Recently I came across the classical 1983 paper A note on screening regression equations by David Freedman. Freedman shows in an impressive way the dangers of data reuse in statistical analyses. The potentially dangerous scenarios include those where the results of one statistical procedure performed on the data are fed into another procedure performed on the same data. As a concrete example Freedman considers the practice of performing variable selection first, and then fitting another model using only the identified variables on the same data that was used to identify them in the first place. Because of the unexpectedly high severity of the problem this phenomenon became known as “Freedman’s paradox”. Moreover, in his paper Freedman derives asymptotic estimates for the resulting errors.

# 5 ways to measure running time of R code

A reviewer asked me to report detailed running times for all (so many ) performed computations in one of my papers, and so I spent a Saturday morning figuring out my favorite way to benchmark R code. This is a quick summary of the options I found to be available.

# The Lean PhD Student — Can The Lean Startup principles be applied to personal productivity in graduate school?

The lean startup methodology consists of a set of principles that were proposed and popularized by Eric Ries in the book The Lean Startup (and elsewhere). He believes that startup success can be engineered by following the lean startup methodology. Eric Ries defines a startup as “a human institution designed to deliver a new product or service under conditions of extreme uncertainty”. If we replace “product or service” by “research result”, that sounds awfully similar to what a PhD student has to do. Indeed, the similarities between being a junior researcher, such as a PhD student, and running a startup have been often pointed out (for example: [1], [2], [3]). In light of this, I propose that the lean startup methodology can also be applied to academic pursuits of a PhD student. Below, I adapt some of the most important lean startup concepts for application to a junior researcher’s personal productivity and academic success.1

1. Please note that I’m writing from the point of view of mathematical, statistical, and computational sciences, rather than from the viewpoint of experimental sciences.

# Understanding the Tucker decomposition, and compressing tensor-valued data (with R code)

In many applications, data naturally form an n-way tensor with n > 2, rather than a “tidy” table. As mentioned in the beginning of my last blog post, a tensor is essentially a multi-dimensional array:

• a tensor of order one is a vector, which simply is a column of numbers,
• a tensor of order two is a matrix, which is basically numbers arranged in a rectangle,
• a tensor of order three looks like numbers arranged in rectangular box (or a cube, if all modes have the same dimension),
• an nth order (or n-way) tensor looks like numbers arranged in an n-hyperrectangle… you get the idea…

# Understanding the CANDECOMP/PARAFAC Tensor Decomposition, aka CP; with R code

A tensor is essentially a multi-dimensional array:

# A comprehensive Linux command cheat sheet

I think that it doesn’t matter what operating system you use — as long as you know your OS of choice well! This is a Linux command cheat sheet covering a wide range of topics. I cannot guarantee that the information is fully up-to-date or even correct. Use at own risk . It is intended primarily as a reference for myself in the future. I have learned most of the material covered below a couple of years ago in the LinuxFoundationX’s Introduction to Linux course offered through edx.org.

# Contours of statistical penalty functions as GIF images

Many statistical modeling problems reduce to a minimization problem of the general form:

# Tired of doing real math 2 — grad school and coffee consumption

Lately I notice a sharp increase in my coffee consumption (reading Howard Schultz’s Starbucks book, which is actually quite good by the way, does not help either ). Having recently transitioned into a new PhD program I started wondering whether my increased coffee consumption has something to do with my higher stress levels in the last few weeks, and how that conjecture generalizes to the rest of my grad school experience. To answer that question I decided to take a look at how much money I have spent at coffee houses over the last few years. …Also, I’m right now over-caffeinated at 1:40am and I have nothing better to do anyway.

# Visualization of MRI data in R

Lately I was getting a little bored with genomic data (and then TCGA2STAT started to give me a segfault on my university’s high performance computing facility too ). So I decided to analyze some brain imaging data that I had lying around instead. The first step is to do some visual data exploration. In this blog post I present some functions which I was able to find for MRI visualization in R, and which I found to be very useful. All functions presented below presuppose an image in the NIfTI data format as input, and are very user-friendly.