Motivation
The project’s RBPF likelihood estimator carries continuous state via per-particle Kalman recursions and discrete state via regime-history particles. Common-random- numbers gives only 1.4–1.6× variance reduction in the project — well below the 10×–100× that CRN achieves in classical particle filtering — because the regime- path resampling fragility dominates. Meanwhile, IMM-style mode mixing (Mazor 1998, Murphy 1998) is known to achieve GPB2 accuracy at GPB1 cost in the mode-known filtering setting, which is the per-particle conditional inside an RBPF. There is essentially no published work that uses the IMM mode-mixing trick as the proposal distribution in an RBPF over Markov regimes.
Hypothesis
An IMM-style mode-mixed proposal at each RBPF step — i.e., propose the regime
at step t from the IMM mode-conditional posterior rather than from the prior
transition Π — will reduce the regime-path resampling fragility and lift CRN
variance reduction from ~1.6× to ≥ 5× on the project’s CRE estimation benchmark.
The cost is one additional per-particle Kalman update per regime transition,
which is cheap relative to the Riccati pricing call.
Approach sketch
- Implement an IMM-mixed proposal in the RBPF, parameterized by an interaction
weight
α ∈ [0, 1]that interpolates from prior-only (α=0, current behavior) to fully-IMM (α=1). - Validate on a controlled synthetic MJLS where the optimal posterior is computable (small regime count, short horizon) — verify the IMM-mixed estimator is unbiased.
- Run on the project’s
est_on_sim_datacells with paired CRN and measure variance reduction vs the prior-only baseline at fixed N=3000. - Independent verifier: a Hamilton-filter cross-check on the same θ values.
Expected outcome
≥ 3× CRN variance reduction at fixed N, equivalently ~3× compute savings to reach the same SEM. If validated, this becomes the production proposal for the RBPF.
Risks
- IMM mixing changes the proposal but does not solve regime-path degeneracy under highly persistent regimes — the variance reduction may flatten on long samples even if it helps on short ones.
- The IMM-mixed proposal must be importance-corrected, which adds an extra density-ratio computation per particle; if this is mis-implemented the estimator becomes biased.
- IMM-mixed proposals may interact badly with the absorbing-NBC feasibility filter in some parameter regions (open question — needs empirical check).
Pilot results
(empty)
Lessons learned
(empty)