Víctor H. Salinas Torres, C. Vásquez, José S. Romeo
{"title":"Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System","authors":"Víctor H. Salinas Torres, C. Vásquez, José S. Romeo","doi":"10.15446/RCE.V42N1.66279","DOIUrl":"https://doi.org/10.15446/RCE.V42N1.66279","url":null,"abstract":"This work presents a Bayesian approach for estimating the limiting availability of an one-unit repairable system. A Bayesian analysis is developed considering an informative prior and a less informative prior distribution, respectively. Simulations are presented to study the performance of the Bayesian solutions. The maximum likelihood method is also revisited. Finally, a case study is considered, the Bayesian methodology is applied to estimate the limiting availability of a palletizer, which is used in the packaging of glass bottles. Extensions to a coherent system are also discussed.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15446/RCE.V42N1.66279","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67050518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Using an Anchor to Improve Linear Predictions with Application to Predicting Disease Progression.","authors":"Alex Karanevich, Jianghua He, Byron J Gajewski","doi":"10.15446/rce.v41n2.68535","DOIUrl":"https://doi.org/10.15446/rce.v41n2.68535","url":null,"abstract":"<p><p>Linear models are some of the most straightforward and commonly used modelling approaches. Consider modelling approximately monotonic response data arising from a time-related process. If one has knowledge as to when the process began or ended, then one may be able to leverage additional assumed data to reduce prediction error. This assumed data, referred to as the \"anchor,\" is treated as an additional data-point generated at either the beginning or end of the process. The response value of the anchor is equal to an intelligently selected value of the response (such as the upper bound, lower bound, or 99<sup>th</sup> percentile of the response, as appropriate). The anchor reduces the variance of prediction at the cost of a possible increase in prediction bias, resulting in a potentially reduced overall mean-square prediction error. This can be extremely effective when few individual data-points are available, allowing one to make linear predictions using as little as a single observed data-point. We develop the mathematics showing the conditions under which an anchor can improve predictions, and also demonstrate using this approach to reduce prediction error when modelling the disease progression of patients with amyotrophic lateral sclerosis.</p>","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":"41 2","pages":"137-155"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6345390/pdf/nihms978249.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36902206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Eduardo Guzmán, Mario A. Vázquez, David del Valle, P. Pérez-Rodríguez
{"title":"Artificial Neuronal Networks: A Bayesian Approach Using Parallel Computing","authors":"Eduardo Guzmán, Mario A. Vázquez, David del Valle, P. Pérez-Rodríguez","doi":"10.15446/RCE.V41N2.55250","DOIUrl":"https://doi.org/10.15446/RCE.V41N2.55250","url":null,"abstract":"An Artificial Neural Network (ANN) is a learning paradigm and automatic processing inspired in the biological behavior of neurons and the brain structure. The brain is a complex system; its basic processing unit are the neurons, which are distributed massively in the brain sharing multiple connections between them. The ANNs try to emulate some characteristics of humans, and can be thought as intelligent systems that perform some tasks in a different way that actual computer does. The ANNs can be used to perform complex activities, for example: pattern recognition and classification, weather prediction, genetic values prediction, etc. The algorithms used to train the ANN, are in general complex, so therefore there is a need to have alternatives which lead to a significant reduction of times employed to train an ANN. In this work, we present an algorithm based in the strategy ``divide and conquer'' which allows to train an ANN with a single hidden layer. Part of the sub problems of the general algorithm used for training are solved by using parallel computing techniques, which allows to improve the performance of the resulting application. The proposed algorithm was implemented using the C++ programming language, and the libraries Open MPI and ScaLAPACK. We present some application examples and we asses the application performance. The results shown that it is possible to reduce significantly the time necessary to execute the program that implements the algorithm to train the ANN.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15446/RCE.V41N2.55250","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45544810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Form-Invariance of the Non-Regular Exponential Family of Distributions","authors":"S. Ghorbanpour, R. Chinipardaz, S. M. R. Alavi","doi":"10.15446/RCE.V41N2.62233","DOIUrl":"https://doi.org/10.15446/RCE.V41N2.62233","url":null,"abstract":"The weighted distributions are used when the sampling mechanism records observations according to a nonnegative weight function. Sometimes the form of the weighted distribution is the same as the original distribution except possibly for a change in the parameters that is called the form-invariant weighted distribution. In this paper, by identifying a general class of weight functions, we introduce an extended class of form-invariant weighted distributions belonging to the non-regular exponential family which included two common families of distribution: exponential family and non-regular family as special cases. Some properties of this class of distributions such as the sufficient and minimal sufficient statistics, maximum likelihood estimation and the Fisher information matrix are studied.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44654968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Reliability in a Multicomponent Stress-Strength Model with Power Lindley Distribution","authors":"Abbas Pak, Arjun K. Gupta, N. B. Khoolenjani","doi":"10.15446/RCE.V41N2.69621","DOIUrl":"https://doi.org/10.15446/RCE.V41N2.69621","url":null,"abstract":"In this paper we study the reliability of a multicomponent stress-strength model assuming that the components follow power Lindley model. The maximum likelihood estimate of the reliability parameter and its asymptotic confidence interval are obtained. Applying the parametric Bootstrap technique, interval estimation of the reliability is presented. Also, the Bayes estimate and highest posterior density credible interval of the reliability parameter are derived using suitable priors on the parameters. Because there is no closed form for the Bayes estimate, we use the Markov Chain Monte Carlo method to obtain approximate Bayes estimate of the reliability. To evaluate the performances of different procedures, simulation studies are conducted and an example of real data sets is provided.