فهرست مطالب مهدی شمس

In the case of large amounts of information, the data should be summarized in such a way that no valuable information is lost. Sufficient statistics are used for this purpose. In this paper, by defining similar statistics, a method for calculating these statistics is presented. Informative statistics are then defined under several different loss functions. The concept of sufficiency is used to identify two characteristics, similarity and informativeness. Finally, under several different loss functions, in the case of Gaussian observation errors and linear systems, informative statistics are found.

The current research was conducted with the aim of studying the scaffolding strategy and providing a new approach for teaching random variables in probability courses of science and engineering students.

In this article, firstly, some issues are raised about active learning and factors such as group work, corrective feedback, and the use of computers that help students learn courses related to statistics and probability. Then the demonstration programs that can replace the classical educational methods were introduced.

In the following, some common misconceptions of students about events, random variables and continuous random variables will be mentioned and these concepts will be analyzed by citing a number of examples. In the last part, the concept of scaffolding and its application in random variable education and a teaching approach in statistics and probability courses are described.

According to the items stated in the article, it is suggested to teach the basic topics of random variables, instead of teaching discrete and continuous random variables separately, random variables should be taught in general.

In this study, a simple generalization of the Lehmann-Scheffe theorem is proposed in cases where UMVUEs exist but a sufficiently complete statistics does not exist. Also, another method is introduced based on the group action. In this method, UMVUE for the unknown parameter is found using  a commutative and associative binary operation.  Finally, the motivation for using the words "completeness" and "unbiasedness" is expressed in such a way that completeness and unbiasedness are not characteristic of a statistic or its parametric form, but a family of distributions of a statistic, and deleting even one point of the parameter space may change the completeness.

Invariance principles is one of the ways to summarize sample information and by these principles invariance or equivariance decision rules are used. In this paper, first, the methods for finding the maximal invariant function are introduced. As a new method, maximal invariant statistics are constructed using equivariant functions. Then, using several equivariant functions, the maximal invariant statistic is obtained. If the group acts uniquely transitively, the equivariant functions will be converted into estimators that can be used in statistical branches. Finally, it is shown that in the case that the group action is not uniquely transitive but a normal subgroup has this property, the maximal invariant statistic can also be calculated.

‎Information inequalities have many applications in estimation theory and statistical decision making‎. ‎This paper describes the application of an information inequality to make the minimax decision in the framework of Bayesian theory‎. ‎In this way‎, ‎first a fundamental inequality for Bayesian risk is introduced under the square error loss function and then its applications are expressed in determining asymptotically and locally minimax estimators in the case of univariate and multivariate‎. ‎In the case that the parameter components are orthogonal‎, ‎the asymptotic-local minimax estimators are obtained for a function of the mean vector and the covariance matrix in the multivariate normal distribution‎. ‎In the end‎, ‎the bounds of information inequality are calculated under a general loss function‎.

In this paper, the Wilcoxon ranked-sum test is generalized to the fuzzy environment based on a sample of fuzzy random variables. In the proposed approach, first by remembering the concept of induced fuzzy random variable from a family of distributions with fuzzy parameter, the fuzzy median of the population and the fuzzy median of a sample of fuzzy random variables are generalized to the fuzzy environment. The large sample property of a sequence of fuzzy sample mean is then investigated based on a popular fuzzy distance. Then a new method for testing fuzzy hypotheses for fuzzy median of a population is extended based on a criterion of belonging of a fuzzy set to the conventional critical region. For this purpose, the fuzzy Wilcoxon test statistic is first defined based on the fuzzy observations. Finally, at a given level of exact significance, a fuzzy test is proposed to test the fuzzy hypotheses of fuzzy median. The proposed method is finally illustrated with a practical example. The proposed approach is compared with other existing methods and the differences are examined.

