A behind-the-scenes blog about research methods at Pew Research Center. For our latest findings, visit pewresearch.org. Identifying causal relationships from observational data is not easy. Still, ...

Capturing dependence among a large number of high-dimensional random vectors is a very important and challenging problem. By arranging n random vectors of length p in the form of a matrix, we develop ...

We present deviation inequalities of random operators of the form $N^{-1}\sum_{i=1}^{N}X_{i}\otimes X_{i}$ from the average operator ${\Bbb E}(X\otimes X)$, where $X ...

People are generally bad at producing random actions, but now it seems that we are all uniquely bad in our own way. This makes it possible to predict how an individual will act randomly, which could ...