Archive for Kolmogorov

Frequency vs. probability

Posted in Statistics with tags , , , , , , , on May 6, 2011 by xi'an

Probabilities obtained by maximum entropy cannot be relevant to physical predictions because they have nothing to do with frequencies.” E.T. Jaynes, PT, p.366

A frequency is a factual property of the real world that we measure or estimate. The phrase `estimating a probability’ is just as much an incongruity as `assigning a frequency’. The fundamental, inescapable distinction between probability and frequency lies in this relativity principle: probabilities change when we change our state of knowledge, frequencies do not.” E.T. Jaynes, PT, p.292

A few days ago, I got the following email exchange with Jelle Wybe de Jong from The Netherlands:

Q. I have a question regarding your slides of your presentation of Jaynes’ Probability Theory. You used the [above second] quote: Do you agree with this statement? It seems to me that a lot of  ‘Bayesians’ still refer to ‘estimating’ probabilities. Does it make sense for example for a bank to estimate a probability of default for their loan portfolio? Or does it only make sense to estimate a default frequency and summarize the uncertainty (state of knowledge) through the posterior? Continue reading

Another review of Search for Certainty

Posted in Books, Statistics with tags , , , , , on February 25, 2010 by xi'an

The best thing about this book is that it will offend and annoy both frequentists and subjectivists. I implore my friends on both sides of the philosophical divide to read the book with an open mind.

Our comments, Andrew‘s and mine‘s, led Larry Wasserman to read Krzysztof Burdzy’s The Search for Certainty to make his own opinion and Andrew just posted Larry’s review. The review is highly positive, arguing that “this is an interesting and important book” and that “Burdzy makes a convincing case that the philosophy of probability is a complete failure“. While remaining utterly unconvinced (that the book has any bearing on the philosophical foundations of Statistics),  I will not engage here into another debate about The Search for Certainty as the readers can check for themselves the strength of Larry’s arguments. Needless to say, I cannot be convinced into redefining probability as an experimental science where Burdzy’s five laws would replace Kolmogorov’s three axioms…

%d bloggers like this: