Laplace Approximation Method Research Articles

Pemodelan Tingkat Kemiskinan di Provinsi Aceh Menggunakan Distribusi Poisson dan Binomial Negatif

This study aims to model the poverty rate in Aceh Province using the Generalized Linear Models (GLMs) approach with the Integrated Nested Laplace Approximation (INLA) method. The models used in this study include Poisson and Negative Binomial regression. The data used includes variables of per capita expenditure, population density, average years of schooling, open unemployment rate, and labor force participation. Multicollinearity tests were conducted using Tolerance and Variance Inflation Factor (VIF) values to ensure the absence of multicollinearity problems between predictor variables. The results show that the Negative Binomial model is better than the Poisson model, as indicated by the smaller WAIC value. The average years of schooling variable has a significant negative effect, while the open unemployment rate has a significant positive effect on the poverty rate. Meanwhile, the variables of expenditure per capita, population density, and labor force participation make smaller and partially insignificant contributions in the model. Thus, increasing access to education and reducing unemployment are key factors in poverty alleviation efforts in Aceh Province. The results of this study are expected to serve as a reference for policy makers in formulating effective strategies to reduce poverty.

Assessing the survival time of hospitalized patients in Eastern Ethiopia during 2019-2020 using the Bayesian approach: A retrospective cohort study.

Severe acute malnutrition remains a significant health challenge, particularly in low- and middle-income countries. The aim of this study was to determine the survival time of under-five children with severe acute malnutrition. A retrospective cohort study was conducted at a hospital, focusing on under-five children with severe acute malnutrition. The study included 322 inpatients admitted to the Chiro hospital in Chiro, Ethiopia, between September 2019 and August 2020, whose data was obtained from medical records. Survival functions were analysed using Kaplan‒Meier plots and log-rank tests. The survival time of severe acute malnutrition was further analysed using the Cox proportional hazards model and Bayesian parametric survival models, employing integrated nested Laplace approximation methods. Among the 322 patients, 118 (36.6%) died as a result of severe acute malnutrition. The estimated median survival time for inpatients was found to be 2 weeks. Model selection criteria favored the Bayesian Weibull accelerated failure time model, which demonstrated that age, body temperature, pulse rate, nasogastric(NG) tube usage, hypoglycemia, anemia, diarrhea, dehydration, malaria, and pneumonia significantly influenced the survival time of severe acute malnutrition. This study revealed that children below 24 months, those with altered body temperature and pulse rate, NG tube usage, hypoglycemia, and comorbidities such as anemia, diarrhea, dehydration, malaria, and pneumonia had a shorter survival time when affected by severe acute malnutrition under the age of five. To reduce the death rate of children under 5 years of age, it is necessary to design community management for acute malnutrition to ensure early detection and improve access to and coverage for children who are malnourished.

Spatiotemporal Bayesian modeling of the risk of congenital syphilis in São Paulo, SP, Brazil

The aim of this study is to analyze the spatiotemporal risk of congenital syphilis (CS) in high-prevalence areas in the city of São Paulo, SP, Brazil, and to evaluate its relationship with socioeconomic, demographic, and environmental variables. An ecological study was conducted based on secondary CS data with spatiotemporal components collected from 310 areas between 2010 and 2016. The data were modeled in a Bayesian context using the integrated nested Laplace approximation (INLA) method. Risk maps showed an increasing CS trend over time and highlighted the areas that presented the highest and lowest risk in each year. The model showed that the factors positively associated with a higher risk of CS were the Gini index and the proportion of women aged 18–24 years without education or with incomplete primary education, while the factors negatively associated were the proportion of women of childbearing age and the mean per capita income.

