Index: Concept Notes - Discrete Latents and Inference Frontier

Concept Notes - Discrete Latents and Inference Frontier

Routing Summary

Three concept notes with no raw source, covering topics in the cluster that the four ingested sources do not teach directly: why NUTS cannot sample discrete parameters and how to marginalise them (E04), stochastic volatility and the inference frontier (E12), and Bayesian HMM practice: label switching, non-homogeneous HMMs, movement HMMs, dwell times (E24, E48, E59, E57). Every note cites the literature and reuses numbers from the ingested sources where available.

• Need why discrete parameters break NUTS, compound steps or changepoint/mixture marginalisation? → Marginalising Discrete Latents - Why NUTS Cannot Sample Discrete Parameters
• Need stochastic volatility, funnels in state-space models or Pareto $\hat{k}$ trust diagnostics? → Stochastic Volatility and the Inference Frontier
• Need label switching, NHMM, dwell times or per-draw decoding? → Bayesian HMMs - Label Switching, Non-Homogeneous Transitions and Dwell Times

Concept Map

Concept	Note	Type	Depends On	Key Result
Marginalisation of discrete latents	Marginalising Discrete Latents - Why NUTS Cannot Sample Discrete Parameters	theorem	—	$p(y
Coal-mining changepoint	Marginalising Discrete Latents - Why NUTS Cannot Sample Discrete Parameters	example	marginalisation	$O(T)$ prefix/suffix sums
Stochastic volatility model	Stochastic Volatility and the Inference Frontier	definition	—	non-centred innovations $z_n$
SV benchmarks across sources	Stochastic Volatility and the Inference Frontier	example	ChEES/MEADS tables	ChEES 2.8x NUTS ESS/gradient
Inference frontier options	Stochastic Volatility and the Inference Frontier	theorem	SV	reparameterise, adapt, many-chain, approximate, Pareto $\hat{k}$
Bayesian HMM	Bayesian HMMs - Label Switching, Non-Homogeneous Transitions and Dwell Times	definition	forward algorithm	Dirichlet rows, marginalised path
Label switching	Bayesian HMMs - Label Switching, Non-Homogeneous Transitions and Dwell Times	theorem	Bayesian HMM	$K!$ modes; ordering
NHMM	Bayesian HMMs - Label Switching, Non-Homogeneous Transitions and Dwell Times	definition	HMM	softmax transitions with covariates

Notes

• Marginalising Discrete Latents - Why NUTS Cannot Sample Discrete Parameters — CONTAINS: Def. no gradient for discrete; compound steps; Thm. marginalisation; coal-mining changepoint with tested code; mixtures; HMM; infeasible cases; PyMC sketch.
• Stochastic Volatility and the Inference Frontier — CONTAINS: SV model; why hard; benchmark table from ChEES/MEADS; options along the frontier; simulation code; PyMC sketch.
• Bayesian HMMs - Label Switching, Non-Homogeneous Transitions and Dwell Times — CONTAINS: Bayesian HMM; EM vs Bayes; label switching; NHMM; movement HMM; dwell times; model checking; single-particle tracking; code.

Sources

• No raw source: concept notes citing Jarrett (1979), Carlin, Gelfand and Smith (1992), Kim, Shephard and Chib (1998), Hughes and Guttorp (1994), Stephens (2000), Jasra et al. (2005), Langrock and Zucchini (2011), Zucchini et al. (2016), Yao et al. (2018), and the Stan User’s Guide (HTML only). Quantitative numbers are taken from the ingested sources in this cluster.

See Also

• Rabiner 1989 - HMM Tutorial - Overview, Hoffman 2021 - ChEES-HMC - Overview, Hoffman 2022 - MEADS - Overview, Betancourt 2015 - HMC for Hierarchical Models - Overview, Monsters and Mixtures, Efficient MCMC.