docs/articles/part2_bayesian_fv.md

ArbIntel Part 2: Smoothing the Noise with Bayesian Statistics and Kalman Filters

In Part 1, we established ArbIntel's unified data pipeline. However, prediction markets are notoriously noisy. A single retail trader's market order on Polymarket can dramatically swipe an illiquid order book, creating a temporary price spike that doesn't reflect a true change in the underlying event's probability.

How do we differentiate between random bid-ask bounce and genuine new information? The answer lies in state-space smoothing and Bayesian updating.

The 1D Kalman Filter

A Kalman Filter is recursive. It estimates the true state of a system (the "Fair Value" of an asset) from a series of incomplete and noisy measurements (the traded prices).

In ArbIntel, we use a 1D implementation:

• State Estimate ($x_t$): Our current belief of the true probability.
• Process Variance ($Q$): How fast we think the true probability fundamentally changes over time (low for stable markets, high for volatile ones).
• Measurement Variance ($R$): The estimated noise in the exchange's order book.

When a new trade occurs, the Kalman Filter calculates the Kalman Gain ($K$)—essentially deciding whether to trust the new market print or our existing belief. This allows ArbIntel to completely ignore short-term liquidity sweeps.

Bayesian Fair Value

While the Kalman filter is great for smoothing, it doesn't establish an intrinsic "Fair Value." For this, we treat the probability of an event resolving "YES" as a Beta distribution, $Beta(\alpha, \beta)$.

1. The Prior: We establish base rates (e.g., incumbents win elections 65% of the time $\rightarrow Beta(65, 35)$).
2. The Update: When trades occur on Polymarket, we adjust our $\alpha$ and $\beta$ parameters scaled by the trade volume. High volume trades shift our belief significantly; low volume trades are treated as noise.

By combining the structural rigidity of a Kalman Filter with the probabilistic updates of a Bayesian model, ArbIntel refuses to be faked out by market microstructure dynamics.

In Part 3, we'll discuss the easiest money in prediction markets: Cross-Platform Arbitrage.