Personalized Dynamic Pricing Based on Improved Thompson Sampling

This study investigates personalized pricing with demand learning. We first encode consumer-personalized feature information into high-dimensional vectors, then establish the relationship between this feature vector and product demand using a logit model, and finally learn demand parameters through historical transaction data. To address the balance between learning and revenue, we introduce the Thompson Sampling algorithm. Considering the difficulty of Bayesian inference in Thompson Sampling owing to high-dimensional feature vectors, we improve the basic Thompson Sampling by approximating the likelihood function of the logit model with the Pólya-Gamma (PG) distribution and by proposing a Thompson Sampling algorithm based on the PG distribution. To validate the proposed algorithm’s effectiveness, we conduct experiments using both simulated data and real loan data provided by the Columbia University Revenue Management Center. The study results demonstrate that the Thompson Sampling algorithm based on the PG distribution proposed outperforms traditional Laplace approximation methods regarding convergence speed and regret value in both real and simulated data experiments. The real-time personalized pricing algorithm developed here not only enriches the theoretical research of personalized dynamic pricing, but also provides a theoretical basis and guidance for enterprises to implement personalized pricing.

Abstract P322: Mapping Geographic Variation in Hypertension Prevalence in United States Congressional Districts Using Spatial Modeling

Introduction: Using spatial methods to explore drivers of hypertension (HTN) risks, commonalities, and differences across geographical areas can be assessed to inform future public health research and advocacy efforts. Objectives: To examine ecological associations between social determinants of health (SDoH), space, and HTN across congressional districts (CDs) in effect for the 118th US Congress. Methods: We obtained aggregate district-level data from Congressional District Health Dashboard on health behaviors, exposures, and outcomes for US CDs in 2019. Primary outcome was HTN prevalence, defined as proportion of adults who self-reported diagnosed HTN. Exposure variables were SDoH: health outcomes (diabetes, obesity, frequent physical and mental distress), health behaviors (physical activity, binge drinking, smoking), clinical care (routine checkups), and physical environment (air pollution). We fitted a hierarchical Bayesian Besag-York-Mollié model using the integrated nested Laplace approximation (INLA) method, which allowed the estimation of spatial autocorrelation of HTN prevalence at CDs level, accounting for SDoH. Results: Across 421 CDs, we found a variation in the modeled linear proportion of 83% across the CDs in the United States after adjusting for known HTN risk factors at the CDs level. A notable degree of variation in HTN prevalence exists within specific CDs, independent of recognized risk factors ( Figure ). These unmeasured variables act as confounding elements, and districts with darker shading indicate increased HTN attributed to the district, while lighter, red-shaded districts exhibit a reduced district-specific proportion of HTN. Conclusions: Our findings show significant geographic variation of HTN beyond known risk factors which underscores the significance of adopting a spatial perspective to understand HTN prevalence. It emphasizes the necessity for tailored public health interventions that consider the unique geographic context of each CDs.

Use of machine learning tools to predict health risks from climate-sensitive extreme weather events: A scoping review

Machine learning (ML) algorithms may play a role in predicting the adverse health impacts of climate-sensitive extreme weather events because accurate prediction of such effects can guide proactive clinical and policy decisions. To systematically review the literature that describe ML algorithms that predict health outcomes from climate-sensitive extreme weather events. A comprehensive literature search was performed in the following databases from inception–October 2022: Ovid MEDLINE, Ovid EMBASE, The Cochrane Library, Web of Science, bioRxiv, medRxiv, Institute of Electrical and Electronic Engineers, Google Scholar, and Engineering Village. The retrieved studies were then screened for eligibility against predefined inclusion/exclusion criteria. The studies were then qualitatively synthesized based on the type of extreme weather event. Gaps in the literature were identified based on this synthesis. Of the 6096 records screened, seven studies met the inclusion criteria. Six of the studies predicted health outcomes from heat waves, and one for flooding. Health outcomes described included 1) all-cause non-age standardized mortality rates, 2) heat-related conditions and 3) post-traumatic stress disorder. Prediction models were developed using six validated ML techniques including non-linear exponential regression, logistic regression, spatiotemporal Integrated Laplace Approximation (INLA), random forest and decision tree methods (DT), and support vector machines (SVM). Use of ML algorithms to assess adverse health impacts from climate-sensitive extreme weather events is possible. However, to fully utilize these ML techniques, better quality data suitable for use is desirable. Development of data standards for climate change and health may help ensure model robustness and comparison across space and time. Future research should also consider health equity implications.

