Search results for: bayesian estimation

Authors: Mohammad Anwar, Shah Waliullah

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This study investigated panel data regression models. This paper used Bayesian and classical methods to study the impact of institutions on economic growth from data (1990-2014), especially in developing countries. Under the classical and Bayesian methodology, the two-panel data models were estimated, which are common effects and fixed effects. For the Bayesian approach, the prior information is used in this paper, and normal gamma prior is used for the panel data models. The analysis was done through WinBUGS14 software. The estimated results of the study showed that panel data models are valid models in Bayesian methodology. In the Bayesian approach, the effects of all independent variables were positively and significantly affected by the dependent variables. Based on the standard errors of all models, we must say that the fixed effect model is the best model in the Bayesian estimation of panel data models. Also, it was proved that the fixed effect model has the lowest value of standard error, as compared to other models.

Keywords: Bayesian approach, common effect, fixed effect, random effect, Dynamic Random Effect Model

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Authors: Xupin Zhang, Maria Caterina Bramati, Enrest Fokoue

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Understanding the career placement of graduates from the university is crucial for both the qualities of education and ultimate satisfaction of students. In this research, we adapt the capabilities of dynamic Bayesian networks to characterize and predict students’ job placement using data from various universities. We also provide elements of the estimation of the indicator (score) of the strength of the network. The research focuses on overall findings as well as specific student groups including international and STEM students and their insight on the career path and what changes need to be made. The derived Bayesian network has the potential to be used as a tool for simulating the career path for students and ultimately helps universities in both academic advising and career counseling.

Keywords: dynamic bayesian networks, indicator estimation, job placement, social networks

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Authors: Ana Staneva, Vessela Stoimenova

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A parametric estimation of the MBP with Power Series offspring distribution family is considered in this paper. The MLE for the parameters is obtained in the case when the observable data are incomplete and consist only with the generation sizes of the family tree of MBP. The parameter estimation is calculated by using the Monte Carlo EM algorithm. The estimation for the posterior distribution and for the offspring distribution parameters are calculated by using the Bayesian approach and the Gibbs sampler. The article proposes various examples with bivariate branching processes together with computational results, simulation and an implementation using R.

Keywords: Bayesian, branching processes, EM algorithm, Gibbs sampler, Monte Carlo methods, statistical estimation

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Authors: Said Ali Al-Hadhrami, Amer Ibrahim Al-Omari

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In this paper, Bayesian estimation for the mean of exponential distribution is considered using Moving Extremes Ranked Set Sampling (MERSS). Three priors are used; Jeffery, conjugate and constant using MERSS and Simple Random Sampling (SRS). Some properties of the proposed estimators are investigated. It is found that the suggested estimators using MERSS are more efficient than its counterparts based on SRS.

Keywords: Bayesian, efficiency, moving extreme ranked set sampling, ranked set sampling

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Authors: Kyugneun Lee, Ikjin Lee

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Parameter estimation with inverse problem often suffers from unfavorable conditions in the real world. Useless data and many input parameters make the problem complicated or insoluble. Data refinement and reformulation of the problem can solve that kind of difficulties. In this research, a method to solve the rank deficient inverse problem is suggested. A multi-physics system which has rank deficiency caused by response correlation is treated. Impeditive information is removed and the problem is reformulated to sequential estimations using Bayesian network (BN) and subset groups. At first, subset grouping of the responses is performed. Feature selection with singular value decomposition (SVD) is used for the grouping. Next, BN inference is used for sequential conditional estimation according to the group hierarchy. Directed acyclic graph (DAG) structure is organized to maximize the estimation ability. Variance ratio of response to noise is used to pairing the estimable parameters by each response.

