Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8

Search results for: Maximum Likelihood method

8 An Estimating Parameter of the Mean in Normal Distribution by Maximum Likelihood, Bayes, and Markov Chain Monte Carlo Methods

Authors: Autcha Araveeporn

Abstract:

This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.

Keywords: Bayes method, Markov Chain Monte Carlo method, Maximum Likelihood method, normal distribution.

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7 A Stochastic Diffusion Process Based on the Two-Parameters Weibull Density Function

Authors: Meriem Bahij, Ahmed Nafidi, Boujemâa Achchab, Sílvio M. A. Gama, José A. O. Matos

Abstract:

Stochastic modeling concerns the use of probability to model real-world situations in which uncertainty is present. Therefore, the purpose of stochastic modeling is to estimate the probability of outcomes within a forecast, i.e. to be able to predict what conditions or decisions might happen under different situations. In the present study, we present a model of a stochastic diffusion process based on the bi-Weibull distribution function (its trend is proportional to the bi-Weibull probability density function). In general, the Weibull distribution has the ability to assume the characteristics of many different types of distributions. This has made it very popular among engineers and quality practitioners, who have considered it the most commonly used distribution for studying problems such as modeling reliability data, accelerated life testing, and maintainability modeling and analysis. In this work, we start by obtaining the probabilistic characteristics of this model, as the explicit expression of the process, its trends, and its distribution by transforming the diffusion process in a Wiener process as shown in the Ricciaardi theorem. Then, we develop the statistical inference of this model using the maximum likelihood methodology. Finally, we analyse with simulated data the computational problems associated with the parameters, an issue of great importance in its application to real data with the use of the convergence analysis methods. Overall, the use of a stochastic model reflects only a pragmatic decision on the part of the modeler. According to the data that is available and the universe of models known to the modeler, this model represents the best currently available description of the phenomenon under consideration.

Keywords: Diffusion process, discrete sampling, likelihood estimation method, simulation, stochastic diffusion equation, trends functions, bi-parameters Weibull density function.

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6 Angle of Arrival Estimation Using Maximum Likelihood Method

Authors: H. K. Hwang, Zekeriya Aliyazicioglu, Solomon Wu, Hung Lu, Nick Wilkins, Daniel Kerr

Abstract:

Multiple-input multiple-output (MIMO) radar has received increasing attention in recent years. MIMO radar has many advantages over conventional phased array radar such as target detection,resolution enhancement, and interference suppression. In this paper, the results are presented from a simulation study of MIMO uniformly-spaced linear array (ULA) antennas. The performance is investigated under varied parameters, including varied array size, pseudo random (PN) sequence length, number of snapshots, and signal to noise ratio (SNR). The results of MIMO are compared to a traditional array antenna.

Keywords: Multiple-input multiple-output (MIMO) radar, phased array antenna, target detection, radar signal processing.

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5 Modeling a Multinomial Logit Model of Intercity Travel Mode Choice Behavior for All Trips in Libya

Authors: Manssour A. Abdulsalam Bin Miskeen, Ahmed Mohamed Alhodairi, Riza Atiq Abdullah Bin O. K. Rahmat

Abstract:

In the planning point of view, it is essential to have mode choice, due to the massive amount of incurred in transportation systems. The intercity travellers in Libya have distinct features, as against travellers from other countries, which includes cultural and socioeconomic factors. Consequently, the goal of this study is to recognize the behavior of intercity travel using disaggregate models, for projecting the demand of nation-level intercity travel in Libya. Multinomial Logit Model for all the intercity trips has been formulated to examine the national-level intercity transportation in Libya. The Multinomial logit model was calibrated using nationwide revealed preferences (RP) and stated preferences (SP) survey. The model was developed for deference purpose of intercity trips (work, social and recreational). The variables of the model have been predicted based on maximum likelihood method. The data needed for model development were obtained from all major intercity corridors in Libya. The final sample size consisted of 1300 interviews. About two-thirds of these data were used for model calibration, and the remaining parts were used for model validation. This study, which is the first of its kind in Libya, investigates the intercity traveler’s mode-choice behavior. The intercity travel mode-choice model was successfully calibrated and validated. The outcomes indicate that, the overall model is effective and yields higher precision of estimation. The proposed model is beneficial, due to the fact that, it is receptive to a lot of variables, and can be employed to determine the impact of modifications in the numerous characteristics on the need for various travel modes. Estimations of the model might also be of valuable to planners, who can estimate possibilities for various modes and determine the impact of unique policy modifications on the need for intercity travel.

