Thinking about:

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…

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…

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…

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…

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…

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…

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…

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