Blog Posts
I sometimes write blog posts on different aspects of statistics, modeling, computation, and so on. I host the posts themselves on HackMD, but have them catalogued here for ease of access. The dates refer to the last time that I modified the post. Please do feel free to get in touch if you have any comments, questions, etc. about these posts!
2024
Slicing and Random Walk Metropolis (June 6)
Vertical and Horizontal Structures in Stochastic Computations (May 22)
Polynomials and Sampling (May 15)
Rare Events from Transport Maps (May 8)
Convex Taylor Polynomials (May 2)
Microcanonical Monte Carlo (April 25)
The Advent of Optimisation in Statistics (April 17)
Learning from Complexity Lower Bounds (April 11)
Lessons from the Bias-Variance Trade-Off (April 3)
2023
Log-Convexity of the C^α Semi-Norm (August 28)
The “Approximation to What?” Principle (August 21)
Denoising-Centric Diffusions (August 14)
Nested Structure in MCMC Algorithms (August 9)
Hoeffding’s Inequality by Convex Ordering (July 31)
Logarithmic Sobolev Inequalities and Logarithmic Lipschitz Regularity (May 19)
Isoperimetric Surrogates for the Gaussian (April 20)
Univariate Log-Concave Rejection Sampling is Solved (March 11)
Iterative Likelihood Approximation (March 6)
Forwards, Backwards, and Stochastic Formulations of Optimal Transport (March 3)
Fitting Control Variates in MCMC (February 28)
Competition between Monte Carlo Methods (February 23)
Decompositions à la Alekseev-Groebner (February 19)
Computation of Heavy-Tailed Measures (February 14)
On the Benefits of Marginalisation for Langevin Diffusions (February 6)
A Mnemonic for Schur Complements (February 2)
Convenient Exponential Families (January 25)
Contractivity from Eventual Exponential Convergence (January 22)
Convergence Diagnostics for MCMC (January 18)
Bregman Cost Functions in Optimal Transport (January 14)
Non-Optimal Transport Maps (January 11)
Scans in Gibbs Sampling (January 8)
Multiple-Try Metropolis via Jump Processes (January 5)
2022
Some Quiet Assumptions in MCMC (December 31)
Strong Convexity and Square Roots (December 30)
Principles of the Monte Carlo Method (December 28)
Minibatch Markov Chain Monte Carlo (December 26)
Unbiased Estimators of the Inverse of the Mean from a Poisson Stream (December 22)
Why not Orlicz norms? (December 20)
Coupling Markov Chains to Avoid Each Other (December 20)
Chasing Constants: Understanding the Nash Inequality (September 18)
Chasing Constants: Eberle’s Reflection Coupling Theorem (September 8)
Chasing Constants: Tightening the Weak Harris Theorem (August 31)
Chasing Constants: Prelude (Spectral Gaps of Markov Chains by Contractivity) (August 23)
2021
Low-Rank Approximations for Subsampling MCMC in Gaussian Process Models (September 1)
Particle Systems for Sampling, and their Limits (August 31)
Control Variates and Controlled Diffusions (August 31)
Simple Variance Reduction for Score Gradient Estimators (August 24)
Coupling Methods in Monte Carlo: Removing Initialisation Bias in MCMC (August 23)
Multigrid Computation (August 18)
Coupling Methods in Monte Carlo: Static Theory (August 16)
Monte Carlo Estimation of Nonlinear Functionals: Unbiased Estimators via Stopping Times (August 9)
Approximate Inference in Unnormalised Models by an Expanded Variational Representation (August 9)
Interacting Particle Systems for Expectation-Maximisation (August 6)
Monte Carlo Estimation of Nonlinear Functionals: Bias Reduction (August 2)
Monte Carlo Estimation of Nonlinear Functionals: Polynomials (July 26)
Splitting Integrators and Normalising Flows (July 23)
Interacting Particle Systems for Approximate Inference (July 22)
From Adaptive MCMC to Interacting Particle Systems (July 21)
Variance Reduction in Monte Carlo Methods: Self-Normalised Importance Sampling (July 19)
Variance Reduction in Monte Carlo Methods: Importance Sampling (July 12)
Variance Reduction in Monte Carlo Methods: Rao-Blackwellisation (July 5)
Variance Reduction in Monte Carlo Methods: Bilinear Strategies (June 29)
Compositional Construction of Functions with Higher-Order Monotonicity Properties (June 6)
From the Method of Moments to Estimation of Normalising Constants (May 26)
Constructing Solutions to Ordinary Differential Equations (May 17)
Bregman Divergences for Generalised Score Matching (May 11)
Forward-Backward Markov Models for Density Estimation (May 6)