In my time working in health science, I have been troubled by the number of times I have encountered statisticians and practitioners of statistics who are absolutely sure that either the variables or residuals in a linear regression must be approximately normally distributed, and the model is invalid otherwise.
This idea is completely false. In this post I want to explore why it is nonetheless so widely believed by professionals in the field.
Eric is a podcaster who has most notably made appearances on the Joe Rogan experience (JRE). He received a PhD in mathematical physics from Harvard in 1992, and between 2013 and 2022 he was a managing director of Thiel Capital - Peter Thiel’s investment firm.
Expected utility theory was first influentially expounded by Swiss mathematician Daniel Bernoulli in the 1700s. It seeks to answer the question of how to weigh up alternatives that are uncertain. For example, say I gave you the option of \( £100 \), or a bet consisting of a \( 50-50 \) chance of receiving \( £250 \), how should you choose? While it may seem easy to answer a single question like this, it turns out that building a general framework for how to make such decisions is not so easy, and if you proceed naively you can easily come a cropper.
It’s one of the first major topics you learn about when taking statistics class. In essence, it allows you to model the mean of a response variable \( y_i \) as depending on some explanatory variables \( x_i \), where the subscript \( i = 1…n \) labels different observations. More concretely,
\[y = X \beta + \epsilon, \tag{1}\]In a previous post, I discussed population ethics and perhaps its foremost unsolved problem, the repugnant conclusion. To recap, the basic idea is that if you believe a small loss in quality of life for a population can be compensated by adding some number of people with lives worth living, then applying the same reasoning repeatedly leads to the conclusion that there is some enormous number of people all leading lives barely worth living that would be preferable to e.g. one billion people all living superlative lives. That seems rather unpalatable to most people.