Ancillarity-Sufficiency Interweaving Strategy

Definition

The Ancillarity-Sufficiency Interweaving Strategy (ASIS) is a Markov chain Monte Carlo technique that combines two complementary data-augmentation parameterizations of a latent-variable model within a single sampler, so that mixing is good across the entire parameter range rather than only where one parameterization happens to work (Yu-Meng 2011; applied to stochastic volatility by Kastner-Frühwirth-Schnatter 2014).

Key Ideas

• Parameterization governs MCMC efficiency. In a data-augmentation sampler, how the latent states are written relative to the parameters determines how strongly latents and parameters are correlated in the posterior — and hence how fast the chain mixes.
• Centered vs non-centered. The centered parameterization (CP) keeps the latent states on their natural scale (a "sufficient" augmentation); the non-centered parameterization (NCP) standardizes them (an "ancillary" augmentation, e.g. $\tilde h_t=(h_t-\mu)/\sigma$). Neither dominates: CP mixes well when the latent signal is strong and NCP when it is weak (Papaspiliopoulos-Roberts-Sköld).
• Interweaving (Yu-Meng 2011). Rather than choose a parameterization, interweave them: within one sweep, update the parameters in the CP, deterministically map the latents to the NCP, and update the parameters again. The Global Interweaving Strategy (GIS) provably improves on both individual samplers — "combining the best of different worlds."
• Robust across the whole parameter space. Because the two parameterizations fail in opposite regimes, interweaving is efficient everywhere, removing the need to pre-select a parameterization or tune to the (unknown) parameter values.

How It Works (Stochastic Volatility)

For the SV model $y_t=e^{h_t/2}\varepsilon_t$, $h_t=\mu+\phi(h_{t-1}-\mu)+\sigma_\eta\eta_t$: the CP breaks down when the volatility-of-volatility $\sigma_\eta$ is small, while the NCP is deficient when the log-variance is highly persistent ($\phi\to1$) — exactly the complementary failure modes ASIS is built for. Kastner-Frühwirth-Schnatter sample the log-volatilities with the Kim-Shephard-Chib / Omori-et-al. auxiliary-mixture (KSC) approximation, then interweave the CP and NCP updates of $(\mu,\phi,\sigma_\eta)$, yielding greatly improved sampling efficiency for all parameters throughout the range — including constellations previously infeasible to estimate. The method is implemented in the stochvol R package.

Why It Matters

• Removes a fragile modelling choice. Practitioners no longer need to guess whether CP or NCP will mix for their data — a decision that otherwise depends on the parameters they are trying to estimate.
• A general recipe. Interweaving applies to a broad class of multilevel/state-space models, wherever centered and non-centered augmentations trade places; SV is the showcase, not the limit.
• Enables hard parameter regions. It makes inference feasible for near-deterministic (small $\sigma_\eta$) or near-unit-root ($\phi\approx1$) volatility, where single-parameterization samplers stall.

Open Questions

• Choosing which pair of augmentations to interweave in more complex hierarchies, and whether more than two can be combined usefully.
• Interaction with the auxiliary-mixture approximation and with multivariate/factor SV extensions.
• Cost-per-iteration vs mixing trade-offs at very large $T$ (though each interweaving step is cheap).

Related

• Data Augmentation
• Stochastic Volatility
• Markov Chain Monte Carlo
• Kastner-Frühwirth-Schnatter (2014) ASIS for Boosting MCMC Estimation of Stochastic Volatility Models
• Gregor Kastner
• Sylvia Frühwirth-Schnatter