Keywords: Bayesian network, feature selection, rank deficiency, statistical inverse analysis

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Authors: Suparman Suparman

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A white noise in autoregressive (AR) model is often assumed to be normally distributed. In application, the white noise usually do not follows a normal distribution. This paper aims to estimate a parameter of AR model that has a exponential white noise. A Bayesian method is adopted. A prior distribution of the parameter of AR model is selected and then this prior distribution is combined with a likelihood function of data to get a posterior distribution. Based on this posterior distribution, a Bayesian estimator for the parameter of AR model is estimated. Because the order of AR model is considered a parameter, this Bayesian estimator cannot be explicitly calculated. To resolve this problem, a method of reversible jump Markov Chain Monte Carlo (MCMC) is adopted. A result is a estimation of the parameter AR model can be simultaneously calculated.

Keywords: autoregressive (AR) model, exponential white Noise, bayesian, reversible jump Markov Chain Monte Carlo (MCMC)

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Authors: Georgiana Onicescu, Yuqian Shen

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Due to the complex nature of geo-referenced data, multicollinearity of the risk factors in public health spatial studies is a commonly encountered issue, which leads to low parameter estimation accuracy because it inflates the variance in the regression analysis. To address this issue, we proposed a two-stage variable selection method by extending the least absolute shrinkage and selection operator (Lasso) to the Bayesian spatial setting, investigating the impact of risk factors to health outcomes. Specifically, in stage I, we performed the variable selection using Bayesian Lasso and several other variable selection approaches. Then, in stage II, we performed the model selection with only the selected variables from stage I and compared again the methods. To evaluate the performance of the two-stage variable selection methods, we conducted a simulation study with different distributions for the risk factors, using geo-referenced count data as the outcome and Michigan as the research region. We considered the cases when all candidate risk factors are independently normally distributed, or follow a multivariate normal distribution with different correlation levels. Two other Bayesian variable selection methods, Binary indicator, and the combination of Binary indicator and Lasso were considered and compared as alternative methods. The simulation results indicated that the proposed two-stage Bayesian Lasso variable selection method has the best performance for both independent and dependent cases considered. When compared with the one-stage approach, and the other two alternative methods, the two-stage Bayesian Lasso approach provides the highest estimation accuracy in all scenarios considered.

Keywords: Lasso, Bayesian analysis, spatial analysis, variable selection

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Authors: Jefferson Hernandez, Juan Padilla

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Estimation of price elasticity of demand is a valuable tool for the task of price settling. Given its relevance, it is an active field for microeconomic and statistical research. Price elasticity in the industry of oil and gas, in particular for fuels sold in gas stations, has shown to be a challenging topic given the market and state restrictions, and underlying correlations structures between the types of fuels sold by the same gas station. This paper explores the Lotka-Volterra model for the problem for price elasticity estimation in the context of fuels; in addition, it is introduced multivariate random effects with the purpose of dealing with errors, e.g., measurement or missing data errors. In order to model the underlying correlation structures, the Inverse-Wishart, Hierarchical Half-t and LKJ distributions are studied. Here, the Bayesian paradigm through Markov Chain Monte Carlo (MCMC) algorithms for model estimation is considered. Simulation studies covering a wide range of situations were performed in order to evaluate parameter recovery for the proposed models and algorithms. Results revealed that the proposed algorithms recovered quite well all model parameters. Also, a real data set analysis was performed in order to illustrate the proposed approach.

Keywords: price elasticity, volume, correlation structures, Bayesian models

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Authors: Linda Smail, Zineb Azouz

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Given a Bayesian network relative to a set I of discrete random variables, we are interested in computing the probability distribution P(S) where S is a subset of I. The general idea is to write the expression of P(S) in the form of a product of factors where each factor is easy to compute. More importantly, it will be very useful to give an interpretation of each of the factors in terms of conditional probabilities. This paper considers a semantic interpretation of the factors involved in computing marginal probabilities in Bayesian networks. Establishing such a semantic interpretations is indeed interesting and relevant in the case of large Bayesian networks.

