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.

Sampling Covariance Matricies with Fixed Total Variance

stats.at.home@gmail.com (Justin and Rachel Silverman) — Thu, 01 Jun 2017 00:00:00 +0000

Introduction

I have been thinking a lot about the concept of Total Variance recently. Total variance (which can be defined as the trace of a covariance matrix) is a measure of global dispersion that has been particularly useful for me when building multivariate models. However, for some reason, I have yet to see this concept discussed much outside of compositional data analysis (see pg. 35 of Lecture Notes on Compositional Data Analysis) or Principle Component Analysis.

Stan on Statistics @ Home

Bayesian Decision Theory Made Ridiculously Simple

Sampling Covariance Matricies with Fixed Total Variance

Introduction