Statistical Thinking

A Hierarchical Gaussian Process Model for Longitudinal Tumour Growth

statistics
bayesian statistics
gaussian process
inference
hierarchical gaussian process
stan
advanced
We have longitudinal tumour size measurements for 10 patients. Each patient has one set of observations over about 100 days, 20 time points, recorded as the total tumour…
Sep 28, 2026

Understanding Gaussian Process: A Foundation

statistics
bayesian statistics
gaussian process
probability
inference
advanced
If you’ve ever wanted to put smooth curves through noisy data and get honest uncertainty estimates along the way, a Gaussian Process (GP) is the best choice. Intuitively, GP…
Sep 3, 2026

Bayesian Updating for Gaussians: A Gentle Derivation of the Posterior Formula

statistics
bayesian statistics
gaussian process
posterior
probability
inference
advanced
Posterior derivations for multivariate Gaussians are often presented as a “known formula” without explanation. In this post, we will derive the posterior for Gaussian…
Aug 19, 2026

Beginner’s guide to Bayesian Statistics: Prior, Likelihood, and Posterior

statistics
bayesian statistics
bayes' theorem
prior
likelihood
posterior
probability
inference
introduction
In the previous post, we introduced the core mechanics of Bayesian statistics: the Bayes’ theorem through two striking examples — Steve the librarian and the rare disease…
Jul 19, 2026

Beginner’s guide to Bayesian Statistics: Bayes’ Theorem

statistics
bayesian statistics
bayes' theorem
probability
inference
introduction
Imagine a man named Steve. He’s shy, helpful, tidy, loves order, and has a passion for details. If I asked you: “Is Steve more likely to be a librarian or a farmer?” — your…
Jul 7, 2026

From Trajectories to Beliefs: State-Space model and Statistical Inference of the Two-Compartment Tumor Model

systems biology
Stochastic Differential Equations
SDE
AR(1)
statistics
inference
state-space model
bayesian statistics
hierarchical bayesian model
stan
advanced
In a previous post, we explored the two-compartment tumour growth model, simulating it both deterministically and stochastically. This model captures the dynamics of…
Jul 5, 2026

From Equations to Trajectories: Deterministic Simulation and Stochastic Processes in the Two-Compartment Tumor Model

systems biology
Ordinary Differential Equations
ODE
Stochastic Differential Equations
SDE
Wiener noise
AR(1)
Stein-Fojo
Two-Compartment Tumour Model
simulation
advanced
Systems biology builds mechanistic models in Odinary Differential Equations (ODEs) or Partial Differential Equations (PDEs) from known biology. It derives mathematical…
Jun 10, 2026

Itô’s Lemma: Turning Stochastic Differential Equations into Linear Form

stochastic calculus
Itô calculus
state equation
SDE
advanced
Itô’s Lemma is a fundamental result in stochastic calculus, also called Itô calculus, that describes how to differentiate a function of a stochastic process, most commonly…
Jun 9, 2026

Mapping the Landscape of Chance – Distributions & A Glimpse of Bayes

statistics
probability
bayesian statistics
distribution
introduction
When we measure something—someone’s blood pressure, today’s rainfall, the number of clicks on an ad—we rarely believe that number fell from the sky fully formed. Instead, we…
May 31, 2026

The Mind’s Guide to Chance – The Rules of the Game

statistics
probability
introduction
The chance of you using probability to navigate life is remarkably high. You glance at a weather forecast and silently calculate the odds before choosing an outfit. You…
May 25, 2026
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