Keywords: Multinomial logit model, improved intercity transport, intercity mode-choice behavior, disaggregate analysis.

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4 The Maximum Likelihood Method of Random Coefficient Dynamic Regression Model

Authors: Autcha Araveeporn

Abstract:

The Random Coefficient Dynamic Regression (RCDR) model is to developed from Random Coefficient Autoregressive (RCA) model and Autoregressive (AR) model. The RCDR model is considered by adding exogenous variables to RCA model. In this paper, the concept of the Maximum Likelihood (ML) method is used to estimate the parameter of RCDR(1,1) model. Simulation results have shown the AIC and BIC criterion to compare the performance of the the RCDR(1,1) model. The variables as the stationary and weakly stationary data are good estimates where the exogenous variables are weakly stationary. However, the model selection indicated that variables are nonstationarity data based on the stationary data of the exogenous variables.

Keywords: Autoregressive, Maximum Likelihood Method, Nonstationarity, Random Coefficient Dynamic Regression, Stationary.

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3 Fusion of Colour and Depth Information to Enhance Wound Tissue Classification

Authors: Darren Thompson, Philip Morrow, Bryan Scotney, John Winder

Abstract:

Patients with diabetes are susceptible to chronic foot wounds which may be difficult to manage and slow to heal. Diagnosis and treatment currently rely on the subjective judgement of experienced professionals. An objective method of tissue assessment is required. In this paper, a data fusion approach was taken to wound tissue classification. The supervised Maximum Likelihood and unsupervised Multi-Modal Expectation Maximisation algorithms were used to classify tissues within simulated wound models by weighting the contributions of both colour and 3D depth information. It was found that, at low weightings, depth information could show significant improvements in classification accuracy when compared to classification by colour alone, particularly when using the maximum likelihood method. However, larger weightings were found to have an entirely negative effect on accuracy.

Keywords: Classification, data fusion, diabetic foot, stereophotogrammetry, tissue colour.

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2 Parameter Estimation using Maximum Likelihood Method from Flight Data at High Angles of Attack

Authors: Rakesh Kumar, A. K. Ghosh

Abstract:

The paper presents the modeling of nonlinear longitudinal aerodynamics using flight data of Hansa-3 aircraft at high angles of attack near stall. The Kirchhoff-s quasi-steady stall model has been used to incorporate nonlinear aerodynamic effects in the aerodynamic model used to estimate the parameters, thereby, making the aerodynamic model nonlinear. The Maximum Likelihood method has been applied to the flight data (at high angles of attack) for the estimation of parameters (aerodynamic and stall characteristics) using the nonlinear aerodynamic model. To improve the accuracy level of the estimates, an approach of fixing the strong parameters has also been presented.

Keywords: Maximum Likelihood, nonlinear, parameters, stall.

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1 Investigation of the Possibility to Prepare Supervised Classification Map of Gully Erosion by RS and GIS

Authors: Ali Mohammadi Torkashvand, Hamid Reza Alipour

Abstract:

This study investigates the possibility providing gully erosion map by the supervised classification of satellite images (ETM+) in two mountainous and plain land types. These land types were the part of Varamin plain, Tehran province, and Roodbar subbasin, Guilan province, as plain and mountain land types, respectively. The position of 652 and 124 ground control points were recorded by GPS respectively in mountain and plain land types. Soil gully erosion, land uses or plant covers were investigated in these points. Regarding ground control points and auxiliary points, training points of gully erosion and other surface features were introduced to software (Ilwis 3.3 Academic). The supervised classified map of gully erosion was prepared by maximum likelihood method and then, overall accuracy of this map was computed. Results showed that the possibility supervised classification of gully erosion isn-t possible, although it need more studies for results generalization to other mountainous regions. Also, with increasing land uses and other surface features in plain physiography, it decreases the classification of accuracy.

Keywords: Supervised classification, Gully erosion, Map.

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