I describe a probabilistic alternative to fractional factorial design based on the Sobol’ low discrepancy quasirandom sequence. This method is robust to aliasing (confounders), is often simpler to implement than traditional fractional factorial sample designs, and produces more accurate results than simple random sampling.

# A probabilistic approach

# Going beyond the Golden Ratio.

I show that for the same reason that the golden ratio, $\phi=1.6180334..$, can be considered the most irrational number, that $1+\sqrt{2}$ can be considered the 2nd most irrational number, and indeed why $(9+\sqrt{221})/10$ can be considered the 3rd most irrational number.

# The Unreasonable Effectiveness

of Quasirandom SequencesI present a new low discrepancy quasirandom sequence that offers substantial improvement over current state-of-the art sequences eg Sobol, Niederreiter,…

# Evenly distributing points on a sphere

How to distribute points on the surface of a sphere as evenly as possibly is an incredibly important problem in maths, science and computing, and mapping the Fibonacci lattice onto the surface of a sphere via equal-area projection is an extremely fast and effective approximate method to achieve this. I show that with only minor modifications it can be made even better.

# Efficient methods to estimate accuracy and variance

for quasi-monte carlo integration.In this brief post, I describes various methods to estimate uncertainty levels associated with numerical approximations of integrals based on quasirandom Monte Carlo (QMC) methods.

# A simple method to construct isotropic quasirandom

blue noise point sequencesI describe a simple method for constructing a sequence of points, that is based on a low discrepancy quasirandom sequence but exhibits enhanced isotropic blue noise properties. This results in fast convergence rates with minimal aliasing artifacts.