Bayesians Versus Frequentists by Jordi Vallverdú

Author:Jordi Vallverdú
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

The strong relationship between his philosophical ideas on the nature of scientific methodology and the role of statistics is completely connected in Neyman’s mind. Even working with Karl Pearson , he was not satisfied with his laboratory, which he considered old-fashioned, neither by his lack of modern mathematical knowledge (which led to a misunderstanding between them, because Pearson was not able to understand the differences between the ideas of independence and lack of correlation, and this led to Neyman’s decision to move to a new research place10). Regardless, this confrontation was not a problem for the posterior cooperative debates with Egon Pearson, Karl Pearson’s son, who occupied (half of)11 the vacant chair left by his father at the university. Egon and Neyman worked together trying to solve a big problem that had emerged from Fisher and Student studies: The small sample tests showed an ad hoc nature, and this resulted in offense for any frequentist expert. After some ideas exchanges with Student, Egon and Neyman created what has been called the “Neyman–Pearson theory of hypothesis testing.” In 1928, they published “On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference: Part I.” Let them convey their ideas:One of the most common as well as most important problems which arise in the interpretation of statistical results, is that of deciding whether or not a particular sample may be judged as likely to have been randomly drawn from a certain population, whose form may be either completely or only partially specified (…) The sum total of the reasons which will weigh with the investigator in accepting or rejecting the hypothesis can very rarely be expressed in numerical terms. All that is possible for him is to balance the results of a mathematical summary, formed upon certain assumptions, against other less precise impressions based upon a priori or a’ posteriori considerations. The tests them- selves give no final verdict, but as tools help the worker who is using them to form his final decision; one man may prefer to use one method, a second another, and yet in the long run there may be little to choose between the value of their conclusions. What is of chief importance in order that a sound judgment may be formed is that the method adopted, its scope and its limitations, should be clearly understood, and it is because we believe this often not to be the case that it has seemed worth while to us to discuss the principles involved in some detail and to illustrate their application to certain important sampling tests (…) [and at the conclusions section, italics are mine] The system adopted will provide a numerical measure, and this must be coordinated in the mind of the statistician with a clear understanding of the process of reasoning on which the test is based. We have endeavored to connect in a logical sequence several of the most simple tests, and in so doing have found it essential to make use of what R.

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