Having discussed differentiation of complex mappings in the preceding notes, we now turn to the integration of complex maps. We first briefly review the situation of integration of (suitably regular) real functions of one variable. Actually there are three closely related concepts of integration that arise in this setting: (i) The signed definite integral, […]

Shravan points me to this article, Twitter Language Use Reflects Psychological Differences between Democrats and Republicans, which begins with the following self-parody of an abstract: Previous research has shown that political leanings correlate with various psychological factors. Show More Summary

Hiking my way to a new appreciation of a classic mathematical paradox -- Read more on ScientificAmerican.com

Sorelle Friedler, Carlos Scheidegger and I just posted a new paper on the arxiv where we try to lay out a framework for talking about fairness in a more precise way. The blog post I link to says more about the paper itself. But I wanted to comment here on the tortuous process that led to this paper. Show More Summary

Wonderful, indeed, to have an RStan book in Japanese: Kentarou Matsuura. 2016. Bayesian Statistical Modeling Using Stan and R. Wonderful R Series, Volume 2. Kyoritsu Shuppan Co., Ltd. Google translate makes the following of the description...Show More Summary

Poll aggregation is great, but one thing that we’ve been saying a lot recently (see also here) is that we can also learn a lot by breaking open a survey and looking at the numbers crawling around inside. Here’s a new example. It comes...Show More Summary

What's the best way to see Euclidean, hyperbolic and elliptic geometry as part of a 1-parameter family.

Anoop Balachandran writes: This is one of the abstracts of the paper i am about to publish: My question is can I really say both training program were effective for increasing power and function? Studies of similar duration employing sedentary control showed either negative or 1-2% changes. Show More Summary

After the New Hampshire primary Nadia Hassan wrote: Some have noted how minor differences in how the candidates come out in these primaries can make a huge difference in the media coverage. For example, only a few thousand voters separate third and fifth and it really impacts how pundits talk about a candidate’s performance. Show More Summary

A year ago it all seemed pretty straightforward. Georges Maltsiniotis gave a talk at the Grothendieck conference on a small part of the 65.000 pages discovered after Grothendieck’s death in Lasserre. He said that Grothendieck’s family has handed over all non-family related material to the Bibliotheque Nationale de France. Show More Summary

When people screw up or cheat in their research, what do their collaborators say? The simplest case is when coauthors admit their error, as Cexun Jeffrey Cai and I did when it turned out that we’d miscoded a key variable in an analysis, invalidating the empirical claims of our award-winning paper. Show More Summary

Nate Cohn at the New York Times arranged a comparative study on a recent Florida pre-election poll. He sent the raw data to four groups (Charles Franklin; Patrick Ruffini; Margie Omero, Robert Green, Adam Rosenblatt; and Sam Corbett-Davies,...Show More Summary

The title of this post is a line that Thomas Basbøll wrote a couple years ago. Before I go on, let me say that the fact that I have not investigated this case in detail is not meant to imply that it’s not important or that it’s not worth investigating. Show More Summary

At the core of almost any undergraduate real analysis course are the concepts of differentiation and integration, with these two basic operations being tied together by the fundamental theorem of calculus (and its higher dimensional generalisations, such as Stokes’ theorem). Similarly, the notion of the complex derivative and the complex line integral (that is to […]

Alexia Gaudeul writes: Maybe you will find this interesting / amusing / frightening, but the Journal of Risk and Uncertainty recently published a paper with a rather obvious multicollinearity problem. The issue does not come up that often in the published literature, so I thought you might find it interesting for your blog. Show More Summary

The replication crisis is a big deal. But it’s a problem in lots of scientific fields. Why is so much of the discussion about psychology research? Why not economics, which is more controversial and gets more space in the news media?Show More Summary

In the title picture the roots of polynomials of degree $\leq 4$ with small coefficients are plotted and coloured by degree: blue=4, cyan=3, red=2, green=1. Sums and products of roots are again roots and by a symmetry we mean a map on all roots, sending sums to sums and products to products and leaving all... Continue reading ?

Solving Statistics Problems Using Stan Stan is a free and open-source probabilistic programming language and Bayesian inference engine. In this talk, we demonstrate the use of Stan for some small fun problems and then discuss some open problems in Stan and in Bayesian computation and Bayesian inference more generally. Show More Summary

Someone sent me this article by psychology professor Susan Fiske, scheduled to appear in the APS Observer, a magazine of the Association for Psychological Science. The article made me a little bit sad, and I was inclined to just keep...Show More Summary

The acupuncture paradox, as we discussed earlier, is: The scientific consensus appears to be that, to the extent that acupuncture makes people feel better, it is through relaxing the patient, also the acupuncturist might help in other ways, encouraging the patient to focus on his or her lifestyle. Show More Summary

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