🌫️ The world is stochastic — driven by chance. "Stochastic" is just the fancy word for random: you can't predict the next outcome exactly, only the odds.

Think of driving in thick fog. The road is there, but you can't see it clearly, so you can only make your best guess about what's ahead. Neuroscience lives in this fog. A single neuron's next spike, the buzz of a cortical column, an animal's next turn — all hard to predict exactly. It might be that with perfect knowledge some of it is predictable, but from where we sit, it looks random. So we reach for probability.

The tool that tames the fog is a generative model — your assumptions about how the hidden world produces the data you actually see. Call the hidden state of the world θ (theta) and the thing you measure x. The model says: "a world in state θ tends to generate observations that look like x."

🤯 The catch: the map from world → data is not one-to-one. State θ₁ can produce observation x₁ — but a different state θ₂ might produce the exact same x₁. So you can't just read the world backward off the data.

The classic example: your 3-D world is flattened onto a 2-D retina. Infinitely many real scenes could cast the same shadow on your eye. Your brain has to infer which one is out there. That inference-under-uncertainty is exactly what probability gives us the language for — and it's the thread running through this whole quest.

🦌 Ilya says: This is why NMA is soaked in statistics. Neurons are noisy and the world is ambiguous — every model you'll build is a bet about a fog-covered road.