Naturally in choosing a point estimator we are interested in choosing an estimator that minimizes the risk function for all parameter space values. In practice, this is not possible due to the large number of estimators. One way to solve this problem (find optimal estimators) is to limit the range of estimators and find the best estimator in the finite range. This limitation leads us to two types of optimal estimators, namely the best equivariant estimator and the minimum risk unbiased estimator, respectively, in terms of limiting ourselves to the class of equivariant or unbiased estimators. In this paper, the role of independence in simplifying the calculation of these estimators is examined. We also deal with the stochastic independence of an invariant function and its comparison with the Basu’s theorem. To find the optimal estimators, the class of estimators can be limited. This limitation can be applied to the class of equivariant or unbiased estimators, which leads to two types of optimal estimators, namely the best equivariant estimator and the minimum risk unbiased estimator, respectively. For this purpose, in addition to the Rao-BlackwellLehmann-Scheffé theorem (Casella and Berger, 2001), two other methods have been proposed by Sathe and Varde (1969) and Eaton and Morris (1970) which can be useful to achieve this goal. In these two methods, by limiting the class of equivariant or unbiased estimators, the estimator with the minimum risk is considered as the optimal estimator. Independence can play a key role in making it easier to calculate the risk function of the best equivariant estimator and the minimum risk unbiased estimator. In fact, the role of independence is to eliminate the conditional probability in calculating the risk function of the best equivariant estimator and the minimum risk unbiased estimator, which in most cases results from Basu’s theorem and the independence of ancillary statistic from complete sufficient statistics. Similar to Basu’s theorem, it can be shown that in certain circumstances an invariant statistic and equivariant function are independent of each other, which can play a role in eliminating the conditional probability by the independence of the maximum invariant statistic from the equivariant sufficient statistic. It is noteworthy that in this case, the completeness assumption of Basu’s theorem has been replaced by equivariance assumption and the ancillarity assumption of Basu’s theorem has been replaced by invariance.

We first introduce the definitions that are needed. In the second part, by limiting the class of equivariant estimators, we create a type of optimal estimator called the best equivariant estimator and show that in groups that act as transitive on the parameter space, an invariant function is independent of the equivariant sufficient statistic. In the third part, by limiting the class of unbiased estimators, we make a type of optimal estimator called minimum risk unbiased estimator, which in a special case where the square error loss function is the same as the minimum variance unbiased estimator, which in the fourth part, in addition to Rao-Blackwell-Lehmann- Scheffé theorem (Casella and Berger, 2001), introduce two other methods proposed by Sathe and Varde (1969) and Eaton and Morris (1970) which, with the help of independence, provide a simpler method for finding a minimum variance unbiased estimator.

The following conclusions were drawn from this research.  In order to find the optimal estimators by limiting the class of estimators to the class of equivariant or unbiased estimators, the independence of complete sufficient statistics from ancillary statistics and applying Basu’s theorem can be a way to simplify calculations.  In some statistical problems with the transitive transformation group, the equivariant function can be used instead of the complete sufficient statistic. In this case, instead of using the Basu’s theorem, the independence of an invariant function and the equivariant sufficient statistic can be inferred. Hence, the assumption of completeness for establishing the Basu’s theorem is replaced by the equivariance and having a transitive transformation group.  Having a transitive group, any invariant function is also ancillary, but the incompleteness of a sufficient statistic can also result in its independence from an invariant statistic. If the group of transitive transformations and complete sufficient statistic is also equivariant, the case of Basu’s theorem concludes this view. The opposite is not always true and can be corrected in such a way that if a complete statistic is also equivariant with a transitive group, it is not necessary that each ancillary statistic be independent of it. Rather, it is possible to find an ancillary statistic that is also invariant, which is independent of the given equivariant complete sufficient statistic. By finding the condition that an ancillary statistic is also invariant, these results can be extended, in which case Basu’s theorem is the result. Of course, this open problem needs further research and it is hoped that researchers will be diligent in generalizing it.

The purpose of this paper is to provide a history of statistics and probability, as well as how these topics originated and developed. The biographies of five great statisticians who have played a key role in evolution of statistics and probability are examined and analyzed. Karl Pearson is the founder of modern statistics and one of the developers of mathematical theory of evolution. Ronald Fisher is a prominent mathematician and statistician. He is known as the father of statistical science. He introduced some important concepts such as Fisher information, the Z-distribution, F- distribution and ancillary statistics. Jerzy Neyman is also one of the grandees of modern statistics whom with the help of Karl Pearson’s son, Egon Pearson, defined some new concepts in the testing of statistical hypothesis such as simple hypothesis, compound hypothesis, type I and II errors, power of a test, critical region and significance level. Debabrata Basu is one of the leading statisticians who has played an important role in most branches of statistics. During his meeting with Fisher, he replaced the Bayesian approach with the Neyman-Pearson approach, the classical framework of statistics. His basic theorem on the relationship between sufficiency, ancillary statistics and independence is one of the most prominent mathematical concepts. Bradley Efron is known for his computer-aided statistical techniques, such as the bootstrap sampling and the Jackknife methods. This scientist has done research in various statistical fields such as astrophysics, clinical trials, differential geometry, empirical Bayes, inference for microarray gene expression data, probability theory, survival analysis, and sampling.

