Writing

The Fisher Information

The Fisher Information

DJ Rich

The Fisher Information quantifies the information an observation carries for a parameter. The quantification becomes intuitive once we see it measuring a certain geometric quality.

The Copula and 2008

The Copula and 2008

DJ Rich

The copula provides a clever means for mixing and matching a set of marginal distributions with the joint-only mechanism of a joint distribution. However, its elegance and utility have been a dangerous lure.

The Matrix Inversion Lemma

The Matrix Inversion Lemma

DJ Rich

The Matrix Inversion Lemma looks intimidating, but it is easy to know when it applies. Doing so offers considerable computational speed ups.

Bayesian Optimization

Bayesian Optimization

DJ Rich

When optimizing a slow-to-evaluate and non-differentiable function, one may think random sampling is the only option--a naive approach likely to disappoint. However, Bayesian optimization, a clever exploit of the function assumed smoothness, disconfirms these intuitions.

The Fundamental Law of Active Management

The Fundamental Law of Active Management

DJ Rich

The Fundamental Law of Active Management decomposes a well known summarizing metric of an investment strategy. The decomposition yields two dimensions along which all strategies may be judged and suggests avenues for improvement.

The Exponential Family

The Exponential Family

DJ Rich

The exponential family is a generalization of distributions, inclusive of many familiar ones plus a universe of others. The general form brings elegant properties, illuminating all distributions within. In this post, we discuss what it is, how it applies and some of its properties.

The Trace as a Measure of Complexity

The Trace as a Measure of Complexity

DJ Rich

For a class of models, the trace provides a measure of model complexity that's useful for managing the bias variance trade-off.

The Conjugate Gradient Method

The Conjugate Gradient Method

DJ Rich

Utilizing a geometric perspective, we find an efficient algorithm for solving a special kind of system of equations.