Where each idea is used on this site

1

How to use this card

Filter, then follow the link

The first table routes an idea from the part that derives it to the page elsewhere that consumes it. The second names each algorithm and what it produces. Type in the box to filter both tables case-insensitively; clear it to see everything again. The foundational definitions these parts assume live in Probability, Interactively.

Route lookup all rows

No row matches that — try a looser word, or clear the box.

💡 An appendix, not another part. Where the first volume collected notation, this one collects destinations: every row answers “I met this method — where is it actually run?”

2

Where each idea is used

From the part that derives it to the page that consumes it

Idea	Volume II part	Where it is used
Likelihood & maximum likelihood	Part 1 · Likelihood and maximum likelihood	Every loss in pretraining is a negative log-likelihood; the scaling arguments in scaling assume the MLE framing.
Prior, posterior, conjugacy	Part 2 · Prior, posterior, conjugacy	Posterior reasoning about model behaviour in evaluation, and the KL-controlled updates of RLHF.
Bias–variance, Fisher information, Cramér–Rao	Part 3 · Is this estimator any good?	Why a fit is biased or high-variance in Nonlinear Optimization, and the error floor of any estimator there.
Confidence vs credible intervals	Part 4 · Confidence vs credible	Reporting uncertainty for a benchmark in evaluation, and landmarks in SLAM.
Hypothesis testing, power, p-hacking	Part 5 · Hypothesis testing, and how it goes wrong	Comparing models or ablations honestly in benchmarks and evaluation.
The bootstrap	Part 6 · The bootstrap	Error bars on a fitted model without a closed-form variance, e.g. robust fits in RANSAC.
Sampling: inverse-CDF, rejection, importance	Part 7 · How to draw a sample	Sampling a token distribution in the decode loop, and the reparameterised draws diffusion and RLHF need.
Monte Carlo integration	Part 8 · Monte Carlo integration	Estimating expectations too hard to integrate, from rendering to the policy gradients behind RLHF.
Random walks, Brownian motion	Part 9 · Random walks & Brownian motion	Diffusion models as time-reversed noise, and the integrated pose error of odometry.
Markov chains & stationarity	Part 10 · Markov chains	The autoregressive state machine of the decode loop, and PageRank-style ranking of research in papers.
MCMC: Metropolis, Gibbs, HMC	Part 11 · MCMC	Drawing from an intractable posterior — calibration and uncertainty in evaluation, and post-processing in Nonlinear Optimization.
Latent variables: EM & the ELBO	Part 12 · Latent variables: EM and the ELBO	Clustering features before a vision pipeline, and the variational objective behind VAEs and the reparameterised sampling in diffusion.
Entropy, cross-entropy, KL, MI	Part 13 · Entropy and information	The training loss of every language model (language models), perplexity in evaluation, and the KL penalty in RLHF.
Bayes nets & factor graphs	Part 14 · Bayes nets and factor graphs	The factor graph a pose graph or SLAM backend solves — pose-graph optimization and SLAM.
Hidden Markov models	Part 15 · Hidden Markov models	Sequence decoding and mode-finding — the same recursion the Bayesian smoother runs in odometry.
The Bayes filter	Part 16 · The Bayes filter	The predict/update recursion every robot runs in odometry and SLAM.
Kalman filter & EKF	Part 17 · The Kalman filter and EKF	Sensor fusion and state estimation in odometry, kinematics and SLAM.
Particle filters	Part 18 · Particle filters	Monte Carlo localization in a map, the non-Gaussian half of robot navigation and SLAM.
Outliers, RANSAC & robust estimation	Part 19 · Outliers, RANSAC and robust estimation	Fitting with gross outliers: RANSAC and the robust losses of gradient descent.
Probability in machine learning	Part 20 · Probability in machine learning	Softmax and temperature in the decode loop and speculative decoding, calibration in evaluation, and the next-token distribution of language models.

3

The algorithms, collected

One method, one output, one part

Algorithm	What it produces	Built in
$\hat\theta = argmax \ell(\theta)$	The parameter whose model makes the data most likely.	Part 1
$\hat\theta = E[\theta\mid D]$ or $argmax p(\theta\mid D)$	A posterior summary — mean, median or mode.	Part 2
`I(θ) = -E[ℓ''(θ)]`	The curvature of the log-likelihood, and the variance floor of any unbiased estimator.	Part 3
Resample with replacement, refit, repeat	An empirical sampling distribution from one dataset.	Part 6
Proposals, accept/reject, weights	Samples from a target you can only evaluate, or a lower-variance expectation.	Part 7
$\frac{1}{N}\sum f(x_i)$	An expectation estimate with a `1/√N` error band.	Part 8
`πP = π`	The long-run distribution of a Markov chain.	Part 10
A chain whose stationary distribution is the target	Posterior samples without an analytic form.	Part 11
Responsibilities, then a maximised lower bound	Parameters of a latent-variable model.	Part 12
Marginals over hidden states, or the optimal path	A decoded sequence.	Part 15
A belief `bel(x)` over the state	The recursive state estimate every filter specialises.	Part 16
`x, P` and the gain `K`	An optimal linear-Gaussian state estimate.	Part 17
A weighted particle set	A non-Gaussian, multi-modal state estimate.	Part 18
A consensus set and a robust fit	Parameters immune to gross outliers.	Part 19
Normalised probabilities, calibrated scores, learned transformations	The probabilistic outputs of modern ML systems.	Part 20

4

Where to start, given where you came from

Three common entry points

From SLAM or odometry, start at the Bayes filter and work forward through the Kalman filter and particle filters; the graphical-model part is the formal backing. From LLM Training, start at information theory: cross-entropy is the loss, KL is the constraint, and perplexity is its exponential. From multi-view geometry, start at robust estimation, which is where the sampling arguments in that guide are actually proved.