نشریه اندیشه آماری
سال بیست و پنجم شماره 2 (پیاپی 50، پاییز و زمستان 1399)

Thomas Bayes, the founder of Bayesian vision, entered the University of Edinburgh in 1719 to study logic and theology. Returning in 1722, he worked with his father in a small church. He also was a mathematician and in 1740 he made a novel discovery which he never published, but his friend Richard Price found it in his notes after his death in 1761, reedited it and published it. But until Laplace, no one cared until the late 18th century, when data did not have equal confidence in Europe. Pierre − Simon Laplace, a young mathematician, believed that probability theory was a key in his hand, and he independently discovered the Bayesian mechanism and published it in 1774. Laplace expressed the principle not in an equation but in words. Today, Bayesian statistics as a discipline of statistical philosophy and the interpretation of probability is very important and has become known as the Bayesian theorem presented after Bayesian death. Allen Turing is a British computer scientist, mathematician and philosopher who is now known as the father of computer science and artificial intelligence. His outstanding achievements during his short life are the result of the adventures of a beautiful mind that was finally extinguished forever with a suspicious death. During World War II, Turing worked in Belchley Park, the center of the British decipherment, and for a time was in charge of the German Navy’s cryptographic analysis. He devised several methods, specifically from Bayesian’s point of view, without breaking his name to crack German codes, as well as the electromechanical machine method that could find the features of the Enigma machine. Finding Enigma can also be considered one of his great works. Alan Turing was a leading scientist who played an important role in the development of computer science and artificial intelligence and the revival of Bayesian thought. Turing provided an effective and stimulating contribution to artificial intelligence through the Turing experiment. He then worked at the National Physics Laboratory in the United Kingdom, presenting one of the prototypes of a stored computer program, though it worked, which was not actually made as the ”Manchester Mark ”. He went to the University of Manchester in 1948 to be recognized as the world’s first real computer. However, later on, the role of Bayesian rule and law in scientific developments becomes more important. Many possible Bayesian methods in the 21st century have made significant advances in the explanation and application of Bayesian statistics in climate development and have solved many of the world’s problems. New global technology has grown on Bayesian ideas, which will be reviewed intion of probability is very important and has become known as the Bayesian theorem presented after Bayesian death. Allen Turing is a British computer scientist, mathematician and philosopher who is now known as the father of computer science and artificial intelligence. His outstanding achievements during his short life are the result of the adventures of a beautiful mind that was finally extinguished forever with a suspicious death. During World War II, Turing worked in Belchley Park, the center of the British decipherment, and for a time was in charge of the German Navy’s cryptographic analysis. He devised several methods, specifically from Bayesian’s point of view, without breaking his name to crack German codes, as well as the electromechanical machine method that could find the features of the Enigma machine. Finding Enigma can also be considered one of his great works. Alan Turing was a leading scientist who played an important role in the development of computer science and artificial intelligence and the revival of Bayesian thought. Turing provided an effective and stimulating contribution to artificial intelligence through the Turing experiment. He then worked at the National Physics Laboratory in the United Kingdom, presenting one of the prototypes of a stored computer program, though it worked, which was not actually made as the ”Manchester Mark ”. He went to the University of Manchester in 1948 to be recognized as the world’s first real computer. However, later on, the role of Bayesian rule and law in scientific developments becomes more important. Many possible Bayesian methods in the 21st century have made significant advances in the explanation and application of Bayesian statistics in climate development and have solved many of the world’s problems. New global technology has grown on Bayesian ideas, which will be reviewed in this article.

Recently with science and technology development, data with functional nature are easy to collect. Hence, statistical analysis of such data is of great importance. Similar to multivariate analysis, linear combinations of random variables have a key role in functional analysis. The role of Theory of Reproducing Kernel Hilbert Spaces is very important in this content. In this paper we study a general concept of Fisher’s linear discriminant analysis that extends the classical multivariate method to the case functional data. A bijective map is used to link a second order process to the reproducing kernel Hilbert space, generated by its within class covariance kernel. Finally a real data set related to Iranian weather data collected in 2008 is also treated.

Statistics stems out from induction. Induction is a long lasting notion in philosophy. The nature of notions in philosophy are such that neither they can be solved completely nor one can leave them forever. One of the most important problem in induction is “the problem of induction”. In this paper we give a short history of induction and discuss some aspects of the problem of induction.

Methods of inferring the population structure‎, ‎its applications in identifying disease models as well as foresighting the physical and mental situation of human beings have been finding ever-increasing importance‎. ‎In this article‎, ‎first‎, ‎motivation and significance of studying the problem of population structure is explained‎. ‎In the next section‎, ‎the applications of inference of population structure in biology and the treatment of various diseases are described‎. ‎Afterward‎, ‎the methods of inferring the population structure as well as detecting the disease model correspond to each subpopulation‎, ‎for populations whose members are admixture or not‎, ‎are described separately‎. ‎To this end‎, ‎the methods of inferring the population structure through the Bayesian approach are emphasized and the reasons for the superiority of Bayesian methods are illustrated‎.

