Prediction Markets as Bayesian Inverse Problems: Uncertainty Quantification, Identifiability, and Information Gain from Price–Volume Histories under Latent Types

Battle Count: 53

The paper is primarily theoretical and focused on prediction markets rather than traditional quantitative trading. However, it has significant relevance: (1) the latent-type mixture model for price increments is directly applicable to understanding order flow and informed trading in any market; (2) the KL projection gap and identifiability framework can diagnose when price signals are informative; (3) the information gain metrics can evaluate signal quality in trading strategies; (4) the stability analysis is relevant for robust signal extraction; (5) the framework for detecting adversarial/manipulative flow is applicable to market surveillance. The connection to prediction markets and oracle architectures is more niche for traditional quant trading.

High complexity due to: (1) Bayesian inverse problem formulation requiring marginal likelihood computation over high-dimensional nuisance parameter space; (2) KL projection gap computation requires optimization over nuisance parameters; (3) SMC implementation with resampling and rejuvenation steps; (4) Variational inference with mean-field approximations; (5) Multiple interacting components (gating, mixture weights, type-specific parameters); (6) Theoretical guarantees require verifying multiple regularity assumptions. The computational complexity table shows SMC at O(N·T·K) per iteration, which is manageable but requires careful tuning.

The paper provides detailed mathematical formulations, algorithms (SMC and VI), and synthetic experiment setups with specific parameter values. However, no code repository is mentioned. The theoretical proofs are fully provided in the appendix. Synthetic experiments use 1000 replications with specified parameters, enabling partial reproducibility. Real market data experiments are mentioned but details are limited in the extract.