Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1724

Search results for: Bayesian estimation

1724 Using Dynamic Bayesian Networks to Characterize and Predict Job Placement

Authors: Xupin Zhang, Maria Caterina Bramati, Enrest Fokoue

Abstract:

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

Procedia PDF Downloads 259
1723 Monte Carlo Methods and Statistical Inference of Multitype Branching Processes

Authors: Ana Staneva, Vessela Stoimenova

Abstract:

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

Procedia PDF Downloads 274
1722 Bayesian Approach for Moving Extremes Ranked Set Sampling

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

Abstract:

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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1721 Bayesian Network and Feature Selection for Rank Deficient Inverse Problem

Authors: Kyugneun Lee, Ikjin Lee

Abstract:

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

Procedia PDF Downloads 173
1720 New Estimation in Autoregressive Models with Exponential White Noise by Using Reversible Jump MCMC Algorithm

Authors: Suparman Suparman

Abstract:

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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1719 A Bayesian Multivariate Microeconometric Model for Estimation of Price Elasticity of Demand

Authors: Jefferson Hernandez, Juan Padilla

Abstract:

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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1718 A Two-Stage Bayesian Variable Selection Method with the Extension of Lasso for Geo-Referenced Data

Authors: Georgiana Onicescu, Yuqian Shen

Abstract:

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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1717 Fault Tree Analysis and Bayesian Network for Fire and Explosion of Crude Oil Tanks: Case Study

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

Abstract:

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

Procedia PDF Downloads 497
1716 Factorization of Computations in Bayesian Networks: Interpretation of Factors

Authors: Linda Smail, Zineb Azouz

Abstract:

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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1715 Credit Risk Prediction Based on Bayesian Estimation of Logistic Regression Model with Random Effects

Authors: Sami Mestiri, Abdeljelil Farhat

Abstract:

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

Procedia PDF Downloads 406
1714 Comparative Study on Daily Discharge Estimation of Soolegan River

Authors: Redvan Ghasemlounia, Elham Ansari, Hikmet Kerem Cigizoglu

Abstract:

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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1713 A Bayesian Model with Improved Prior in Extreme Value Problems

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

Abstract:

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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1712 Bayesian Estimation under Different Loss Functions Using Gamma Prior for the Case of Exponential Distribution

Authors: Md. Rashidul Hasan, Atikur Rahman Baizid

Abstract:

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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1711 Bayesian Using Markov Chain Monte Carlo and Lindley's Approximation Based on Type-I Censored Data

Authors: Al Omari Moahmmed Ahmed

Abstract:

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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1710 Forecasting Models for Steel Demand Uncertainty Using Bayesian Methods

Authors: Watcharin Sangma, Onsiri Chanmuang, Pitsanu Tongkhow

Abstract:

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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1709 Spatial Econometric Approaches for Count Data: An Overview and New Directions

Authors: Paula Simões, Isabel Natário

Abstract:

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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1708 Spatial Time Series Models for Rice and Cassava Yields Based on Bayesian Linear Mixed Models

Authors: Panudet Saengseedam, Nanthachai Kantanantha

Abstract:

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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1707 Optimal Bayesian Control of the Proportion of Defectives in a Manufacturing Process

Authors: Viliam Makis, Farnoosh Naderkhani, Leila Jafari

Abstract:

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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1706 PostureCheck with the Kinect and Proficio: Posture Modeling for Exercise Assessment

Authors: Elham Saraee, Saurabh Singh, Margrit Betke

Abstract:

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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1705 Parameter Estimation of Additive Genetic and Unique Environment (AE) Model on Diabetes Mellitus Type 2 Using Bayesian Method

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

Abstract:

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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1704 Don't Just Guess and Slip: Estimating Bayesian Knowledge Tracing Parameters When Observations Are Scant

Authors: Michael Smalenberger

Abstract:

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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1703 Estimating Occupancy in Residential Context Using Bayesian Networks for Energy Management

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

Abstract:

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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1702 The Generalized Pareto Distribution as a Model for Sequential Order Statistics

Authors: Mahdy ‎Esmailian, Mahdi ‎Doostparast, Ahmad ‎Parsian

Abstract:

‎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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1701 Estimation and Forecasting with a Quantile AR Model for Financial Returns

Authors: Yuzhi Cai

Abstract:

This talk presents a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. We establish that the joint posterior distribution of the model parameters and future values is well defined. The associated MCMC algorithm for parameter estimation and forecasting converges to the posterior distribution quickly. We also present a combining forecasts technique to produce more accurate out-of-sample forecasts by using a weighted sequence of fitted QAR models. A moving window method to check the quality of the estimated conditional quantiles is developed. We verify our methodology using simulation studies and then apply it to currency exchange rate data. An application of the method to the USD to GBP daily currency exchange rates will also be discussed. The results obtained show that an unequally weighted combining method performs better than other forecasting methodology.

