulation-based approaches for EPN recovery modelling. [ABSTRACT FROM AUTHOR]

Integration of Bayesian parameter estimation (BPE) with model‐based design of experiments (MBDoE) aims to estimate process parameters efficiently and systematically. To achieve more efficient use of resources by iteratively selecting informative experiments based on current knowledge about the parameters, an integrated method with BPE and MBDoE is proposed in this article. A built‐in Markov Chain Monte Carlo is also developed to yield not only the distribution profile of the estimated parameters but also aid in the determination of stopping criteria and the estimation of noise. Two applications of dynamic batch reactor systems are presented. Comparative analysis substantiates the superior performance of this approach in terms of parameter accuracy and the efficiency of experimentation. [ABSTRACT FROM AUTHOR]

The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power of α , and then used as the prior distribution in the analysis of the replication data. Posterior distribution and Bayes factor hypothesis tests related to the power parameter α quantify the degree of compatibility between the original and replication study. Inferences for other parameters, such as effect sizes, dynamically borrow information from the original study. The degree of borrowing depends on the conflict between the two studies. The practical value of the approach is illustrated on data from three replication studies, and the connection to hierarchical modeling approaches explored. We generalize the known connection between normal power priors and normal hierarchical models for fixed parameters and show that normal power prior inferences with a beta prior on the power parameter α align with normal hierarchical model inferences using a generalized beta prior on the relative heterogeneity variance I 2 . The connection illustrates that power prior modeling is unnatural from the perspective of hierarchical modeling since it corresponds to specifying priors on a relative rather than an absolute heterogeneity scale. [ABSTRACT FROM AUTHOR]

In the near future, space-borne gravitational wave (GW) detector LISA can open the window of low-frequency band of GW and provide new tools to test gravity theories. In this work, we consider multi-parameter tests of GW generation and propagation where the deformation coefficients are varied simultaneously in parameter estimation and the principal component analysis (PCA) method are used to transform posterior samples into new bases for extracting the most informative components. The dominant components can be more sensitive to potential departures from general relativity (GR). We extend previous works by employing Bayesian parameter estimation and performing both tests with injections of GR and injections of subtle GR-violated signals. We also apply multi-parameter tests with PCA in the phenomenological test of GW propagation. This work complements previous works and further demonstrates the enhancement provided by the PCA method. Considering a supermassive black hole binary system as the GW source, we show that subtle departures will be more obvious in posteriors of PCA parameters. The departures less than 1σ in original parameters can yield significant departures in first 5 dominant PCA parameters.

Based on VaR and VaB research methods, this paper constructs a regression model based on industry risk-return value metrics using a Bayesian-expected quantile regression algorithm in the context of big data. The parameters of the Bayesian model are estimated using the decision function, and then the metric effects of the model are evaluated using AIC and BIC. Finally, the relationship between industry risk and return is evaluated using the Bayesian-Expectation Quartile regression model. Under the Bayesian-Expectile model, the difference between the correlation coefficients of AIC (−0.7431, −0.9563, −0.7872, −0.9137) and BIC (−0.0547, −0.0768, −0.0559) is relatively small, reflecting the fact that the Internet financial innovations have not significantly pushed up the risk-free rate of return of the society while pushing up the society’s financing cost. In addition, the three models used in this paper have close EvaR prediction results for information technology, daily consumption and telecommunication services, indicating that the credibility of the industry risk prediction results proposed in this paper is high. The relationship between idiosyncratic volatility and the adjusted return for the next period is related to the time-varying nature of the characteristics of individual stocks, as well as the individual stocks of industry-risk firms. Incorporating factors that affect conditional equity premiums into the time-varying conditions of individual stocks can more accurately reflect the risk-taking of individual stocks of risky firms.

Metabolic fluxes are the rates of life-sustaining chemical reactions within a cell and metabolites are the components. Determining the changes in these fluxes is crucial to understanding diseases with metabolic causes and consequences. Kinetic flux profiling (KFP) is a method for estimating flux that utilizes data from isotope tracing experiments. In these experiments, the isotope-labeled nutrient is metabolized through a pathway and integrated into the downstream metabolite pools. Measurements of proportion labeled for each metabolite in the pathway are taken at multiple time points and used to fit an ordinary differential equations model with fluxes as parameters. We begin by generalizing the process of converting diagrams of metabolic pathways into mathematical models composed of differential equations and algebraic constraints. The scaled differential equations for proportions of unlabeled metabolite contain parameters related to the metabolic fluxes in the pathway. We investigate flux parameter identifiability given data collected only at the steady state of the differential equation. Next, we give criteria for valid parameter estimations in the case of a large separation of timescales with fast-slow analysis. Bayesian parameter estimation on simulated data from KFP experiments containing both irreversible and reversible reactions illustrates the accuracy and reliability of flux estimations. These analyses provide constraints that serve as guidelines for the design of KFP experiments to estimate metabolic fluxes., Competing Interests: Declarations: The authors have no relevant financial or non-financial interests to disclose. The authors declare that the data supporting the findings of this study are available within the paper or its supplementary information files. This work was supported by Grants NIH RO1 DK104998 (EBT), NIH RO1 DK138664 (EBT), University of Iowa Distinguished Scholar Award (EBT)., (© 2024. The Author(s).)

In the near future, space-borne gravitational wave (GW) detector LISA can open the window of low-frequency band of GW and provide new tools to test gravity theories. In this work, we consider multi-parameter tests of GW generation and propagation where the deformation coefficients are varied simultaneously in parameter estimation and the principal component analysis (PCA) method are used to transform posterior samples into new bases for extracting the most informative components. The dominant components can be more sensitive to potential departures from general relativity (GR). We extend previous works by employing Bayesian parameter estimation and performing both tests with injections of GR and injections of subtle GR-violated signals. We also apply multi-parameter tests with PCA in the phenomenological test of GW propagation. This work complements previous works and further demonstrates the enhancement provided by the PCA method. Considering a supermassive black hole binary system as the GW source, we show that subtle departures will be more obvious in posteriors of PCA parameters. The departures less than 1 σ in original parameters can yield significant departures in first 5 dominant PCA parameters. • Multi-parameter tests of GW generation and propagation. • PCA is helpful in capturing potential subtle departures. • Using the Bayesian tool in parameter estimation. [ABSTRACT FROM AUTHOR]