PRB-30

Bernoulli KL

KL between two coins.

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GoverningBernoulli KL

Governing equation

D=p\\ln(p/q)+(1-p)\\ln((1-p)/(1-q))

where

p: p (—)
q: q (—)
D: Bernoulli KL (nat)

Lecture brief

Historical brief

Bernoulli trials, Poisson, Gauss, Bayes and Shannon entropy turned chance into a calculus of belief and noise. The lab computes likelihood, interval and information in SI-free counts. This sheet (PRB-30 — Bernoulli KL) is the form associated with Bernoulli KL. Working symbols: $p$ , $q$ $\rightarrow$ $D$ . KL between two coins. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

D

from

p

q

in Probability & statistics via

D=p\\ln(p/q)+(1-p)\\ln((1-p)/(1-q))

KL between two coins. Use it when a real probability & statistics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

p = 0.600\,\mathrm{—}

q = 0.400\,\mathrm{—}

, the governing relation

D=p\\ln(p/q)+(1-p)\\ln((1-p)/(1-q))

yields

D = 0.081\,\mathrm{nat}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

p p0.6 —q q0.4 —

Outputs

Bernoulli KL D0.081 nat

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

KL between two coins. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube