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1981 | Buch

Statistical Computing Kapitel lesen Erstes Kapitel lesen

Computing in Statistical Science through APL

verfasst von: Francis John Anscombe

Verlag: Springer New York

Buchreihe : Springer Series in Statistics

Enthalten in: Professional Book Archive

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Über dieses Buch

A t the terminal seated, the answering tone: pond and temple bell. ODAY as in the past, statistical method is profoundly affected by T resources for numerical calculation and visual display. The main line of development of statistical methodology during the first half of this century was conditioned by, and attuned to, the mechanical desk calculator. Now statisticians may use electronic computers of various kinds in various modes, and the character of statistical science has changed accordingly. Some, but not all, modes of modern computation have a flexibility and immediacy reminiscent of the desk calculator. They preserve the virtues of the desk calculator, while immensely exceeding its scope. Prominent among these is the computer language and conversational computing system known by the initials APL. This book is addressed to statisticians. Its first aim is to interest them in using APL in their work-for statistical analysis of data, for numerical support of theoretical studies, for simulation of random processes. In Part A the language is described and illustrated with short examples of statistical calculations. Part B, presenting some more extended examples of statistical analysis of data, has also the further aim of suggesting the interplay of computing and theory that must surely henceforth be typical of the develop­ ment of statistical science.

Inhaltsverzeichnis

Frontmatter

Statistical Computing

Chapter 1. Statistical Computing
Abstract
Ever since high-speed stored-program digital computers became available round about 1950 they have been applied to statistical work. Their influence has grown gradually. The computer did not immediately have the vital part in statistics that it had in, say, space exploration. Yet we now see that the computer is exercising a profound effect on the science of statistics, transforming not only methods of operation but also basic ideas and understanding and objectives. And the transforming is still far from complete.
Francis John Anscombe

Description of APL

Frontmatter
Chapter 2. Origins
Abstract
Computers perform logical tasks—numerical calculation and symbol arranging. A procedure for carrying out such a task is sometimes called an algorithm. (The dictionaries say the word ought to be “algorism” and it means the Arabic decimal system of arithmetic, named after an Arabic mathematician of the ninth century A.D.; but with spelling and meaning just stated the word is widely used in computing circles.) A precise specification of an algorithm, especially one so coded that it may be followed by a computer, is also called a program. A program consists of a sequence of statements or commands; some statements specify one or more entities in terms of operations on other entities; other statements, known as branches, specify which statement shall next be executed. A set of statements that are executed repeatedly, because a branch at the end returns execution to the beginning of the set, is called a loop.
Francis John Anscombe
Chapter 3. Primitive Scalar Functions
Abstract
One communicates with an APL system through a computer terminal. There is a keyboard much like that of an ordinary typewriter, through which the user gives instructions, and there is a display device permitting the user to see both what he has typed and what response the computer makes. Some terminals are indeed typewriters, and the input and the output appear typed on a roll of paper, which can be kept afterwards as a record of the proceedings. The printing is done by a typeball or other printing device, on a carrier that moves across the page to type a line. Other terminals show input and output on a cathode-ray tube (television screen). These have some advantages over printing terminals: output comes fast, and they are relatively inexpensive; but there is no record to take away; an auxiliary device must be used to obtain a permanent copy. All the illustrations for this book have been produced on a (quite slow) printing terminal with typeball, which yields the most legible record; and that is the kind of terminal that will be referred to.
Francis John Anscombe
Chapter 4. Arrays
Abstract
This chapter is concerned with description and formation of arrays. Three new symbols representing primitive nonscalar (“mixed”) functions are introduced. The following chapter will deal with extension to arrays of the primitive scalar functions that we have already met, and will introduce some further primitive mixed functions.
Francis John Anscombe
Chapter 5. Primitive Functions on Arrays
Abstract
The primitive monadic scalar functions that we met in Chapter 3 are extended to non-scalar arrays element by element. If f stands for such a function and X is any array, fX means the array formed by applying f to each element of X; fX has the same size as X.
Francis John Anscombe
Chapter 6. Defined Functions
Abstract
We have seen the use of an APL terminal in the style of a desk calculator. Commands have been executed as soon as entered. If commands are to be executed only once, that is usually the best mode of operation. But if the same, or similar, commands are to be executed repeatedly, or if they are not very simple and brief, it may be preferable to have them in the form of a stored program. For example, the numerical integration in line 21 of Figure A:6 is not a very simple command and it incorporates a choice of values for the two parameters called n and h in the text. If we knew, perhaps from an error analysis, that the chosen values were satisfactory, the calculation need only be done once. But in the absence of a good error bound we should investigate the precision of the result empirically by repeating the calculation with different values for n and h. Then it will be easier to have the procedure entered as a stored program, with explicit parameters, instead of typing it out afresh each time. Similarly, the two graphical displays in Figure A:7 result from not-very-simple commands, the kind the user can just as soon get wrong as get right the first time he tries them. They might be better expressed in a more general form as stored programs that can be tested, corrected if wrong, and then used with some assurance.
Francis John Anscombe
Chapter 7. Illustrations
Abstract
Expression of statistical calculations in APL will now be illustrated by some short examples. The first two are carried out in simple dialog style, without defined functions. The other examples use defined functions and a slightly richer vocabulary.
Francis John Anscombe
Chapter 8. Comments
Abstract
The foregoing account of APL is far from complete. Many things have not been said. The following have not been explained:
(i)
how to sign on and off,
 
(ii)
how to move material in and out of storage,
 
(iii)
how to correct an error in typing,
 
(iv)
how to add to, emend or “edit” a function definition,
 
(v)
how to obtain items of information such as: (a) the amount of unused space remaining in the active workspace, (b) the number of users of the system currently signed on, (c) the amount of central-processor time used since sign-on, (d) the names of stored workspaces.
 
Francis John Anscombe
Backmatter

Experiments in Statistical Analysis

Frontmatter
Chapter 9. Changing Attitudes
Abstract
Statistical analysis of data is the oldest part of statistical science as we have it today—going back more than three hundred years to John Graunt’s study of the London bills of mortality. The purpose of statistical analysis may be stated vaguely as obtaining a right understanding of the data. Some kinds of data do not pose any special problem of understanding, and then nothing called statistical analysis is done. Other kinds of data seem to defy complete detailed explanation and understanding. They invite being thought of in terms of variability, randomness or noise, masking the relations or properties that we should like to examine.
Francis John Anscombe
Chapter 10. Time Series: Yale Enrolment
Abstract
As an example of examination of a time series, let us consider the enrolment of students at Yale University. Information concerning the numbers of students enrolled in the various schools and programs can be obtained for each academic year from 1796/97 onwards. The University was founded in 1701. For most years before 1796 the enrolment is not known directly, though Welch and Camp (1899) made estimates from the numbers of degrees awarded. For present purposes we shall start at 1796, and use the counts of total enrolment listed in Figure B:2, a time series of length 180.
Francis John Anscombe
Chapter 11. Regression: Public School Expenditures
Abstract
A typical example of material to which simple regression methods can be applied is information in the Statistical Abstract of the United States 1970 concerning public school expenditures and other quantities possibly related thereto. Table 181 (p. 122) lists estimated per-capita expenditures during 1970, in dollars, on public school education in each of the fifty states together with the District of Columbia (which for present purposes will be referred to as a state). The schools are elementary and secondary schools, and some other programs under the jurisdiction of local boards of education are also included; state universities are not included. The total estimated expenditures have been divided by the estimated resident population size of each state to give per-capita expenditures (not expenditures per student).
Francis John Anscombe
Chapter 12. Contingency Tables and Pearson-Plackett Distributions
Abstract
The preceding two chapters have addressed various forms of regression analysis, topics that are among those most commonly encountered in statistical analysis of data. We turn now to the more primitive subject of categorical (qualitative, attribute) variables and their association in contingency tables.
Francis John Anscombe
Backmatter
Metadaten
Titel
Computing in Statistical Science through APL
verfasst von
Francis John Anscombe
Copyright-Jahr
1981
Verlag
Springer New York
Electronic ISBN
978-1-4613-9450-1
Print ISBN
978-1-4613-9452-5
DOI
https://doi.org/10.1007/978-1-4613-9450-1