Question

Week 9 Discussion

Choose a historical statistician, or someone who made effective use of statistics. Write 1-2 paragraphs about what they did and why their contributions are notable. Include sources.

Answer 1

Thomas Bayes, a minister and mathematician whose name is literally attached to statistical inference.
Very few details are known about Bayes, but his impact on statistics is remarkable considering that he published only two papers in his lifetime.
His primary contribution was Bayes Rule, a law of conditional probability.
Thomas Bayes able to have so much influence on the field of statistics with only a single paper (on calculus).  An inverse probability problem. For the binomial distribution with probability of success p, Bayes set out to find the distribution of p given an observed number of successes. He found that if he assumed that p was uniformly distributed, then the distribution of p given the observed number of successes has a beta distribution.

The binomial problem detailed was a special case of what has now become known as Bayes Theorem. Bayes Theorem (also known as Bayes Law or Bayes Rule) can be stated

where Pr(A) is the probability of event A happening and Pr(A | B) is the probability of event A happening given that event B has happened. Bayes Theorem is thought of as inverting or turning around conditional probabilities.

Bayes Rule serves as the foundation and motivation for the extremely popular field of Bayesian data analysis. The key idea behind Bayesian analysis is that we can use prior information in conjunction with our observed data to make better decisions. Bayesian ideas have been used to approach problems in virtually every corner of statistics. In fact, there is a long list of techniques that contain the words Bayes or Bayesian
According to this Bayesian view, all quantities are one of two kinds: known and unknown to the person making he inference. Known quantities are obviously defined by their known values. Unknown quantities are described by a joint probability distribution. Bayesian inference is seen not as a branch of statistics, but instead as a new way of looking at the complete view of statistics.