Saturday, April 23, 2016

History Stats: Jerzy Neyman

Jerzy Neyman

Jerzy Neyman was a world-class statistician, who has had a lasting influence on modern statistical thinking. Neyman was born in Russia to a noble family with a lawyer as a father. He attended university in Russia, and initially, he pursued training in physics. Fortunately, he was too clumsy in the lab to be a successful physicist, so he went into mathematics. After university, Neyman took on multiple jobs and struggled financially. During this period, he was given the opportunity to spend a year in the lab of Karl Pearson, another major contributor to the field of statistics. Unfortunately, Neyman disagreed with Karl on many aspects of modern mathematics, and Neyman almost terminated his internship in Pearson’s lab. Luckily, Neyman persevered and was able to secure a Rockefeller fellowship with the help of Karl that allowed him to spend time in Paris. During this time, he almost left statistics, but luckily, Egon Pearson, Karl Pearson’s son, reached out to Neyman in a letter where Egon questioned many of the fundamental assumptions of statistics at the time, which were largely influenced by Bayesian thinking. Neyman and Egon agreed on these issues, and they collaboratively began to develop a solution to these issues.
The main issue that Pearson and Neyman had with the current approaches of RA Fisher and “Student”, also known as Gosset, was the ad hoc nature of the assumptions being made and the conclusions that were then drawn based on limited sample size and lack of truly testing alternative hypotheses. Further, these approaches didn’t account for the concepts of error or statistical power. In response to this, Pearson developed the likelihood ratio criterion. In this approach, the maximum likelihood of achieving a specific result under the hypothesis and under the alternatives being considered is tested. Neyman and Pearson published this approach in 1928 in a fundamental two-part paper, “On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference”, and these landmark papers introduced the concepts of the types of error, statistical power, and also difference in the types of hypotheses. Although this publication satisfied Pearson, Neyman was not satisfied as he always wanted specific logic behind the statistical methods being used, and he felt that many of the assumptions made in this approach still were not founded in logic. With Pearson now taking the backseat, Neyman continued to develop more and more logical approaches building off of the likelihood ratio criterion, and he eventually established the concept that there is a single statistical test that is the most powerful for testing a specific hypothesis, a central concept in Neyman-Pearson hypothesis testing. After this work, Neyman did not stop and continued to be a pioneer in statistical thinking, he continued to work on other important statistical problems including sampling and probability, which led him to develop cohesive methods for comparing populations via confidence intervals. This work was directly inspired by his previous experiences working with census data, and ultimately, the development of these methods led him to clash with RA Fisher.
After making significant contributions to the field, it is not surprising that Neyman was eventually offered a position at Berkeley, a prestigious US institution, and eventually after some political struggles, he was able to establish his own department where he focused on applied statistical problems. In his career, he trained many students and was a great mentor as he typically paid his students out of his own pocket if he could not afford them through his budget. His approach and the establishment of the concepts of error, confidence intervals, sampling, and the Neyman-Pearson theory of hypothesis testing have forever shaped modern statistical approaches, particularly in the biological sciences. In fact without his landmark work, the concepts of power and null hypothesis significance testing would not have been developed, and we would likely still be relying on underpowered studies and not recognizing many possibilities such as false-positive and false negatives.

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