Keywords: combining forecasts, MCMC, quantile modelling, quantile forecasting, predictive density functions

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1700 Bayesian Reliability of Weibull Regression with Type-I Censored Data

Authors: Al Omari Moahmmed Ahmed

Abstract:

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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1699 The Response of the Central Bank to the Exchange Rate Movement: A Dynamic Stochastic General Equilibrium-Vector Autoregressive Approach for Tunisian Economy

Authors: Abdelli Soulaima, Belhadj Besma

Abstract:

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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1698 Bayesian Estimation of Hierarchical Models for Genotypic Differentiation of Arabidopsis thaliana

Authors: Gautier Viaud, Paul-Henry Cournède

Abstract:

Plant growth models have been used extensively for the prediction of the phenotypic performance of plants. However, they remain most often calibrated for a given genotype and therefore do not take into account genotype by environment interactions. One way of achieving such an objective is to consider Bayesian hierarchical models. Three levels can be identified in such models: The first level describes how a given growth model describes the phenotype of the plant as a function of individual parameters, the second level describes how these individual parameters are distributed within a plant population, the third level corresponds to the attribution of priors on population parameters. Thanks to the Bayesian framework, choosing appropriate priors for the population parameters permits to derive analytical expressions for the full conditional distributions of these population parameters. As plant growth models are of a nonlinear nature, individual parameters cannot be sampled explicitly, and a Metropolis step must be performed. This allows for the use of a hybrid Gibbs--Metropolis sampler. A generic approach was devised for the implementation of both general state space models and estimation algorithms within a programming platform. It was designed using the Julia language, which combines an elegant syntax, metaprogramming capabilities and exhibits high efficiency. Results were obtained for Arabidopsis thaliana on both simulated and real data. An organ-scale Greenlab model for the latter is thus presented, where the surface areas of each individual leaf can be simulated. It is assumed that the error made on the measurement of leaf areas is proportional to the leaf area itself; multiplicative normal noises for the observations are therefore used. Real data were obtained via image analysis of zenithal images of Arabidopsis thaliana over a period of 21 days using a two-step segmentation and tracking algorithm which notably takes advantage of the Arabidopsis thaliana phyllotaxy. Since the model formulation is rather flexible, there is no need that the data for a single individual be available at all times, nor that the times at which data is available be the same for all the different individuals. This allows to discard data from image analysis when it is not considered reliable enough, thereby providing low-biased data in large quantity for leaf areas. The proposed model precisely reproduces the dynamics of Arabidopsis thaliana’s growth while accounting for the variability between genotypes. In addition to the estimation of the population parameters, the level of variability is an interesting indicator of the genotypic stability of model parameters. A promising perspective is to test whether some of the latter should be considered as fixed effects.

Keywords: bayesian, genotypic differentiation, hierarchical models, plant growth models

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1697 Optimized Dynamic Bayesian Networks and Neural Verifier Test Applied to On-Line Isolated Characters Recognition

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

Abstract:

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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1696 Bayesian Inference for High Dimensional Dynamic Spatio-Temporal Models

Authors: Sofia M. Karadimitriou, Kostas Triantafyllopoulos, Timothy Heaton

Abstract:

Reduced dimension Dynamic Spatio-Temporal Models (DSTMs) jointly describe the spatial and temporal evolution of a function observed subject to noise. A basic state space model is adopted for the discrete temporal variation, while a continuous autoregressive structure describes the continuous spatial evolution. Application of such a DSTM relies upon the pre-selection of a suitable reduced set of basic functions and this can present a challenge in practice. In this talk, we propose an online estimation method for high dimensional spatio-temporal data based upon DSTM and we attempt to resolve this issue by allowing the basis to adapt to the observed data. Specifically, we present a wavelet decomposition in order to obtain a parsimonious approximation of the spatial continuous process. This parsimony can be achieved by placing a Laplace prior distribution on the wavelet coefficients. The aim of using the Laplace prior, is to filter wavelet coefficients with low contribution, and thus achieve the dimension reduction with significant computation savings. We then propose a Hierarchical Bayesian State Space model, for the estimation of which we offer an appropriate particle filter algorithm. The proposed methodology is illustrated using real environmental data.

Keywords: multidimensional Laplace prior, particle filtering, spatio-temporal modelling, wavelets

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1695 Effect of Progressive Type-I Right Censoring on Bayesian Statistical Inference of Simple Step–Stress Acceleration Life Testing Plan under Weibull Life Distribution

Authors: Saleem Z. Ramadan

Abstract:

This paper discusses the effects of using progressive Type-I right censoring on the design of the Simple Step Accelerated Life testing using Bayesian approach for Weibull life products under the assumption of cumulative exposure model. The optimization criterion used in this paper is to minimize the expected pre-posterior variance of the PTH percentile time of failures. The model variables are the stress changing time and the stress value for the first step. A comparison between the conventional and the progressive Type-I right censoring is provided. The results have shown that the progressive Type-I right censoring reduces the cost of testing on the expense of the test precision when the sample size is small. Moreover, the results have shown that using strong priors or large sample size reduces the sensitivity of the test precision to the censoring proportion. Hence, the progressive Type-I right censoring is recommended in these cases as progressive Type-I right censoring reduces the cost of the test and doesn't affect the precision of the test a lot. Moreover, the results have shown that using direct or indirect priors affects the precision of the test.

Keywords: reliability, accelerated life testing, cumulative exposure model, Bayesian estimation, progressive type-I censoring, Weibull distribution

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