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Blog

Blog

HMC by Hand: Gradients, Heartbeats, PDEs and Other Tales

by-hand
mcmc
algorithms
non-linear
educational

We already saw in previous posts how to set up your own Hamiltonian Monte Carlo (HMC) sampler to explore the parameter space. However, there was something we didn’t cover in that or other posts: how to set up the gradient function that will guide the sampler through the parameter space. So buckle up! We’ll dive right into the nitty gritty of math, gradients and partial derivatives by hand!

Apr 19, 2025
56 min

So, You Think You Can Model a Heartbeat?

cardiovascular
non-linear
simulation
educational

Your heart isn’t a metronome, it’s a chaotic jazz drummer. Dive with me into the math madness behind why your heartbeat skyrockets during burpees and how a non-linear model (featuring logistic functions and elderly Zumba warriors) decodes this cardiac drama. Spoiler: Your Fitbit is shook. Code, curves, and caffeine included.

Mar 24, 2025
32 min

Going NUTS: A Step-by-Step Guide to Adaptive Hamiltonian Sampling in R

HMC
MCMC
algorithms
educational

You may have wonder what’s the engine behind many Bayesian analysis in modern research? Well, in this post we’ll not only cover the fundamentals, but we’ll also build from the ground-up a fully functional Hamiltonian Monte Carlo with No-U-Turn-Sampler (HMC-NUTS), the bad boy behind the hood of the Bayesian inference monster truck.

Jan 21, 2025
41 min

Decoding the Neuron’s Spark: Building Intuition for Action Potential Dynamics

non-linear
neuroscience
educational

Action potentials are the language of neurons. In this post we build a simplified model to explain how these electrical signals are generated. We’ll explore the role of ion channels and build an intuitive understanding of neuronal firing.

Jan 6, 2025
35 min

Modeling Lymphocyte Dynamics: Agent-Based Simulations and Non-Linear Equations

non-linear
simulation
biology
educational

In this post, we’ll take you step by step through building and playing with a model of lymphocyte dynamics. So, grab your keyboard, and let’s whip up a recipe for understanding how T cells become the immune system’s MVPs.

Dec 23, 2024
40 min

Non-linear models: A Case for Synaptic Plasticity

non-linear
educational
neuroscience

In this second edition we’ll be discussing the role of long term potentiation and depression, a form of neuroplasticity, and their dynamics using non-linear models. Here, we’ll dig deep into the statistical intricacies of the overlapping dynamics of synaptic neuroplasticity.

Dec 14, 2024
35 min
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