Keywords: Bayesian networks, D-Separation, level two Bayesian networks, factorization of computation

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Authors: B. Zerouali, M. Kara, B. Hamaidi, H. Mahdjoub, S. Rouabhia

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In this paper, a safety analysis for crude oil tanks to prevent undesirable events that may cause catastrophic accidents. The estimation of the probability of damage to industrial systems is carried out through a series of steps, and in accordance with a specific methodology. In this context, this work involves developing an assessment tool and risk analysis at the level of crude oil tanks system, based primarily on identification of various potential causes of crude oil tanks fire and explosion by the use of Fault Tree Analysis (FTA), then improved risk modelling by Bayesian Networks (BNs). Bayesian approach in the evaluation of failure and quantification of risks is a dynamic analysis approach. For this reason, have been selected as an analytical tool in this study. Research concludes that the Bayesian networks have a distinct and effective method in the safety analysis because of the flexibility of its structure; it is suitable for a wide variety of accident scenarios.

Keywords: bayesian networks, crude oil tank, fault tree, prediction, safety

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Authors: Sami Mestiri, Abdeljelil Farhat

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The aim of this current paper is to predict the credit risk of banks in Tunisia, over the period (2000-2005). For this purpose, two methods for the estimation of the logistic regression model with random effects: Penalized Quasi Likelihood (PQL) method and Gibbs Sampler algorithm are applied. By using the information on a sample of 528 Tunisian firms and 26 financial ratios, we show that Bayesian approach improves the quality of model predictions in terms of good classification as well as by the ROC curve result.

Keywords: forecasting, credit risk, Penalized Quasi Likelihood, Gibbs Sampler, logistic regression with random effects, curve ROC

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Authors: Eva L. Sanjuán, Jacinto Martín, M. Isabel Parra, Mario M. Pizarro

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In Extreme Value Theory, inference estimation for the parameters of the distribution is made employing a small part of the observation values. When block maxima values are taken, many data are discarded. We developed a new Bayesian inference model to seize all the information provided by the data, introducing informative priors and using the relations between baseline and limit parameters. Firstly, we studied the accuracy of the new model for three baseline distributions that lead to a Gumbel extreme distribution: Exponential, Normal and Gumbel. Secondly, we considered mixtures of Normal variables, to simulate practical situations when data do not adjust to pure distributions, because of perturbations (noise).

Keywords: bayesian inference, extreme value theory, Gumbel distribution, highly informative prior

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Authors: Redvan Ghasemlounia, Elham Ansari, Hikmet Kerem Cigizoglu

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Hydrological modeling in arid and semi-arid regions is very important. Iran has many regions with these climate conditions such as Chaharmahal and Bakhtiari province that needs lots of attention with an appropriate management. Forecasting of hydrological parameters and estimation of hydrological events of catchments, provide important information that used for design, management and operation of water resources such as river systems, and dams, widely. Discharge in rivers is one of these parameters. This study presents the application and comparison of some estimation methods such as Feed-Forward Back Propagation Neural Network (FFBPNN), Multi Linear Regression (MLR), Gene Expression Programming (GEP) and Bayesian Network (BN) to predict the daily flow discharge of the Soolegan River, located at Chaharmahal and Bakhtiari province, in Iran. In this study, Soolegan, station was considered. This Station is located in Soolegan River at 51° 14՜ Latitude 31° 38՜ longitude at North Karoon basin. The Soolegan station is 2086 meters higher than sea level. The data used in this study are daily discharge and daily precipitation of Soolegan station. Feed Forward Back Propagation Neural Network(FFBPNN), Multi Linear Regression (MLR), Gene Expression Programming (GEP) and Bayesian Network (BN) models were developed using the same input parameters for Soolegan's daily discharge estimation. The results of estimation models were compared with observed discharge values to evaluate performance of the developed models. Results of all methods were compared and shown in tables and charts.

Keywords: ANN, multi linear regression, Bayesian network, forecasting, discharge, gene expression programming

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Authors: Md. Rashidul Hasan, Atikur Rahman Baizid

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The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and then compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). In our real life, we always try to minimize the loss and we also want to gather some prior information (distribution) about the problem to solve it accurately. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study, we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. Finally, mean square error (MSE) of the estimators are obtained and then presented graphically.

Keywords: Bayes estimator, maximum likelihood estimator (MLE), modified linear exponential (MLINEX) loss function, Squared Error (SE) loss function, non-linear exponential (NLINEX) loss function

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Authors: Al Omari Moahmmed Ahmed

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These papers describe the Bayesian Estimator using Markov Chain Monte Carlo and Lindley’s approximation and the maximum likelihood estimation of the Weibull distribution with Type-I censored data. The maximum likelihood method can’t estimate the shape parameter in closed forms, although it can be solved by numerical methods. Moreover, the Bayesian estimates of the parameters, the survival and hazard functions cannot be solved analytically. Hence Markov Chain Monte Carlo method and Lindley’s approximation are used, where the full conditional distribution for the parameters of Weibull distribution are obtained via Gibbs sampling and Metropolis-Hastings algorithm (HM) followed by estimate the survival and hazard functions. The methods are compared to Maximum Likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the better method in scale and shape parameters, the survival and hazard functions.

Keywords: weibull distribution, bayesian method, markov chain mote carlo, survival and hazard functions

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Authors: Watcharin Sangma, Onsiri Chanmuang, Pitsanu Tongkhow

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A forecasting model for steel demand uncertainty in Thailand is proposed. It consists of trend, autocorrelation, and outliers in a hierarchical Bayesian frame work. The proposed model uses a cumulative Weibull distribution function, latent first-order autocorrelation, and binary selection, to account for trend, time-varying autocorrelation, and outliers, respectively. The Gibbs sampling Markov Chain Monte Carlo (MCMC) is used for parameter estimation. The proposed model is applied to steel demand index data in Thailand. The root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) criteria are used for model comparison. The study reveals that the proposed model is more appropriate than the exponential smoothing method.

Keywords: forecasting model, steel demand uncertainty, hierarchical Bayesian framework, exponential smoothing method

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Authors: Viliam Makis, Farnoosh Naderkhani, Leila Jafari

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In this paper, we present a model and an algorithm for the calculation of the optimal control limit, average cost, sample size, and the sampling interval for an optimal Bayesian chart to control the proportion of defective items produced using a semi-Markov decision process approach. Traditional p-chart has been widely used for controlling the proportion of defectives in various kinds of production processes for many years. It is well known that traditional non-Bayesian charts are not optimal, but very few optimal Bayesian control charts have been developed in the literature, mostly considering finite horizon. The objective of this paper is to develop a fast computational algorithm to obtain the optimal parameters of a Bayesian p-chart. The decision problem is formulated in the partially observable framework and the developed algorithm is illustrated by a numerical example.

Keywords: Bayesian control chart, semi-Markov decision process, quality control, partially observable process

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Authors: Paula Simões, Isabel Natário

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This paper reviews a number of theoretical aspects for implementing an explicit spatial perspective in econometrics for modelling non-continuous data, in general, and count data, in particular. It provides an overview of the several spatial econometric approaches that are available to model data that are collected with reference to location in space, from the classical spatial econometrics approaches to the recent developments on spatial econometrics to model count data, in a Bayesian hierarchical setting. Considerable attention is paid to the inferential framework, necessary for structural consistent spatial econometric count models, incorporating spatial lag autocorrelation, to the corresponding estimation and testing procedures for different assumptions, to the constrains and implications embedded in the various specifications in the literature. This review combines insights from the classical spatial econometrics literature as well as from hierarchical modeling and analysis of spatial data, in order to look for new possible directions on the processing of count data, in a spatial hierarchical Bayesian econometric context.

Keywords: spatial data analysis, spatial econometrics, Bayesian hierarchical models, count data

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Authors: Panudet Saengseedam, Nanthachai Kantanantha

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This paper proposes a linear mixed model (LMM) with spatial effects to forecast rice and cassava yields in Thailand at the same time. A multivariate conditional autoregressive (MCAR) model is assumed to present the spatial effects. A Bayesian method is used for parameter estimation via Gibbs sampling Markov Chain Monte Carlo (MCMC). The model is applied to the rice and cassava yields monthly data which have been extracted from the Office of Agricultural Economics, Ministry of Agriculture and Cooperatives of Thailand. The results show that the proposed model has better performance in most provinces in both fitting part and validation part compared to the simple exponential smoothing and conditional auto regressive models (CAR) from our previous study.

Keywords: Bayesian method, linear mixed model, multivariate conditional autoregressive model, spatial time series

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Authors: Elham Saraee, Saurabh Singh, Margrit Betke

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Evaluation of a person’s posture while exercising is important in physical therapy. During a therapy session, a physical therapist or a monitoring system must assure that the person is performing an exercise correctly to achieve the desired therapeutic effect. In this work, we introduce a system called POSTURECHECK for exercise assessment in physical therapy. POSTURECHECK assesses the posture of a person who is exercising with the Proficio robotic arm while being recorded by the Microsoft Kinect interface. POSTURECHECK extracts unique features from the person’s upper body during the exercise, and classifies the sequence of postures as correct or incorrect using Bayesian estimation and majority voting. If POSTURECHECK recognizes an incorrect posture, it specifies what the user can do to correct it. The result of our experiment shows that POSTURECHECK is capable of recognizing the incorrect postures in real time while the user is performing an exercise.

Keywords: Bayesian estimation, majority voting, Microsoft Kinect, PostureCheck, Proficio robotic arm, upper body physical therapy

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Authors: Andi Darmawan, Dewi Retno Sari Saputro, Purnami Widyaningsih

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Diabetes mellitus (DM) is a chronic disease in human that occurred if pancreas cannot produce enough of insulin hormone or the body uses ineffectively insulin hormone which causes increasing level of glucose in the blood, or it was called hyperglycemia. In Indonesia, DM is a serious disease on health because it can cause blindness, kidney disease, diabetic feet (gangrene), and stroke. The type of DM criteria can also be divided based on the main causes; they are DM type 1, type 2, and gestational. Diabetes type 1 or previously known as insulin-independent diabetes is due to a lack of production of insulin hormone. Diabetes type 2 or previously known as non-insulin dependent diabetes is due to ineffective use of insulin while gestational diabetes is a hyperglycemia that found during pregnancy. The most one type commonly found in patient is DM type 2. The main factors of this disease are genetic (A) and life style (E). Those disease with 2 factors can be constructed with additive genetic and unique environment (AE) model. In this article was discussed parameter estimation of AE model using Bayesian method and the inheritance character simulation on parent-offspring. On the AE model, there are response variable, predictor variables, and parameters were capable of representing the number of population on research. The population can be measured through a taken random sample. The response and predictor variables can be determined by sample while the parameters are unknown, so it was required to estimate the parameters based on the sample. Estimation of AE model parameters was obtained based on a joint posterior distribution. The simulation was conducted to get the value of genetic variance and life style variance. The results of simulation are 0.3600 for genetic variance and 0.0899 for life style variance. Therefore, the variance of genetic factor in DM type 2 is greater than life style.

Keywords: AE model, Bayesian method, diabetes mellitus type 2, genetic, life style

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Authors: Rithvik Reddy Adapa, Xin Wang

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Phasor Measurement Units (PMUs) are very sophisticated measuring devices that find amplitude, phase and frequency of various voltages and currents in a power system. Particle filter is a state estimation technique that uses Bayesian inference. Particle filters are widely used in pose estimation and indoor navigation and are very reliable. This paper studies and compares four different particle filters as PMUs namely, generic particle filter (GPF), genetic algorithm particle filter (GAPF), particle swarm optimization particle filter (PSOPF) and adaptive particle filter (APF). Two different test signals are used to test the performance of the filters in terms of responsiveness and correctness of the estimates.

