scholarly journals Multi-Ellipsoidal Extended Target Tracking with Variational Bayes Inference

2021 ◽  
Author(s):  
BARKIN TUNCER ◽  
Emre Özkan ◽  
Umut Orguner
Keyword(s):  
Target Tracking ◽  
Real Data ◽  
Variational Bayes ◽  
Inference Problem ◽  
Recursive Filtering ◽  
Conjugate Priors ◽  
Bayes Inference ◽  
Symmetric Positive Definite ◽  
Extended Target ◽  
Proposed Model

<div>In this work, we propose a novel extended target tracking algorithm, which is capable of representing a target or a group of targets with multiple ellipses. Each ellipse is modeled by an unknown symmetric positive-definite random matrix. The proposed model requires solving two challenging problems. First, the data association problem between the measurements and the sub-objects. Second, the inference problem that involves non-conjugate priors and likelihoods which needs to be solved within the recursive filtering framework. We utilize the variational Bayes inference method to solve the association problem and to approximate the intractable true posterior. The performance of the proposed solution is demonstrated in simulations and real-data experiments. The results show that our method outperforms the state-of-the-art methods in accuracy with lower computational complexity.</div>

scholarly journals Multi-Ellipsoidal Extended Target Tracking with Variational Bayes Inference

2021 ◽  
Author(s):  
BARKIN TUNCER ◽  
Emre Özkan ◽  
Umut Orguner
Keyword(s):  
Target Tracking ◽  
Real Data ◽  
Variational Bayes ◽  
Inference Problem ◽  
Recursive Filtering ◽  
Conjugate Priors ◽  
Bayes Inference ◽  
Symmetric Positive Definite ◽  
Extended Target ◽  
Proposed Model

<div>In this work, we propose a novel extended target tracking algorithm, which is capable of representing a target or a group of targets with multiple ellipses. Each ellipse is modeled by an unknown symmetric positive-definite random matrix. The proposed model requires solving two challenging problems. First, the data association problem between the measurements and the sub-objects. Second, the inference problem that involves non-conjugate priors and likelihoods which needs to be solved within the recursive filtering framework. We utilize the variational Bayes inference method to solve the association problem and to approximate the intractable true posterior. The performance of the proposed solution is demonstrated in simulations and real-data experiments. The results show that our method outperforms the state-of-the-art methods in accuracy with lower computational complexity.</div>

Variational Bayes Inference for the DINA Model

2020 ◽  
Vol 45 (5) ◽  
pp. 569-597
Author(s):  
Kazuhiro Yamaguchi ◽  
Kensuke Okada
Keyword(s):  
Real Data ◽  
Variational Bayes ◽  
Diagnostic Assessment ◽  
Model Parameters ◽  
Mcmc Method ◽  
Inference Method ◽  
Bayes Inference ◽  
Dina Model ◽  
Mcmc Estimation ◽  
Parameter Values

In this article, we propose a variational Bayes (VB) inference method for the deterministic input noisy AND gate model of cognitive diagnostic assessment. The proposed method, which applies the iterative algorithm for optimization, is derived based on the optimal variational posteriors of the model parameters. The proposed VB inference enables much faster computation than the existing Markov chain Monte Carlo (MCMC) method, while still offering the benefits of a full Bayesian framework. A simulation study revealed that the proposed VB estimation adequately recovered the parameter values. Moreover, an example using real data revealed that the proposed VB inference method provided similar estimates to MCMC estimation with much faster computation.

scholarly journals Properties and Inference for a New Class of Generalized Rayleigh Distributions with an Application

2019 ◽  
Vol 17 (1) ◽  
pp. 700-715
Author(s):  
Hayrinisa Demirci Biçer
Keyword(s):  
Survival Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Least Square ◽  
Statistical Characteristics ◽  
Data Sets ◽  
Alpha Power ◽  
Inference Problem ◽  
Proposed Model ◽  
Generalized Rayleigh Distribution

Abstract In the present paper, we introduce a new form of generalized Rayleigh distribution called the Alpha Power generalized Rayleigh (APGR) distribution by following the idea of extension of the distribution families with the Alpha Power transformation. The introduced distribution has the more general form than both the Rayleigh and generalized Rayleigh distributions and provides a better fit than the Rayleigh and generalized Rayleigh distributions for more various forms of the data sets. In the paper, we also obtain explicit forms of some important statistical characteristics of the APGR distribution such as hazard function, survival function, mode, moments, characteristic function, Shannon and Rényi entropies, stress-strength probability, Lorenz and Bonferroni curves and order statistics. The statistical inference problem for the APGR distribution is investigated by using the maximum likelihood and least-square methods. The estimation performances of the obtained estimators are compared based on the bias and mean square error criteria by a conducted Monte-Carlo simulation on small, moderate and large sample sizes. Finally, a real data analysis is given to show how the proposed model works in practice.