Estimation for stochastic differential equation mixed models using approximation methods

<abstract><p>We used a class of stochastic differential equations (SDE) to model the evolution of cattle weight that, by an appropriate transformation of the weight, resulted in a variant of the Ornstein-Uhlenbeck model. In previous works, we have dealt with estimation, prediction, and optimization issues for this class of models. However, to incorporate individual characteristics of the animals, the average transformed size at maturity parameter $ \alpha $ and/or the growth parameter $ \beta $ may vary randomly from animal to animal, which results in SDE mixed models. Obtaining a closed-form expression for the likelihood function to apply the maximum likelihood estimation method is a difficult, sometimes impossible, task. We compared the known Laplace approximation method with the delta method to approximate the integrals involved in the likelihood function. These approaches were adapted to allow the estimation of the parameters even when the requirement of most existing methods, namely having the same age vector of observations for all trajectories, fails, as it did in our real data example. Simulation studies were also performed to assess the performance of these approximation methods. The results show that the approximation methods under study are a very good alternative for the estimation of SDE mixed models.</p></abstract>

Mapping brucellosis risk in Kenya and its implications for control strategies in sub-Saharan Africa

In Sub-Saharan Africa (SSA), effective brucellosis control is limited, in part, by the lack of long-term commitments by governments to control the disease and the absence of reliable national human and livestock population-based data to inform policies. Therefore, we conducted a study to establish the national prevalence and develop a risk map for Brucella spp. in cattle to contribute to plans to eliminate the disease in Kenya by the year 2040. We randomly generated 268 geolocations and distributed them across Kenya, proportionate to the area of each of the five agroecological zones and the associated cattle population. Cattle herds closest to each selected geolocation were identified for sampling. Up to 25 cattle were sampled per geolocation and a semi-structured questionnaire was administered to their owners. We tested 6,593 cattle samples for Brucella immunoglobulin G (IgG) antibodies using an Enzyme-linked immunosorbent assay (ELISA). We assessed potential risk factors and performed spatial analyses and prevalence mapping using approximate Bayesian inference implemented via the integrated nested Laplace approximation (INLA) method. The national Brucella spp. prevalence was 6.8% (95% CI: 6.2–7.4%). Exposure levels varied significantly between agro-ecological zones, with a high of 8.5% in the very arid zone with the lowest agricultural potential relative to a low of 0.0% in the agro-alpine zone with the highest agricultural potential. Additionally, seroprevalence increased with herd size, and the odds of seropositivity were significantly higher for females and adult animals than for males or calves. Similarly, animals with a history of abortion, or with multiple reproductive syndromes had higher seropositivity than those without. At the herd level, the risk of Brucella spp. transmission was higher in larger herds, and herds with a history of reproductive problems such as abortion, giving birth to weak calves, or having swollen testes. Geographic localities with high Brucella seroprevalence occurred in northern, eastern, and southern regions of Kenya all primarily characterized by semi-arid or arid agro-ecological zones dominated by livestock pastoralism interspersed with vast areas with mixed livestock-wildlife systems. The large spatial extent of our survey provides compelling evidence for the widespread geographical distribution of brucellosis risk across Kenya in a manner easily understandable for policymakers. Our findings can provide a basis for risk-stratified pilot studies aiming to investigate the cost-effectiveness and efficacy of singular and combined preventive intervention strategies that seek to inform Kenya’s Brucellosis Control Policy.

