IndisputableMonolith.Statistics.BayesianFilteringFromVFE
This module constructs Bayesian filtering from variational free energy on finite recognition partitions. It defines likelihood, evidence, single-step updates, sequence iteration, and a consistency certificate. Statisticians applying active inference or RS-derived dynamics cite it to ground filtering in the RCL. The module consists entirely of layered definitions that import and extend the VFE construction.
claim$F[q;p]=E_q[E]+KL[q||p_{prior}]$ extended by $Likelihood$, $evidence$, $bayesStep$, $iterFilter$, and $BayesianFilteringCert$ on finite partitions.
background
The module operates in the Statistics domain and imports the VFE module, whose doc-comment states it implements variational free energy on a finite recognition partition with monotone descent under the ledger update. The Friston VFE is given explicitly as $F[q;p]=E_q[E]+KL[q||p_{prior}]$. Sibling definitions introduce likelihood functions, evidence computation, the Bayesian update step, iteration over lists, and a certificate that the filter satisfies the VFE property.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the filtering layer that extends the VFE construction from RCL into sequential inference. It directly supports the certificate $bayesianFilteringCert_holds$ and places Bayesian methods inside the Recognition Science statistics domain. No downstream modules are recorded, so its role is to close the definitional bridge between VFE descent and filtering operations.
scope and limits
- Does not derive the underlying VFE expression.
- Does not address continuous or infinite partitions.
- Does not prove convergence rates or error bounds.
- Does not connect to the phi-ladder or T5-T8 forcing steps.