Ergodicity often hides behind a veil of mathematical complexity, yet at its core, it offers a profoundly simple and insightful lens through which to view and understand probability and time. At its heart, it challenges us to distinguish between two distinct types of averages: the ensemble average and the time average. To grasp this distinction, let […]
Statistics & Econometrics
In 1958, with the publication of the twenty-fifth volume of Econometrica, Trygve Haavelmo assessed the role of econometrics in advancing economics. While he praised its ‘repair work’ and ‘clearing-up work,’ he also found reason for despair: We have found certain general principles which would seem to make good sense. Essentially, these principles are based on […]
With the above cautions in mind, we may view each statistical analysis as a thought experiment in a fictional “small world” or “toy example” sharply restricted by its simplifying assumptions. The questions that motivated the study must be translated properly into this fictional world; statistical methods then answer the questions via mathematical deductions from the […]
As has been long and widely emphasized in various terms … frequentism and Bayesianism are incomplete both as learning theories and as philosophies of statistics, in the pragmatic sense that each alone are insufficient for all sound applications. Notably, causal justifications are the foundation for classical frequentism, which demands that all model constraints be deduced […]
Imagine you are a Bayesian turkey. You hold a nonzero prior belief in the hypothesis (H): People are nice vegetarians who would never eat a turkey. Every day I see the sun rise is further confirmation of this fact. Each day you survive and are not eaten constitutes new evidence (e). You dutifully update your […]
There are three fundamental differences between statistical and causal assumptions. First, statistical assumptions, even untested, are testable in principle, given sufficiently large sample and sufficiently fine measurements. Causal assumptions, in contrast, cannot be verified even in principle, unless one resorts to experimental control … Second, statistical assumptions can be expressed in the familiar language of […]
An ongoing concern is that excessive focus on formal modeling and statistics can lead to neglect of practical issues and to overconfidence in formal results … Analysis interpretation depends on contextual judgments about how reality is to be mapped onto the model, and how the formal analysis results are to be mapped back into reality. […]
According to Guy Routh, econometrics is nothing but “mock empiricism, with statistics subjected to econometric torture until they admit to effects of which they are innocent.” Similarly, Mark Blaug in his The Methodology of Economics argued that econometric testing is like “playing tennis with the net down.” Although these are rather harsh judgments, I believe […]
. Good overview — but one thing one ought to pay more attention to is the following: Even if both sampling and assignment are made in an ideal random way, performing standard randomised experiments only gives you averages. The problem here is that although we may get an estimate of the ‘true’ average causal effect, […]