Are ride-hailing services safer than taxis? A multivariate spatial approach with accommodation of exposure uncertainty

Despite many research efforts on ride-hailing services and taxis, limited studies have compared the safety performance of the two modes. A major challenge is the need for reliable mode-specific exposure data to model their safety outcomes. Moreover, crash frequencies of the two modes by injury severities tend to be spatially and inherently correlated. To fully address these issues, this study proposes a novel multivariate conditional autoregressive model considering measurement errors in mode-specific exposures (MVCARME). More specially, a classical measurement error structure accommodates the uncertainty of estimated mode-specific exposures, and a multivariate spatial specification is adopted to capture potential spatial and inherent correlations. The model estimation is accelerated by an integrated nest Laplace approximation method. The census tracts in the city of Chicago are set as the spatial analysis unit. The mode-specific exposures (vehicle-mile-traveled) in each census tract are estimated by trip assignments using ride-hailing and taxi trip data in 2019. The modeling results indicate that both ride-hailing crashes and taxi crashes are positively associated with transportation factors (e.g., vehicle-mile-traveled, mode-specific vehicle-mile-traveled, and traffic signal numbers), land use factors (i.e., number of educational and alcohol-related sites), and demographic factors (e.g., median household income, transit ratio, and walk ratio). By comparison, the proposed model outperforms the others (i.e., negative binomial models and multivariate conditional autoregressive model) by yielding the lowest deviance information criterion (DIC), Watanabe-Akaike information criterion (WAIC), mean absolute error (MAE), and root-mean-square error (RMSE). According to the results of t-tests, ride-hailing services are found to be prone to a higher risk of minor injury crashes compared with taxis, despite no significant difference between the risks of severe injury crashes. Methodologically, this study adds a robust safety evaluation approach for comparing crash risks of different modes to the literature. At the same time, practically, it provides researchers, practitioners, and policy-makers insights into the safety management of various mobility alternatives.

Covariance–Based Rational Approximations of Fractional SPDEs for Computationally Efficient Bayesian Inference

ABSTRACT The stochastic partial differential equation (SPDE) approach is widely used for modeling large spatial datasets. It is based on representing a Gaussian random field u on R d as the solution of an elliptic SPDE L β u = W where L is a second-order differential operator, 2 β ∈ N is a positive parameter that controls the smoothness of u and W is Gaussian white noise. A few approaches have been suggested in the literature to extend the approach to allow for any smoothness parameter satisfying β > d / 4 . Even though those approaches work well for simulating SPDEs with general smoothness, they are less suitable for Bayesian inference since they do not provide approximations which are Gaussian Markov random fields (GMRFs) as in the original SPDE approach. We address this issue by proposing a new method based on approximating the covariance operator L − 2 β of the Gaussian field u by a finite element method combined with a rational approximation of the fractional power. This results in a numerically stable GMRF approximation which can be combined with the integrated nested Laplace approximation (INLA) method for fast Bayesian inference. A rigorous convergence analysis of the method is performed and the accuracy of the method is investigated with simulated data. Finally, we illustrate the approach and corresponding implementation in the R package rSPDE via an application to precipitation data which is analyzed by combining the rSPDE package with the R-INLA software for full Bayesian inference. Supplementary materials for this article are available online.

Shape reconstructions by using plasmon resonances with enhanced sensitivity

This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel reconstruction scheme of using plasmon resonances with significantly enhanced sensitivity and resolution. First, by spectral analysis we establish a sharp quantitative relationship between the sensitivity of the reconstruction and the plasmon resonance. It shows that the sensitivity functional blows up when plasmon resonance occurs. Hence, the signal to noise ratio is significantly improved and the robustness and effectiveness of the reconstruction are ensured. Second, a variational regularization method is proposed to overcome the ill-posedness, and an alternating iteration method is introduced to automatically select the regularization parameters. Third, we use Laplace approximation method to capture the statistical information of the target scattering object. Both rigorous theoretical analysis and extensive numerical experiments are conducted to validate the promising features of our method.

