Breakthroughs in Statistics: Foundations and Basic Theory by Seymour Geisser (auth.), Samuel Kotz, Norman L. Johnson

By Seymour Geisser (auth.), Samuel Kotz, Norman L. Johnson (eds.)

This can be a quantity selection of seminal papers within the statistical sciences written prior to now a hundred years. those papers have each one had an excellent effect at the improvement of statistical conception and perform over the past century. each one paper is preceded through an creation written via an expert within the box delivering historical past details and assessing its impact. Readers will get pleasure from a clean outlook on now well-established gains of statistical thoughts and philosophy by way of turning into conversant in the methods they've been constructed. it really is was hoping that a few readers can be influenced to check a number of the references supplied within the Introductions (and additionally within the papers themselves) and so reach a deeper heritage wisdom of the root in their paintings.

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2. The Purpose of Statistical Methods In order to arrive at a distinct formulation of statistical problems, it is necessary to define the task which the statistician sets himself: briefly, and in its most concrete form, the object of statistical methods is the reduction of data. A quantity of data, which usually by its mere bulk is incapable of entering the mind, is to be replaced by relatively few quantities which shall adequately represent the whole, or which, in other words, shall contain as much as possible, ideally the whole, of the relevant information contained in the original data.

A reasonable model for such a situation is that the chance of z protozoa on a plate is Poisson-distributed with expected value e/aX, where e is the density or number of protozoa per unit volume of the original solution, and x the dilution level. A large number of such series were made daily for a variety of organisms. It proved either physically impossible or economically prohibitive to count the number of such organisms on every plate for many such series in order to estimate e. First, Fisher suggests that only those plates containing no organisms be counted; the chance of such an occurrence at level x is Px = exp( - O/a By this device, an experimentally feasible situation is attained that produces a joint likelihood for Yx , the number of sterile plates at level x, as X ).

A statistic satisfies the criterion of sufficiency when no other statistic which can be calculated from the same sample provides any additional information as to the value of the parameter to be estimated. ) Validity. The region of validity ofa statistic is the region comprised within its contour of zero efficiency. ) 1. The Neglect of Theoretical Statistics Several reasons have contributed to the prolonged neglect into which the study of statistics, in its theoretical aspects, has fallen. In spite of the immense amount of fruitful labour which has been expended in its practical applications, the basic principles of this organ of science are still in a state of obscurity, and it cannot be denied that, during the recent rapid development of practical methods, fundamental problems have been ignored and fundamental paradoxes left unresolved.

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