# Sampling on the sphere from $f(x) \propto x^TAx$

## TL;DR

This paper introduces a sampling method for generating random unit vectors on a sphere according to a density proportional to quadratic forms, with an accompanying R implementation.

## Contribution

It presents a novel sampling technique for vectors on the sphere based on quadratic form densities, including a practical R implementation.

## Key findings

- Effective sampling from the specified distribution on the sphere.
- Implementation in R facilitates practical application.
- Potential use in statistical and machine learning models.

## Abstract

A method for drawing random samples of unit vectors $x$ in $R^p$ with density proportional to $x^TAx$ where $A$ is a symmetric, positive definite matrix. Includes an R function which implements the method.