Data fusion in a two-stage spatio-temporal model using the INLA-SPDE approach

This paper proposes a two-stage estimation approach for a spatial misalignment scenario that is motivated by the epidemiological problem of linking pollutant exposures and health outcomes. We use the integrated nested Laplace approximation method to estimate the parameters of a two-stage spatio-temporal model — the first stage models the exposures using data fusion while the second stage links the health outcomes to exposures. The first stage is based on the Bayesian melding model, which assumes a common latent field for the different data sources for the pollutants. The second stage fits a generalized linear mixed model using the spatial averages of the estimated latent field, and additional spatial and temporal random effects. Uncertainty from the first stage is accounted for by simulating repeatedly from the posterior predictive distribution of the latent field. A simulation study was carried out to assess the impact of the sparsity of the data on the monitors, number of time points, and the specification of the priors in terms of the biases, RMSEs, and coverage probabilities of the parameters and the block-level exposure estimates. The results show that the parameters are generally estimated correctly but there is difficulty in estimating the Matèrn field parameters. The effect of exposures on the health outcomes is the primary parameter of interest for spatial epidemiologists and health policy makers, and our results show that the proposed method estimates these very well. The proposed method is applied to measurements of NO2 concentration and respiratory hospitalizations for year 2007 in England. The results show that an increase in NO2 levels is significantly associated with an increase in the relative risks of the health outcome. Also, there is a strong spatial structure in the risks, a strong temporal autocorrelation, and a significant spatio-temporal interaction effect.

Assessing survival time of outpatients with cervical cancer: at the university of Gondar referral hospital using the Bayesian approach

BackgroundCervical cancer is the 4th most common cancer in women worldwide. as well as the 4th most common cause of cancer-related death. The main objective of this study was to identify factors that affect the survival time of outpatients with cervical cancer.MethodsA retrolective study including outpatients with cervical cancer was carried out in a hospital. To achieve the aim, 322 outpatients with cervical cancer were included in the study based on the data taken from the medical records of patients enrolled from May 15, 2018, to May 15, 2022, at the University of Gondar referral hospital, Gondar, Ethiopia. The Kaplan–Meier plots and log-rank test were used for the comparison of survival functions; the Cox-PH model and Bayesian parametric survival models were used to analyze the survival times of outpatients with cervical cancer. Integrated nested Laplace approximation methods have been applied.ResultsOut of a total of 322 patients, 118 (36.6%) died as outpatients. The estimated median survival time for patients was 42 months. Using model selection criteria, the Bayesian log-normal accelerated failure time model was found to be appropriate. According to the results of this model, oral contraceptive use, HIV, stage, grade, co-morbid disease, history of abortion, weight, histology type, FIGO stage, radiation, chemotherapy, LVSI, metastatic number, regional nodes examined, and tumor size all have a significant impact on the survival time of outpatients with cervical cancer. The Bayesian log-normal accelerated failure time model accurately predicted the survival time of cervical cancer outpatients.ConclusionsThe findings of this study suggested that reductions in weight, treatment, the presence of comorbid disease, the presence of HIV, squamous cell histology type, having a history of abortion, oral contraceptive use, a large tumor size, an increase in the International Federation of Gynecologists and Obstetricians stage, an increase in metastasis number, an increase in grade, positive regional nodes, lymphatic vascular space invasion, and late stages of cancer all shortened the survival time of cervical cancer outpatients.