Keywords: phasor measurement unit, particle filter, genetic algorithm, particle swarm optimisation, state estimation

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Authors: Al Omari Moahmmed Ahmed

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In the Bayesian, we developed an approach by using non-informative prior with covariate and obtained by using Gauss quadrature method to estimate the parameters of the covariate and reliability function of the Weibull regression distribution with Type-I censored data. The maximum likelihood seen that the estimators obtained are not available in closed forms, although they can be solved it by using Newton-Raphson methods. The comparison criteria are the MSE and the performance of these estimates are assessed using simulation considering various sample size, several specific values of shape parameter. The results show that Bayesian with non-informative prior is better than Maximum Likelihood Estimator.

Keywords: non-informative prior, Bayesian method, type-I censoring, Gauss quardature

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Authors: Isha Saxena, Behzad Kazemtabrizi, Matthias C. M. Troffaes, Christopher Crabtree

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The calculations done at the beginning of the life of a wind farm are rarely reliable, which makes it important to conduct research and study the failure and repair rates of the wind turbines under various conditions. This miscalculation happens because the current models make a simplifying assumption that the failure/repair rate remains constant over time. This means that the reliability function is exponential in nature. This research aims to create a more accurate model using sensory data and a data-driven approach. The data cleaning and data processing is done by comparing the Power Curve data of the wind turbines with SCADA data. This is then converted to times to repair and times to failure timeseries data. Several different mathematical functions are fitted to the times to failure and times to repair data of the wind turbine components using Maximum Likelihood Estimation and the Posterior expectation method for Bayesian Parameter Estimation. Initial results indicate that two parameter Weibull function and exponential function produce almost identical results. Further analysis is being done using the complex system analysis considering the failures of each electrical and mechanical component of the wind turbine. The aim of this project is to perform a more accurate reliability analysis that can be helpful for the engineers to schedule maintenance and repairs to decrease the downtime of the turbine.

Keywords: reliability, bayesian parameter inference, maximum likelihood estimation, weibull function, SCADA data

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Authors: Mohamed Raouf Benmakrelouf, Wafa Karouche, Joseph Rynkiewicz

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In this paper, we propose an alternative method to construct a Bayesian Network (BN). This method relies on a convolutional neural network (CNN classifier), which determinates the edges of the network skeleton. We train a CNN on a normalized empirical probability density distribution (NEPDF) for predicting causal interactions and relationships. We have to find the optimal Bayesian network structure for causal inference. Indeed, we are undertaking a search for pair-wise causality, depending on considered causal assumptions. In order to avoid unreasonable causal structure, we consider a blacklist and a whitelist of causality senses. We tested the method on real data to assess the influence of education on the voting intention for the extreme right-wing party. We show that, with this method, we get a safer causal structure of variables (Bayesian Network) and make to identify a variable that satisfies the backdoor criterion.

Keywords: Bayesian network, structure learning, optimal search, convolutional neural network, causal inference

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Authors: Redouane Tlemsani, Redouane, Belkacem Kouninef, Abdelkader Benyettou

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In this paper, our system is a Markovien system which we can see it like a Dynamic Bayesian Networks. One of the major interests of these systems resides in the complete training of the models (topology and parameters) starting from training data. The Bayesian Networks are representing models of dubious knowledge on complex phenomena. They are a union between the theory of probability and the graph theory in order to give effective tools to represent a joined probability distribution on a set of random variables. The representation of knowledge bases on description, by graphs, relations of causality existing between the variables defining the field of study. The theory of Dynamic Bayesian Networks is a generalization of the Bayesians networks to the dynamic processes. Our objective amounts finding the better structure which represents the relationships (dependencies) between the variables of a dynamic bayesian network. In applications in pattern recognition, one will carry out the fixing of the structure which obliges us to admit some strong assumptions (for example independence between some variables).

