The True Title of Bayes's Essay

As someone whose Ph.D. dissertation was in the area of Bayesian Econometrics, I was fascinated to read this recent paper by Stephen Stigler: "The True Title of Bayes's Essay". It appeared this month in Statistical Science, 2013, vol. 28(3), 283-288.

The abstract of the paper is succinct, but very clear:

"New evidence is presented that Richard Price gave Thomas Bayes's famous essay a very different title from the commonly reported one. It is argued that this implies Price almost surely and Bayes not improbably embarked upon this work seeking a defensive tool to combat David Hume on an issue in theology."

So, it wasn't just intended to provide a painful experience for those being introduced to probability theory for the first time, after all!

October Means Nobel Prizes

Yes, it's almost that time of year again!  The recipient(s) of the 2013 Nobel Prize in Economic Sciences (abbreviated title) will be announced in less than two weeks' time - Monday 14 October, to be precise.

Thomson Reuters have made their predictions for the likely recipients in each field, including Economics.

I particularly like one of their three potential "winning teams":

"Sir David F. Hendry

Professor of Economics

University of Oxford

Oxford, England, UK

-and-

M. Hashem Pesaran

John Elliot Distinguished Chair in Economics & Professor of Economics, and Emeritus Professor of Economics & Fellow of Trinity College, Cambridge

University of Southern California, Los Angeles, CA, USA 

and University of Cambridge, Cambridge, England, UK

-and-

Peter C.B. Phillips

Sterling Professor of Economics and Professor of Statistics

Yale University

New Haven, CT, USA

For their contributions to economic time-series, including modeling, testing and forecasting."

© 2013, David E. Giles

In What Sense is the "Adjusted" R-Squared Unbiased?

In a post yesterday, I showed that the usual coefficient of determination (R²) is an upward -biased estimator of the "population R²", in the following sense. If there is really no linear relationship between y and the (non-constant) regressors in a linear multiple regression model, then E[R²] > 0. However, both E[R²] and Var.[R²] → 0 as n → ∞. So, R² is a consistent estimator of the (zero-valued) population R².

At the end of that post I posed the following questions:

"You might ask yourself, what emerges if we go through a similar analysis using the "adjusted" coefficient of determination? Is the "adjusted R²" more or less biased than R² itself, when there is actually no linear relationship between y and the columns of X?"

Here's the answer.......