particle-filter

Create a PredictionMarketParticleFilter with a prior probability, then call update() with each new observation such as a market price or poll result. The filter propagates particles in logit space, reweights by likelihood, and returns a smoothed estimate via estimate().

A bootstrap particle filter estimates a hidden state, such as a true event probability, from noisy sequential observations. It is used for live tracking scenarios like election night returns or market prices where estimates must update as data streams in.

Resample when the effective sample size (ESS = 1 / sum of squared weights) falls below N/2, indicating weight degeneracy. This implementation uses systematic resampling, which has lower variance than multinomial resampling.

Modeling the random walk in logit space keeps particle values unbounded during propagation while guaranteeing probabilities stay within [0,1] after applying the sigmoid transform. This avoids particles drifting outside valid probability ranges.

Set process_vol higher (0.01-0.10) to make the filter more responsive to real changes, and obs_noise higher to smooth noisy observations more aggressively. High process_vol with low obs_noise trusts the data; the reverse trusts the model.

Particle filters require tuning of process and observation noise, and too few particles cause noisy estimates while too many slow computation. They also assume the state-space model is roughly correct, so misspecified dynamics degrade accuracy.