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Sampling Distribution of the OLS Estimator

http://gregorygundersen.com/blog/2021/08/26/ols-estimator-sampling-distribution/

As introduced in my previous posts on ordinary least squares (OLS), the linear regression model...

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Visualizing Drawdown

http://gregorygundersen.com/blog/2021/08/27/drawdown/

In finance or economics, drawdown is a measure of the decline of a variable, say a stock’s...

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Residual Sum of Squares in Terms of Pearson’s Correlation

http://gregorygundersen.com/blog/2021/09/01/ols-rss-correlation/

In simple linear regression, or ordinary least squares (OLS) with a single explanatory variable,...

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Solving Geometric Series

http://gregorygundersen.com/blog/2021/09/02/geometric-series/

I can never remember the closed-form solution for the sum of an infinite geometric series,

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Hypothesis Testing for OLS

http://gregorygundersen.com/blog/2021/09/09/ols-hypothesis-testing/

Imagine we fit ordinary least squares (OLS),

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Coefficient of Determination

http://gregorygundersen.com/blog/2021/08/09/coefficient-of-determination/

Consider a linear model

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Multicollinearity

http://gregorygundersen.com/blog/2021/07/12/multicollinearity/

Linearly dependent predictors

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Portfolio Theory: Why Diversification Matters

http://gregorygundersen.com/blog/2021/05/04/portfolio-theory/

Most people with even a passing interest in financial markets have heard that diversification...

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Linear Independence, Basis, and the Gram–Schmidt algorithm

http://gregorygundersen.com/blog/2021/04/24/linear-independence/

Definitions

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The ELBO in Variational Inference

http://gregorygundersen.com/blog/2021/04/16/variational-inference/

Variational inference

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Proof that Mutual Information Is Symmetric

http://gregorygundersen.com/blog/2020/11/10/proof-symmetry-mutual-information/

The mutual information (MI) between two random variables captures how much information entropy...

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A Python Demonstration that Mutual Information Is Symmetric

http://gregorygundersen.com/blog/2020/11/11/demo-symmetry-mutual-information/

In a previous post, I showed mathematically that mutual information (MI) is a symmetric...

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Conjugate Analysis for the Multivariate Gaussian

http://gregorygundersen.com/blog/2020/11/18/bayesian-mvn/

The goal of this post is to derive the likelihood, posterior, and posterior predictive for a...

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The Unscented Transform

http://gregorygundersen.com/blog/2020/11/19/unscented-transform/

The unscented transform (UT) was originally prosed by Jeffrey Uhlmann as part of his PhD thesis...

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Inference for Hidden Markov Models

http://gregorygundersen.com/blog/2020/11/28/hmms/

The simplest probabilistic model of sequential data is that the data are i.i.d. We assume the...

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Why Shouldn’t I Invert That Matrix?

http://gregorygundersen.com/blog/2020/12/09/matrix-inversion/

In a recent research meeting, I was told, “Never invert a matrix.” The person went on to explain...

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Fast Computation of the Multivariate Normal PDF for Multiple Parameters

http://gregorygundersen.com/blog/2020/12/12/group-multivariate-normal-pdf/

In a previous post, I discussed a fast and numerically stable implementation of the multivariate...

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Understanding Dirichlet–Multinomial Models

http://gregorygundersen.com/blog/2020/12/24/dirichlet-multinomial/

Multivariate beta distribution

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A Python Implementation of the Multivariate Skew Normal

http://gregorygundersen.com/blog/2020/12/29/multivariate-skew-normal/

Probability density function

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Simple Linear Regression and Correlation

http://gregorygundersen.com/blog/2021/08/25/ols-correlation/

<!– What’s the relationship between OLS and correlation?

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