01
μ₀ = 0.00
Before any data, the prior is broad and undecided. A gaussian with shoulders wider than the page.
예상
│
the shape
of what you think
will happen.
focus lens
↓
II.
likelihood
p(data | θ)
There is a word you are about to think, and there is a slightly different word you will end up thinking. The gap between them is where this page lives.
A forecast is not a promise. It is a probability density stretched over the possibilities, slightly bunched near the ones you have seen before, thinner at the edges where the things you have not yet learned still live.
Every Korean reading of 예상 carries the same wobble: the pre- in prefigure, the fore- in foresee, the quiet machinery by which the future is rehearsed before it becomes the present.
What you are reading is a sample drawn, right now, from a field of possible readings. Scroll to update the prior. The numbers on the left will settle, then disturb, then settle again — as all numbers eventually do.
The likelihood is merely the shadow the data casts back on the parameter space. Turn the data around and the shadow lengthens. Turn it again and the shadow recomputes.
III.
evidence
posterior-update timeline — 12 moments
02
n = 1, Δμ = +0.14
One observation arrives. The peak slides right by a fraction of a sigma; the tails quietly contract.
03
n = 7, σ → 0.82
Seven more readings. The bell narrows. The span between what you expect and what you doubt shrinks.
04
outlier at x = 3.4σ
A point arrives that should not have. The tail briefly fattens. The posterior inhales.
05
n = 24
Two dozen samples. The mode is locatable now — you could point at it without embarrassment.
06
mixture emerges
Two modes resolve where one seemed enough. The world turns out to have been two worlds.
07
BF₁₀ = 12.6
Evidence tips the comparison. The rarer model is quietly preferred.
08
drift detected
The mean has been sliding for six steps. Expectation is on the move.
09
regime change
The old parameters no longer explain the new data. You abandon them without ceremony.
10
τ → ∞
The posterior sharpens toward a needle. Certainty increases; the world begins to feel thin.
11
surprise event
A cluster of tail events in a row. The sharpened needle splits back into a cloud.
12
H(X) ↑
Entropy climbs again. The page has learned what it does not know.
t → 00 / 12
IV.
posterior
p(θ | data) — twelve entangled cells
Hover a cell. Watch its six neighbors ripple in phase. Expectation is never local; every posterior is entangled with the posteriors next to it.
the expected value of this page is no longer well‑defined.
seed = 0x00000000
·
n = 0
·
H = 0.000