Design and Analysis of an Effective Multi-Barriers Model Based on Non-Stationary Gaussian Random Fields

In this paper, we propose an extension to the barrier model, i.e., the Multi-Barriers Model, which could characterize an area of interest with different types of obstacles. In the proposed model, the area of interest is divided into two or more areas, which include a general area of interest with sampling points and the rest of the area with different types of obstacles. Firstly, the correlation between the points in space is characterized by the obstruction degree of the obstacle. Secondly, multiple Gaussian random fields are constructed. Then, continuous Gaussian fields are expressed by using stochastic partial differential equations (SPDEs). Finally, the integrated nested Laplace approximation (INLA) method is employed to calculate the posterior mean of parameters and the posterior parameters to establish a spatial regression model. In this paper, the Multi-Barriers Model is also verified by using the geostatistical model and log-Gaussian Cox model. Furthermore, the stationary Gaussian model, the barrier model and the Multi-Barriers Model are investigated in the geostatistical data, respectively. Real data sets of burglaries in a certain area are used to compare the performance of the stationary Gaussian model, barrier model and Multi-Barriers Model. The comparison results suggest that the three models achieve similar performance in the posterior mean and posterior distribution of the parameters, as well as the deviance information criteria (DIC) value. However, the Multi-Barriers Model can better interpret the spatial model established based on the spatial data of the research areas with multiple types of obstacles, and it is closer to reality.

Spatio-temporal distribution characteristics of the risk of viral hepatitis B incidence based on INLA in 14 prefectures of Xinjiang from 2004 to 2019.

This study aimed to explore the spatio-temporal distribution characteristics and risk factors of hepatitis B (HB) in 14 prefectures of Xinjiang, China, and to provide a relevant reference basis for the prevention and treatment of HB. Based on HB incidence data and risk factor indicators in 14 prefectures in Xinjiang from 2004 to 2019, we explored the distribution characteristics of the risk of HB incidence using global trend analysis and spatial autocorrelation analysis and established a Bayesian spatiotemporal model to identify the risk factors of HB and their spatio-temporal distribution to fit and extrapolate the Bayesian spatiotemporal model using the Integrated Nested Laplace Approximation (INLA) method. There was spatial autocorrelation in the risk of HB and an overall increasing trend from west to east and north to south. The natural growth rate, per capita GDP, number of students, and number of hospital beds per 10, 000 people were all significantly associated with the risk of HB incidence. From 2004 to 2019, the risk of HB increased annually in 14 prefectures in Xinjiang, with Changji Hui Autonomous Prefecture, Urumqi City, Karamay City, and Bayangol Mongol Autonomous Prefecture having the highest rates.

High resolution spatial-temporal downscaling model for historical daily precipitation using INLA

Precipitation and precipitation extremes have long been challenging to estimate. Significant progress has been made with successive generations of Earth system models capable of simulating our climate with a global coverage. In this paper, a new statistical approach is presented based on the integrated nested Laplace approximation (INLA) method to downscale historical daily precipitation rates. The spatial and spatio-temporal structures were used in a Bayesian approach, to produce a daily 5 km regular grid for continental Portugal. Results show the capability of the method to provide fast results aligned with the observations, but still underestimating precipitation events higher than 100 mm/day.

Bayesian species distribution models integrate presence‐only and presence–absence data to predict deer distribution and relative abundance

Using geospatial data of wildlife presence to predict a species distribution across a geographic area is among the most common tools in management and conservation. The collection of high‐quality presence–absence (PA) data through structured surveys is, however, expensive, and managers usually have access to larger amounts of low‐quality presence‐only (PO) data collected by citizen scientists, opportunistic observations and culling returns for game species. Integrated species distribution models (ISDMs) have been developed to make the most of the data available by combining the higher‐quality, but usually scarcer and more spatially restricted, PA data with the lower‐quality, unstructured, but usually more extensive PO datasets. Joint‐likelihood ISDMs can be run in a Bayesian context using integrated nested laplace approximation methods that allow the addition of a spatially structured random effect to account for data spatial autocorrelation. Here, we apply this innovative approach to fit ISDMs to empirical data, using PA and PO data for the three prevalent deer species in Ireland: red, fallow and sika deer. We collated all deer data available for the past 15 years and fitted models predicting distribution and relative abundance at a 25 km2resolution across the island. Model predictions were associated to spatial estimate of uncertainty, allowing us to assess the quality of the model and the effect that data scarcity has on the certainty of predictions. Furthermore, we checked the performance of the three species‐specific models using two datasets, independent deer hunting returns and deer densities based on faecal pellet counts. Our work clearly demonstrates the applicability of spatially explicit ISDMs to empirical data in a Bayesian context, providing a blueprint for managers to exploit unexplored and seemingly unusable data that can, when modelled with the proper tools, serve to inform management and conservation policies.

