نشریه اندیشه آماری
سال بیست و یکم شماره 1 (پیاپی 41، بهار و تابستان 1395)

ýA Bayesian network is a graphical model that represents a set of random variables and their causal relationship via a Directed Acyclic Graph (DAG)ý. ýThere are basically two methods used for learning Bayesian networký: ýparameter-learning and structure-learningý. ýOne of the most effective structure-learning methods is K2 algorithmý. ýBecause the performance of the K2 algorithm depends on node orderingý, ýmore effective node ordering inference methods are neededý. ýIn this paperý, ýbased on the fact that the parent and child variables are identified by estimated Markov Blanket (MB)ý, ýwe first estimate the MB of a variable using Grow-Shrink algorithmý, ýthen determine the candidate parents of a variable by evaluating the conditional frequencies using Dirichlet probability density functioný. ýThen the candidate parents are used as input for the K2 algorithmý. ýExperimental results for most of the datasets indicate that our proposed method significantly outperforms previous methodý.

ýIn this paperý, ýcollinearity in regression models is introduced and then the procedures on how toý " ýremove itý" ýare studiedý. ýMoreover preliminary definitions have been givený. ýAnd the end of this paperý, ýcollinearity in regression model will be recognition and a solution will be introduced for remove itý.

ýThere are different types of classification methods for classifying the certain dataý. ýAll the time the value of the variables is not certain and they may belong to the interval that is called uncertain dataý. ýIn recent yearsý, ýby assuming the distribution of the uncertain data is normalý, ýthere are several estimation for the mean and variance of this distributioný. ýIn this paperý, ýwe consider the mean and variance for each of the start and end of intervalsý. ýThus we assume that the distribution of uncertain data is bivariate normal distributioný. ýWe used the maximum likelihood to estimate the means and variances of the bivariate normal distributioný. ýFinallyý, ýBased on the Naive Bayesian classificationý, ýwe propose a Bayesian mixture algorithm for classifying the certain and uncertain dataý. ýThe experimental results show that the proposed algorithm has high accuracy.

Tolerance interval is a random interval that contains a proportion of the population with a determined confidence level and is applied in many application fields such as reliability and quality control. In this educational paper, we investigate different methods for computing tolerance interval for the binomial random variable using the package Tolerance in statistical software R.

ýA Poisson distribution is well used as a standard model for analyzing count dataý. ýSo the Poisson distribution parameter estimation is widely applied in practiceý. ýProviding accurate confidence intervals for the discrete distribution parameters is very difficultý. ýSo farý, ýmany asymptotic confidence intervals for the mean of Poisson distribution is providedý. ýIt is known that the coverage probability of the confidence interval (L(X),U(X)) is a function of distribution parameterý. ýSince Poisson distribution is discreteý, ýcoverage probability of confidence intervals for Poisson mean has no closed form and the exact calculation of confidence coefficientý, ýaverage coverage probability and maximum coverage probabilities for this intervalsý, ýis very difficultý. ýMethodologies for computing the exact average coverage probabilities as well as the exact confidence coefficients of confidence intervals for one-parameter discrete distributions with increasing bounds are proposed by Wang (2009)ý. ýIn this paperý, ýwe consider a situation that the both lower and upper bounds of the confidence interval is increasingý. ýIn such situationsý, ýwe explore the problem of finding an exact maximum coverage probabilities for confidence intervals of Poisson meaný. ýDecision about confidence intervals optimalityý, ýbased on simultaneous evaluation of confidence coefficientý, ýaverage coverage probability and maximum coverage probabilitiesý, ýwill be more reliableý.

ýThe classic F-test is usually used for testing the effects of factors in homoscedastic two-way ANOVA modelsý. ýHoweverý, ýthe assumption of equal cell variances is usually violated in practiceý. ýIn recent yearsý, ýseveral test procedures have been proposed for testing the effects of factorsý. ýIn this paperý, ýthe two methods that are approximate degree of freedom (ADF) and parametric bootstrap (PB) approaches are evaluated in terms of type one error and powerý. ýThe simulation results show that these two methods have satisfactory performance in terms of type one error and their power is very close to each other approximatelyý. ýHoweverý, ýthe ADF method is very easy to implement in comparison with PB appreach which is simulation-based method and consequently time consumingý.

ýBy existing censor and skewness in survival dataý, ýsome models such as weibull are used to analyzing survival dataý.
ýIn addition, parametric and semiparametric models can be obtained from baseline hazard function of Cox model to fit to survival dataý. ýHowever these models are popular because of their simple usage but do not consider unknown risk factorsý, ýthat's why cannot introduce the best fit to the data necessarilyý.
ýIn this paper by considering multiple random effects in Cox modelý, ýfrailty models are introducedý. ýThen using presented modelsý, ýesophageal cancer data in Golestan were modeled and fitted models were evaluated and compared based on generalized coefficient of determination criterioný.

ýIn this paperý, ýwe have studied the analysis an interval linear regression model for fuzzy dataý.
ýIn section oneý, ýwe have introduced the concepts required in this thesis and then we illustrated linear regression fuzzy sets and some primary definitionsý. ýIn section twoý, ýwe have introduced various methods of interval linear regression analysisý. ýIn section threeý, ýwe have implemented numerical examples of the chapter twoý. ýFinallyý, ýwe have improved some methods of interval linear regression analysis that considered in section fourý. ýWe will showed performance of three methods by several examplesý. ýAll computations of examples are done by alabama package by R softwareý.

ýCensored samples are discussed in experiments of life-testing; i.eý. ýwhenever the experimenter does not observe the failure times of all units placed on a life testý. ýIn recent yearsý, ýinference based on censored sampling is consideredý, ýso that about the parameters of various distributions such as ýnormalý, ýexponentialý, ýgammaý, ýRayleighý, ýWeibullý, ýlog normalý, ýinverse Gaussianý, ýlogisticý, ýLaplaceý, ýand Paretoý, ýhas been inferred based on censored samplingý.
In this paperý, ýa procedure for exact hypothesis testing and obtaining confidence interval for mean of the exponential distribution under Type-I progressive hybrid censoring is proposedý. ýThený, ýperformance of the proposed confidence interval is evaluated using simulationý. ýFinallyý, ýthe proposed procedures are performed on a data setý.

ýBasu’s theorem is one of the most elegant results of classical statisticsý. ýSuccinctly putý, ýthe theorem saysý: ýif T is a complete sufficient statistic for a family of probability measuresý, ýand V is an ancillary statisticý, ýthen T and V are independentý. ýA very novel application of Basu’s theorem appears recently in proving the infinite divisibility of certain statisticsý. ýIn addition to Basu’s theoremý, ýthis application requires a version of the Goldie-Steutel lawý. ýBy using Basu’s theorem that a large class of functions of random variablesý, ýtwo of which are independent standard normalý, ýis infinitely divisibleý. ýThe next result provides a representation of functions of normal variables as the product of two random variablesý, ýwhere one is infinitely divisibleý, ýwhile the other is notý, ýand the two are independently distributedý.