One of the challenges for decision-makers in insurance and finance is choosing the appropriate criteria for making decisions. Mathematical expectation, expected utility, and distorted expectation are the three most common measures in this area. In this article, we study these three criteria, and by providing some examples, we review and compare the decisions made by each measure.

The current article is a translation of a paper published in Significance journal, 2020, Vol. 17, No. 4 captioned as “C.R. Rao’s ‎Centurychr(chr(chr('39') 39chr('39')) 39chr(chr('39') 39chr('39'))) chr (chr(chr('39') 39chr('39')) 39chr(chr('39')39chr('39'))) ‎, which has been scripted as a perception of an appreciation  note by involvements of  Bradley Efron, Shun-ichi Amari, Donald B. Rubin, Arni S. R. Srinivasa Rao and David R. Cox. Therefore, it is not possible to address this manuscript as a scientific paper, which is regularly accepted among the researchers. Evidently, the proposed translated article is prepared with the focus on appreciating professor Rao’s a century contribution in statistics. With this intention, Persian speakers, i.e., those who are somehow associated with statistics, could become aware of professor Rao’s invaluable role in spreading the statistics around the world. Absolutely, individuals that have achieved a bachelor’s degree in statistics, are familiar with at least two well-known titles:“Cramer-Rao’s inequalitychr (chr(chr('39')39chr('39')) 39chr(chr('39')39chr('39'))) chr(chr(chr('39') 39chr('39')) 39chr(chr('39') 39chr ('39'))) and “Rao-Blackwell theoremchr(chr(chr('39')39chr('39')) 39chr(chr('39')39chr('39')))chr(chr(chr('39')39chr('39')) 39chr(chr ('39')39chr('39'))) , possessing Rao’s designation in both titles. Needless to say, that mentioning his remarkable role in statistics and learning more about his outstanding character by some renowned statisticians, who have also made remarkable impacts on statistics, is a must. In accordance with the author of this paper, advantageous activities of Rao, some of which have come to this paper, can be considered as a model for those who enter in various fields of statistics and intend to follow Rao’s scientific and social life.

In this study, we first introduce the Banach lattice random elements and some of their properties. Then, using the order defined in Banach lattice space, we introduce and characterize the order negatively dependence Banach lattice random elements by the order defined in Banach lattice space. Finally, we obtain some limit theorems for the sequence of order negatively dependence Banach lattice random elements.

The Internet of Things is suggested as the upcoming revolution in the Information and communication technology due to its very high capability of making various businesses and industries more productive and efficient. This productivity comes from the emergence of innovation and the introduction of new capabilities for businesses. Different industries have shown varying reactions to IOT, but what is clear is that IOT has applications in all Businesses. These applications have made significant progress in some industries such as health and transportation but is under development in others, namely agriculture and animal husbandry. In fact, the production of data bases on the Internet of Things is one of the main pillars in the field of big data and data science, Therefore, statistical concepts and models that are used in data science can be beneficially implemented in such data. Among the valid statistical models, Bayesian statistics for data is being utilized in these studies. In this research the fundamentals of Bayesian statistics for big data and most notably the data produced by IOT is explained. They have been Pragmatically examined in both road traffic as well as people’s social behavior towards using vehicles, which have had practically and scientifically valid results.

In analyzing longitudinal data with counted responses, normal distribution is usually used for distribution of the random efffects. However, in some applications random effects may not be normally distributed. Misspecification of this distribution may cause reduction of efficiency of estimators. In this paper, a generalized log-gamma distribution is used for the random effects which includes the normal one as a special case. As the frquentist analysis faces with complex computation, the Bayesian analysis of this model is investigated and then it is utilized for analyzing two real data sets. Also, some simulation studies are conducted to evaluate the performance of the relevant models.

There are two reasons that 2013 named as Statistics year. First, it was 300 year after written the book, Ars Conjectandi, by Bernoulli and the second, presentation of Bayes article 250 year ago. Hald (2007) beleive that the development period of Probability and Statistics is started from Bernoulli and ended by Fisher. This article expaline the role of Bernoulli book in Statistics.

In conventional methods for spatial survival data modeling, it is often assumed that the coefficients of explanatory variables in different regions have a constant effect on survival time. Usually, the spatial correlation of data through a random effect is also included in the model. But in many practical issues, the factors affecting survival time do not have the same effects in different regions. In this paper, we consider the spatial effects of factors affecting survival time are not the same in the different areas. For this purpose, spatial regression models and spatial varying coefficient models are introduced. Next, the Bayesian estimates of their parameters are presented. Three models of classical regression, spatial regression and spatial varying coefficient regression are used to analyze Esophageal cancer survival data. The relative risk of various factors is examined and evaluated.

In this paper, we first define longitudinal-dynamic heteroscedastic hierarchical  normal  models. These models can be used to fit longitudinal data in which the dependency structure is constructed through a dynamic model rather than observations. We discuss different methods for estimating the hyper-parameters. Then the corresponding estimates for the hyper-parameter that causes the association in the model will be presented. The comparison among various  empirical estimators  is illustrated through a simulation study. Finally, we apply our methods to a  real dataset.