Radiation dose estimation with time-since-exposure uncertainty using the gamma -H2AX biomarker

To predict the health effects of accidental or therapeutic radiation exposure, one must estimate the radiation dose that person received. A well-known ionising radiation biomarker, phosphorylated gamma -H2AX protein, is used to evaluate cell damage and is thus suitable for the dose estimation process. In this paper, we present new Bayesian methods that, in contrast to approaches where estimation is carried out at predetermined post-irradiation times, allow for uncertainty regarding the time since radiation exposure and, as a result, produce more precise results. We also use the Laplace approximation method, which drastically cuts down on the time needed to get results. Real data are used to illustrate the methods, and analyses indicate that the models might be a practical choice for the gamma -H2AX biomarker dose estimation process.

Optimizing Training and Transmission Overheads for Secure URLLC Against Randomly Distributed Eavesdroppers

In this article, we focus on the pilot-assisted transmission design for secure ultra-reliable and low-latency communication (URLLC) systems, which has not yet been studied in the existing literatures. In each transmission period of this system, the multi-antenna controller sends confidential URLLC messages integrated with artificial noise (AN) to a single-antenna actuator for some mission-critical operations (e.g., remote control), and while an unknown number of passive eavesdroppers attempt to intercept this confidential message in a non-colluding manner. Since the conventional ergodic secrecy capacity is not accurate to describe the maximal achievable secrecy rate of URLLC with short blocklength coding, we establish the concept of achievable effective secrecy rate (AESR) to measure the secrecy performance of our URLLC system, which is defined as the average number of information bits can be transmitted per channel use under given reliability and information leakage constraints. Due to the exact expression of AESR has an intractable form, we derive a closed-form approximation on the AESR to simplify the calculation, via leveraging the Laplace approximation and Gaussian-Chebyshev quadrature method. Following by this approximation, we propose an efficient two-dimensional search algorithm to determine the optimal transmission parameters that maximize the AESR, i.e., the training pilot length and the power allocation ratio between confidential data signals and AN. Furthermore, the asymptotic performance of AESR in the high-SNR regime is also analyzed to gain more insights. Numerical results validate the accuracy of theoretical approximations presented in this paper, and illustrate how the particular system parameters impact the AESR of our considered URLLC system.

Bayesian-based method for the simultaneous identification of structural damage and moving force

The input force is usually difficult to measure directly in the damage identification due to the system uncertainty and noise uncertainty. A Bayesian method for the simultaneous identification of damage and moving force is proposed. The moving force on the structure are transformed into equivalent nodal forces through the element function, and these equivalent nodal forces are expanded by using Chebyshev orthogonal polynomials. The posterior probability density function of the damage parameter and the force orthogonal parameter under Bayesian theory is deduced in time-domain. The prior information of the Chebyshev orthogonal polynomials adopts the uniform prior, and the damage parameters adopt the Gaussian prior in accordance with the characteristics of each parameter. The Laplace approximation method for time domain data is used to determine the hyperparameters of elemental damage and moving force. The first-order and second-order sensitivities of the dynamic response with damage and force parameters are derived to update the hyperparameters and to accelerate gradient-based system identification. The uncertainty of the identified results of damage parameters is quantified by using an approximate Gaussian distribution. Two numerical cases of a simply supported beam and the Tanjiang Bridge on the Shen-Mao Railway show that the proposed method can simultaneously identify the elemental damage and moving forces with uncertainty quantified.