Effective factors on the number of decayed and filled teeth using the Conway-Maxwell-Poisson count model

BACKGROUND AND AIM: Recognizing the factors affecting the number of decayed and filled teeth has a major role in oral health. Dental data usually suffer from over-dispersion and excess zero frequencies. The purpose of this study was to use the Conway-Maxwell-Poisson (COM-Poisson) model to determine some of the factors affecting the number of decayed and filled teeth. METHODS: In this cross-sectional study, a sample of 1000 people from a cohort study in Shahrekord City, Iran, aged 35-70 years, was selected through systematic sampling. The data were analyzed using the Bayesian approach through Markov chain Monte Carlo (MCMC) simulation by OpenBUGS. Zero-inflated Poisson (ZIP), COM-Poisson model, and zero-inflated Com-Poisson (ZICMP) model were fitted on the data and compared using the deviance information criterion (DIC). RESULTS: The mean numbers of decayed and filled teeth were 0.77 ± 1.63 and 4.37 ± 4.62, respectively. The Com-Poisson and ZICMP showed to be better fit for the number of decayed and filled teeth, respectively. Those people who were younger, male, smokers, diabetics, did not floss, and did not use mouthwash had significantly more number of decayed teeth (P < 0.05). Those people who were younger, female, non-diabetics, non-smokers, employed, literate, had less body mass index (BMI), flossed, and got higher score of quality of life had significantly more number of filled teeth (P < 0.05). CONCLUSION: By controlling such factors as education, BMI, flossing, using mouthwash, smoking, diabetes, and quality of life, we could improve the oral health. KEYWORDS: Bayes’ Theorem; Conway-Maxwell-Poisson Distribution; Decayed, Missing, and Filled Teeth; Zero-inflate

Bayesian system identification and dynamic virtualization using incomplete noisy measurements

This study presents the application of Bayesian Expectation-Maximization (BEM) methodology to coupled state-input-parameter estimation in both linear and nonlinear structures. The BEM is built upon a Bayesian foundation, which utilizes the EM algorithm to deliver accurate estimates for latent states, model parameters, and input forces while updating noise characteristics effectively. This feature allows for quantifying associated uncertainties using response-only measurements. The proposed methodology is equipped with a recursive backward-forward Bayesian estimator that provides smoothed estimates of the state, input, and parameters during the Expectation step. Next, these estimates help calculate the most probable values of the noise parameters based on the observed data. This adaptive approach to the coupled estimation problem allows for real-time quantification of estimation uncertainties, whereby displacement, velocity, acceleration, strain, and stress states can be reconstructed for all degrees-of-freedom through virtual sensing. Through numerical examples, it is demonstrated that the BEM accurately estimates the unknown quantities based on the measured quantities, not only when a fusion of displacement and acceleration measurements is available but also in the presence of acceleration-only response measurements

Bayesian Optimal Sensor Placement for Virtual Sensing and Strain Reconstruction

A Bayesian optimal sensor placement (OSP) framework is presented for virtual sensing in structures using output-only vibration measurements. Particularly, this probabilistic OSP scheme aims to enhance the reconstruction of dynamical responses (e.g., accelerations, displacements, strain, stresses) for updating structural reliability and safety, as well as fatigue lifetime prognosis. The OSP framework is formulated using information theory. The information gained from a sensor configuration is defined as the Kullback-Liebler divergence (KL-div) between the prior and posterior distributions of the response quantities of interest (QoI). The Gaussian nature of the response estimate for linear models of structures is employed, and the information gain is characterized in terms of the reconstruction error covariance matrix. A Kalman-based input-state estimation technique is integrated within an existing OSP strategy, aiming to obtain estimates of response QoI and their uncertainties. The design variables include the location, type and number of sensors. Heuristic algorithms are used to solve optimization problem and provide computationally efficient solutions. The effectiveness of the method is demonstrated using an example from structural dynamics

Quantification of Aleatory Uncertainty in Modal Updating Problems using a New Hierarchical Bayesian Framework