An efficient extended target detection method based on region growing and contour tracking algorithm

2017 ◽  
Vol 232 (5) ◽  
pp. 825-836 ◽  
Author(s):  
Bo Yan ◽  
LP Xu ◽  
JZH Yan ◽  
Cong Li
Keyword(s):  
Target Detection ◽  
Simulated Data ◽  
Region Growing ◽  
Real Data ◽  
Tracking Algorithm ◽  
Contour Tracking ◽  
Optimal Parameters ◽  
Extended Target ◽  
Proposed Model ◽  
Resolution Cell

Extended target detection in the presence of K-distributed clutter has gained a special interest in recent years. High-resolution radars allow a target to be found in several resolution cells. Therefore, the detection rate and the false alarm rate of an extended target should be analyzed by these cells jointly rather than in one single resolution cell. A detector in which all the cells whose magnitude affected by one target are considered jointly is present. The performance and optimal parameters of the detector are analyzed in detail. Meanwhile, the large amount of calculation caused by enormous raw data is also considered. Then, an efficient method based on region growing algorithm and contour tracking algorithm is proposed. Only part of the resolution cells is scanned once with the proposed method, while all the cells are scanned at least one times in the existing methods. Therefore, considerable calculations are saved. Furthermore, the proposed method and several existing methods are performed with real data and simulated data, and the results show that the proposed model is practical and efficient to detect the extended targets in K-distributed clutters.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

scholarly journals An adaptive social distancing SIR model for COVID-19 disease spreading and forecasting

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Said Gounane ◽  
Yassir Barkouch ◽  
Abdelghafour Atlas ◽  
Mostafa Bendahmane ◽  
Fahd Karami ◽  
...  
Keyword(s):  
Mathematical Theory ◽  
Real Data ◽  
Sir Model ◽  
Epidemic Threshold ◽  
Social Distancing ◽  
Sir Epidemic ◽  
Proposed Model ◽  
Disease Spreading ◽  
The Government ◽  
The Impact

Abstract Recently, various mathematical models have been proposed to model COVID-19 outbreak. These models are an effective tool to study the mechanisms of coronavirus spreading and to predict the future course of COVID-19 disease. They are also used to evaluate strategies to control this pandemic. Generally, SIR compartmental models are appropriate for understanding and predicting the dynamics of infectious diseases like COVID-19. The classical SIR model is initially introduced by Kermack and McKendrick (cf. (Anderson, R. M. 1991. “Discussion: the Kermack–McKendrick Epidemic Threshold Theorem.” Bulletin of Mathematical Biology 53 (1): 3–32; Kermack, W. O., and A. G. McKendrick. 1927. “A Contribution to the Mathematical Theory of Epidemics.” Proceedings of the Royal Society 115 (772): 700–21)) to describe the evolution of the susceptible, infected and recovered compartment. Focused on the impact of public policies designed to contain this pandemic, we develop a new nonlinear SIR epidemic problem modeling the spreading of coronavirus under the effect of a social distancing induced by the government measures to stop coronavirus spreading. To find the parameters adopted for each country (for e.g. Germany, Spain, Italy, France, Algeria and Morocco) we fit the proposed model with respect to the actual real data. We also evaluate the government measures in each country with respect to the evolution of the pandemic. Our numerical simulations can be used to provide an effective tool for predicting the spread of the disease.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals Transition models for count data: a flexible alternative to fixed distribution models

2021 ◽  
Author(s):  
Moritz Berger ◽  
Gerhard Tutz
Keyword(s):  
Count Data ◽  
Regression Models ◽  
Negative Binomial ◽  
Real Data ◽  
Distribution Models ◽  
Explanatory Variables ◽  
Excess Zeros ◽  
Proposed Model ◽  
Transition Models ◽  
Fixed Distribution

AbstractA flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and Negative Binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared in simulations and by utilizing several real data applications from the area of health and social science.

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