The present work is aimed to extend the common pollution indices into the fuzzy environment. For this purpose, a method was developed for converting the heavy metal contamination in soil by fuzzy numbers. Then, the most commonly used pollution indices are defined as fuzzy numbers by applying the alpha-cuts approach. To evaluate the degree of heavy metal contamination in a specific level, a degree of belonging was also suggested.

During the coronavirus outbreak and expansion of virtual courses in universities and schools, there have been many concerns about the quality of education and the challenges facing professors and students in virtual education. In this article, after reviewing the types of online education, learning resources and teachers’ role in virtual education, the advantages and disadvantages of this type of education with emphasis on statistics and mathematics are discussed. Also, some tips are proposed for improving IT infrastructure to optimize e-learning. Finally, suggestions for improving e-learning methods are provided.

Now day, using of stem cells and nanoparticles in the differentiation of stem cells is considered as a therapeutic approach. The purpose of this study was to synthesize and characterize nanocomposite polyacrylic polycarboxylic acid containing nanoparticles of biologically active glass 45S5 crushed and assessment effect of this composite on the propagation and growth of bone marrow derived mesenchymal stem cells in the external environment.
 

In this experimental study, the bioactive glass nanoparticles were synthesized by planetary milling and coated on electrospun polyolactic acid nanofibers. The physicochemical and biological properties of the composite nanocarbon were evaluated by X-ray diffraction, scanning electron microscopy, MTT, acridine orange, and alkaline phosphatase assays.
 

The physicochemical properties showed that the structure of synthesis bioactive glass and the lactic acid poly lactic acid fibers were completely nano size and the uniform distribution of nanoparticles was well placed on the fiber. The cell analysis demonstrated the significant increase proliferation and differentiation of mesenchymal stem cells to bone cells.In the MTT assay, cell survival was expressed in the composite nanostructure after 7 days of cell culture (1.96 ± 0.2), while the control sample (0.76 ± 0.08).
 

According to the results of this study, the composite nanoscale composite is not cytotoxicity effects and has biocompatible. It is useful in bone tissue repair.

‎In this paper after introduce Ito integral we discuss filtering problem‎. ‎In filtering problem there are two stochastic differential equations (system and observation) that given the observations we must find the best estimate for the random process of the system based on these observations‎. ‎At last we give some useful examples‎.

‎In this paper‎, ‎after introducing exponential family and a history of work done by researchers in the field of statistics‎, ‎some applications of this family in statistical inference especially in estimation problem‎,‎statistical hypothesis testing and statistical information theory concepts will be discussed‎.

  Glasses and glass-ceramics are a group of biological substances that form hydroxyapatite against a simulated solution of the body and can be used in many clinical cases that require the production and repair of bone. The purpose of this study was to create a 45S5 bioactive glass nanoparticle and evaluate its impact on staining and differentiation of mesenchymal stem cells into bone cells.

In this experimental research, the nanocomposite of the bioaccuminant 45S5 was synthesized by the fusion method and planetary mill was converted to the nanoscale structure; then, its physicochemical and structural properties were investigated. The bioactivity was evaluated using a simulated body solution. The growth, amplification and differentiation of mesenchymal stem cells in the vicinity of nanoparticles were investigated.

Biomedical evaluation indicated the formation of hydroxyapatite on nanoparticles after zinc immersion in the body was simulated. Cell experiments also confirmed the lack of toxicity of the glass nanoparticles and its stimulating effect for the growth, proliferation and differentiation of mesenchymal cells in bone cells. In the bone differentiation, the activity of alkaline phosphatase in the glass nanoparticle was expressed after 14 days of differentiation (0.55 ± 0.07), while it was the control sample (0.15 ± 0.03).