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15446/RCE.V41N2.69621","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48316021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Construction of the Design Matrix for Generalized Linear Mixed-Effects Models in the Context of Clinical Trials of Treatment Sequences.","authors":"Francisco J Diaz","doi":"10.15446/rce.v41n2.63332","DOIUrl":"10.15446/rce.v41n2.63332","url":null,"abstract":"<p><p>The estimation of carry-over effects is a difficult problem in the design and analysis of clinical trials of treatment sequences including cross-over trials. Except for simple designs, carry-over effects are usually unidentifiable and therefore nonestimable. Solutions such as imposing parameter constraints are often unjustified and produce differing carry-over estimates depending on the constraint imposed. Generalized inverses or treatment-balancing often allow estimating main treatment effects, but the problem of estimating the carry-over contribution of a treatment sequence remains open in these approaches. Moreover, washout periods are not always feasible or ethical. A common feature of designs with unidentifiable parameters is that they do not have design matrices of full rank. Thus, we propose approaches to the construction of design matrices of full rank, without imposing artificial constraints on the carry-over effects. Our approaches are applicable within the framework of generalized linear mixed-effects models. We present a new model for the design and analysis of clinical trials of treatment sequences, called Antichronic System, and introduce some special sequences called Skip Sequences. We show that carry-over effects are identifiable only if appropriate Skip Sequences are used in the design and/or data analysis of the clinical trial. We explain how Skip Sequences can be implemented in practice, and present a method of computing the appropriate Skip Sequences. We show applications to the design of a cross-over study with 3 treatments and 3 periods, and to the data analysis of the STAR*D study of sequences of treatments for depression.</p>","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":"41 2","pages":"191-233"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7100378/pdf/nihms-1050552.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37782716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair","authors":"C. Gómez, Nelfi Gertrudis González Alvarez","doi":"10.15446/RCE.V41N1.59929","DOIUrl":"https://doi.org/10.15446/RCE.V41N1.59929","url":null,"abstract":"This paper develops simultaneous confidence bands using computer intensive methods based on resampling, for the expected discounted warranty costs in coherent systems under physical minimal repair, that is, when the system is observed at its components level and only the component that causes the fault is minimally repaired. For this purpose, it is shown that, under the framework of the Martingale processes and the central limit resampling theorem (CLRT) over stochastic processes, the discounted warranty cost processes satisfy the conditions set by the central limit resampling theorem (CLRT). Additionally, a simulation study is performed on the most relevant variables, such that the finite sample features of the proposed bands may be assessed, based on their actual coverage probabilities. The results in the considered scenarios show that resampling-based simultaneous confidence bands have coverage probabilities that are close to the nominal coverage. In particular, the agreement is good when there are 100 systems or more where a large number of resamples are used for the approximation.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":"28 1","pages":"1-30"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83474421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Bivariate Model based on Compound Negative Binomial Distribution","authors":"M. Omair, Fatimah E. Almuhayfith, A. Alzaid","doi":"10.15446/RCE.V41N1.57803","DOIUrl":"https://doi.org/10.15446/RCE.V41N1.57803","url":null,"abstract":"A new bivariate model is introduced by compounding negative binomial and geometric distributions. Distributional properties, including joint, marginal and conditional distributions are discussed. Expressions for the product moments, covariance and correlation coefficient are obtained. Some properties such as ordering, unimodality, monotonicity and self-decomposability are studied. Parameter estimators using the method of moments and maximum likelihood are derived. Applications to traffic accidents data are illustrated.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":"33 1","pages":"87-108"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83042965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Estimating dynamic Panel data. A practical approach to perform long panels.","authors":"Romilio Labra Lillo, Celia Torrecillas","doi":"10.15446/RCE.V41N1.61885","DOIUrl":"https://doi.org/10.15446/RCE.V41N1.61885","url":null,"abstract":"Panel data methodology is one of the most popular tools for quantitative analyses in the field of social sciences, particularly on topics related to economics and business. This technique allows us simultaneously addressing individual effects, numerous periods, and in turn, the endogeneity of the model or independent regressors. Despite these advantages, there are several methodological and practical limitations to perform estimations using this tool. Two types of models can be estimated with Panel data. While those of static nature have been the most developed, for performing dynamic models still remain some theoretical and practical constraints. This paper focus precisely on the latter, dynamics panel data, using an approach that combines theory and praxis, and paying special attention on estimations with macro database, that is to say, dataset with a long period of time and a small number of individuals, also called long panels.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":"13 1","pages":"31-52"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87437976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}