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Bayesian Decision Theory Made Ridiculously Simple

stats.at.home@gmail.com (Justin and Rachel Silverman) — Thu, 12 Oct 2017 00:00:00 +0000

Bayesian Decision Theory is a wonderfully useful tool that provides a formalism for decision making under uncertainty. It is used in a diverse range of applications including but definitely not limited to finance for guiding investment strategies or in engineering for designing control systems. In what follows I hope to distill a few of the key ideas in Bayesian decision theory. In particular I will give examples that rely on simulation rather than analytical closed form solutions to global optimization problems. My hope is that such a simulation based approach will provide a gentler introduction while allowing readers to solve more difficult problems right from the start.

Follow-up on Error Analysis

stats.at.home@gmail.com (Justin and Rachel Silverman) — Wed, 02 Aug 2017 00:00:00 +0000

I wanted to write a quick post responding to a question that we received about our last post (Error Analysis Made Ridiculously Simple).

Can you give an example of how to generate an estimate of the error? It’s easy enough when measuring a table, as long as your meter stick is accurate: measure 1,000 times and make an inference. But in a setting where you don’t actually know the true outcome – let’s say you are trying to model household income – I’m not sure how to generate a reasonable guess of the size of the error. I suppose sometimes surveys provide error bands, but I don’t really trust them. The implication would be that they have some estimate of “true” income, which seems implausible. Even the administrative data they might be matching the surveys to is measured with error (e.g. people lie on tax returns, etc.).

Error Analysis Made Ridiculously Simple

stats.at.home@gmail.com (Justin and Rachel Silverman) — Fri, 21 Jul 2017 00:00:00 +0000

Introduction

All measurements have uncertainty. This is not a subjective opinion but an objective fact that should never be ignored. In light of this, I have always been curious about how infrequently uncertainty is actually taken into account in science.

Measure Theory Made Ridiculously Simple

stats.at.home@gmail.com (Justin and Rachel Silverman) — Mon, 26 Jun 2017 00:00:00 +0000

During my first few years of medical school I became a big fan of the [Subject] Made Rediculously Simple book series (as in Clinical Microbiology Made Rediculously Simple). I found that the authors did a great job of simplifying the subject matter, sometimes to the point of absurdity, while getting the core concepts across in a memorable way. For some time now I have wished that similar tools were available for mathematics. While I may not have the same artistry or comical flare that those authors have, here I attempt to take the Made Rediculously Simple flare to explain some of the core concepts of measure theory. This post is designed for those who have a background in basic calculus and recognize that measure theory plays some important (although perhaps cryptic) role in modern probability and statistics.