Keywords: Arabic on line character recognition, dynamic Bayesian network, pattern recognition, networks

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Authors: Manar Amayri, Hussain Kazimi, Quoc-Dung Ngo, Stephane Ploix

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A general approach is proposed to determine occupant behavior (occupancy and activity) in residential buildings and to use these estimates for improved energy management. Occupant behaviour is modelled with a Bayesian Network in an unsupervised manner. This algorithm makes use of domain knowledge gathered via questionnaires and recorded sensor data for motion detection, power, and hot water consumption as well as indoor CO₂ concentration. Two case studies are presented which show the real world applicability of estimating occupant behaviour in this way. Furthermore, experiments integrating occupancy estimation and hot water production control show that energy efficiency can be increased by roughly 5% over known optimal control techniques and more than 25% over rule-based control while maintaining the same occupant comfort standards. The efficiency gains are strongly correlated with occupant behaviour and accuracy of the occupancy estimates.

Keywords: energy, management, control, optimization, Bayesian methods, learning theory, sensor networks, knowledge modelling and knowledge based systems, artificial intelligence, buildings

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Authors: Michael Smalenberger

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Intelligent tutoring systems (ITS) are computer-based platforms which can incorporate artificial intelligence to provide step-by-step guidance as students practice problem-solving skills. ITS can replicate and even exceed some benefits of one-on-one tutoring, foster transactivity in collaborative environments, and lead to substantial learning gains when used to supplement the instruction of a teacher or when used as the sole method of instruction. A common facet of many ITS is their use of Bayesian Knowledge Tracing (BKT) to estimate parameters necessary for the implementation of the artificial intelligence component, and for the probability of mastery of a knowledge component relevant to the ITS. While various techniques exist to estimate these parameters and probability of mastery, none directly and reliably ask the user to self-assess these. In this study, 111 undergraduate students used an ITS in a college-level introductory statistics course for which detailed transaction-level observations were recorded, and users were also routinely asked direct questions that would lead to such a self-assessment. Comparisons were made between these self-assessed values and those obtained using commonly used estimation techniques. Our findings show that such self-assessments are particularly relevant at the early stages of ITS usage while transaction level data are scant. Once a user’s transaction level data become available after sufficient ITS usage, these can replace the self-assessments in order to eliminate the identifiability problem in BKT. We discuss how these findings are relevant to the number of exercises necessary to lead to mastery of a knowledge component, the associated implications on learning curves, and its relevance to instruction time.

Keywords: Bayesian Knowledge Tracing, Intelligent Tutoring System, in vivo study, parameter estimation

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Authors: Abdelli Soulaima, Belhadj Besma

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The paper examines the choice of the central bank toward the movements of the nominal exchange rate and evaluates its effects on the volatility of the output growth and the inflation. The novel hybrid method of the dynamic stochastic general equilibrium called the DSGE-VAR is proposed for analyzing this policy experiment in a small scale open economy in particular Tunisia. The contribution is provided to the empirical literature as we apply the Tunisian data with this model, which is rarely used in this context. Note additionally that the issue of treating the degree of response of the central bank to the exchange rate in Tunisia is special. To ameliorate the estimation, the Bayesian technique is carried out for the sample 1980:q1 to 2011 q4. Our results reveal that the central bank should not react or softly react to the exchange rate. The variance decomposition displayed that the overall inflation volatility is more pronounced with the fixed exchange rate regime for most of the shocks except for the productivity and the interest rate. The output volatility is also higher with this regime with the majority of the shocks exempting the foreign interest rate and the interest rate shocks.

Keywords: DSGE-VAR modeling, exchange rate, monetary policy, Bayesian estimation

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Authors: Mahdy ‎Esmailian, Mahdi ‎Doostparast, Ahmad ‎Parsian

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‎In this article‎, ‎sequential order statistics (SOS) censoring type II samples coming from the generalized Pareto distribution are considered‎. ‎Maximum likelihood (ML) estimators of the unknown parameters are derived on the basis of the available multiple SOS data‎. ‎Necessary conditions for existence and uniqueness of the derived ML estimates are given‎. Due to complexity in the proposed likelihood function‎, ‎a useful re-parametrization is suggested‎. ‎For illustrative purposes‎, ‎a Monte Carlo simulation study is conducted and an illustrative example is analysed‎.

Keywords: bayesian estimation‎, generalized pareto distribution‎, ‎maximum likelihood estimation‎, sequential order statistics

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