According to the progenies, mesenchymal stem cells can propagate and grow on the nanoparticles of the synthesized bioactive glass and, in addition to not being toxic, stimulate and stimulate cell growth.

In this paper we explain a necessary and sufficent condition for independence between any arbitrary statistics with sufficient statistics which is also maximum likelihood estimator in a general exponential family with location and scale parameter namely generalized normal distribution. At the end, it is shown that the converse is true except in the asymptotic cases.

Evaluation is a fundamental part of art criticism. Contrasting interpretations and conflicting evaluations with regard to a single work of art had led some thinkers to believe that there is no objective ground for evaluation. On the other hand, integration of evaluation and interpretation may aggravate the situation, in favor of relativism. We will argue that not only objective evaluations are not out of reach in art criticism, but that objectivity is surmised in the practice of criticism and evaluation. We hold that it is possible to find solutions for some problems and objections proposed by the proponents of relativism in evaluation. This can be done by focusing on contextualization, the intention of the author, and the relation of artistic form to the choices of the artist. Along with the elucidation of these ideas, we try to illustrate them by an example taken from the recent Iranian cinema.

Modest actual intentionalism’ is a view held by Noël Carroll, who maintains that the meaning of an artwork is determined by the successfully realized intentions of its author. After calling himself modest actual intentionalist, for a long time, Carroll recently has chosen to change position and, now, he holds a view which he calls ‘modest actual mentalism’. Why he preferred to change his account and how is the latter position different from the former? He did not offer a clear account of the constitution of meaning in his former period, but it seems that he accepts a framework which is based on M-intentions. I argue that this framework is not always suitable for the explanation of meaning. Works of art have implications that are not intended by their writers and I claim that some intentionalists, like Carroll, tend to cover such cases by regarding them as an aspect of the work’s significance, or, are inclined to link them with the unconscious intentions of the author. The former relate those implications solely to the responses of audiences which, I argue, is counterintuitive, on some occasions; and the latter is not justified by a framework, based on M-intentions. I argue that because of these fundamental problems in intentionalism, Carroll, chose to shift to mentalism, which is more powerful and resilient with regard to some counterexamples

Variations of different theories in analytic philosophy of art have caused long debates about literary interpretation. Intentionalism and anti-intentionalism are the two main avenues and theorists have developed different positions, which lean towards each of the two. Along with the arguments for or against the link between the authorial intentions and the literary text, a question could be asked of different parties of the debate, that is, how the meaning of a piece of literature is constituted. In other words, how the meaning of a poem or a novel takes its shape? In this regard, I think, concentrating on the philosophy of language and theories of meaning would be much helpful. It seems to me that for answering this question one needs to withdraw from a Gricean theory of meaning. I argue that neither intentionalists nor anti-intentionalist, do not answer this question deftly. I will try to investigate some answers given to this question by two moderate intentionalists, Robert Stecker and Paisley Livingston, in order to show in which respects their answers are problematic. At last, I argue that Relevance Theory, developed by Deirdre Wilson and Dan Sperber, could answer this question in a way that dissolves some of the hard cases in the philosophy of interpretation.

ýGiven the importance of Markov chains in information theoryý, ýthe definition of conditional probability for these random processes can also be defined in terms of mutual informationý. ýIn this paperý, ýthe relationship between the concept of sufficiency and Markov chains from the perspective of information theory and the relationship between probabilistic sufficiency and algorithmic sufficiency is determinedý.

Based on one given Bayesian model of multivariate normal with unknown mean vector parameter and known variance marix we will find an empirical Bayes confidence interval for the mean vector components which have normal distribution. we will find this empirical Bayes confidence interval as a conditional form on ancillary statistic ( ancillary statistic or noninformative statistic ) . In both cases (i . e . unconditional empirical Bayes confidence intervalthe empirical Bayes confidence interval in invariant and also conditional empirical Bayes confidence interval ) the empirical Bayes confidence interval is invariant with respect to the group with given confidence level.

In this paper, by using a Cramer - Rao inequality we obtained a lower bound minimax risk based on a random sample of random stopping time, in a condition of the truncated parameter space.
Finally, as applications, we obtained minimax estimators under censored data, Koziol - Green model and exponential distribution family.

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.