Identification of structural damage requires reliable assessments of damage-sensitive quantities, including natural frequencies, mode shapes, and damping ratios. Lack of knowledge about the correct value of these parameters introduces a particular sort of uncertainty often referred to as epistemic uncertainty. This class of uncertainty is reducible in a sense that it can be decreased by enhancing the modeling accuracy and collecting new information. On the contrary, such damage-sensitive parameters might also have intrinsic randomness arising from unknown phenomena and effects, which gives rise to an irreducible category of uncertainty often referred to as aleatory uncertainty. The present Bayesian modal updating methodologies can produce reasonable quantification of the epistemic uncertainties, while they often fail to account for the aleatory uncertainties. In this paper, a new multilevel (hierarchical) probabilistic modeling framework is proposed to bridge this significant gap in uncertainty quantification and propagation of structural dynamics inverse problems. Since multilevel model calibration schemes establish a complicated model structure associated with additional parameters and variables, their computational costs are often considerable, if not prohibitive. To reduce the computational costs, the modal updating procedure is simplified using a second-order Taylor expansion approximation. This approximation is combined with a Markov chain Monte-Carlo (MCMC) sampling method to compute marginal posterior distributions of quantities of interest. The proposed framework is illustrated using one simple experimental example. As a result, it is demonstrated that the proposed framework surpasses the present Bayesian modal updating methods as it accounts for both the aleatory and epistemic uncertainties.Financial support from the Hong Kong research grants councils under grant numbers 16234816 and 16212918 is gratefully appreciated. The last author gratefully acknowledges the European Commission for its support of the Marie Sklodowska Curie program through the ETN DyVirt project (GA 764547). This paper is completed as a part of the second authors PhD dissertation conducted jointly at Sharif University of Technology and the Hong Kong University of Science and Technology. The second author would like to gratefully appreciate kind support and supervision of Professor Fayaz R. Rofooei at Sharif University of Technology. We would also like to express our sincere appreciation to Professor Chih-chen Chang for generously sharing sensors, prototypes, and laboratory facilities

A New Online Bayesian Approach for the Joint Estimation of State and Input Forces using Response-only Measurements

In this paper, a recursive Bayesian-filtering technique is presented for the joint estimation of the state and input forces. By introducing new prior distributions for the input forces, the direct transmission of the input into the state is eliminated, which allows removing low-frequency error components from the predictions and estimations. Eliminating such errors is of practical significance to the emerging fatigue monitoring methodologies. Furthermore, this new technique does not require a priori knowledge of the input covariance matrix and provides a powerful method to update the noise covariance matrices in a real-time manner. The performance of this algorithm is demonstrated using one numerical example and compared it with the state-of-the-art algorithms. Contrary to the present methods which often produce unreliable and inaccurate estimations, the proposed method provides remarkably accurate estimations for both the state and input.Financial support from the Hong Kong research grants councils under grant numbers 16234816 and 16212918 is gratefully appreciated. The last author gratefully acknowledges the European Commission for its support of the Marie Sklodowska Curie program through the ETN DyVirt project (GA 764547). This paper is completed as a part of the second authors PhD dissertation conducted jointly at Sharif University of Technology and the Hong Kong University of Science and Technology. The second author would like to gratefully appreciate kind support and supervision of Professor Fayaz R. Rofooei at Sharif University of Technology

Input-State-Parameter-Noise Identification and Virtual Sensing in Dynamical Systems: A Bayesian Expectation-Maximization (BEM) Perspective

Structural identification and damage detection can be generalized as the simultaneous estimation of input forces, physical parameters, and dynamical states. Although Kalman-type filters are efficient tools to address this problem, the calibration of noise covariance matrices is cumbersome. For instance, calibration of input noise covariance matrix in augmented or dual Kalman filters is a critical task since a slight variation in its value can adversely affect estimations. The present study develops a Bayesian Expectation-Maximization (BEM) methodology for the uncertainty quantification and propagation in coupled input-state-parameter-noise identification problems. It also proposes the incorporation of input dummy observations for stabilizing low-frequency components of the latent states and mitigating potential drifts. In this respect, the covariance matrix of the dummy observations is also calibrated based on the measured data. Additionally, an explicit formulation is provided to study the theoretical observability of the Bayesian estimators, which helps characterize the minimum sensor requirements. Ultimately, the BEM is tested and verified through numerical and experimental examples, wherein sensor configurations, multiple input forces, and abrupt stiffness changes are investigated. It is confirmed that the BEM provides accurate estimations of states, input, and parameters while characterizing the degree of belief in these estimations based on the posterior uncertainties driven by applying a Bayesian perspective