Probabilistic beliefs in forecasting and prediction markets: aggregation, inference and liquidity under mechanism constraints

This thesis studies how probabilistic beliefs are aggregated, expressed, and inferred in forecasting platforms and prediction markets. In both settings, observed probabilities reflect not only underlying information but also the mechanisms underlying forecast and trade generation. A central difficulty is that the available data are often incomplete, irregular, or systematically filtered by institutional design. The thesis addresses how meaningful belief dynamics can be recovered under these constraints.

The thesis consists of three self-contained papers. The first develops a Bayesian method for dynamically aggregating human probability forecasts submitted over time. Forecast sequences are modelled as evolving distributions, and a change-point framework is used to identify structural shifts in collective belief. The resulting aggregation weights adapt to bursts of activity and periods of inactivity, providing a flexible alternative to fixed recency-weighting schemes.

The second paper examines belief inference from sparse limit order books in prediction markets. In thin markets, visible orders reflect only a subset of trader beliefs, since moderate beliefs are often unobserved. A simulation-based inversion approach is introduced that combines a parametric belief model with an explicit visibility mechanism, allowing latent belief distributions to be inferred from truncated order-book snapshots while remaining consistent with observed prices.

The third paper studies liquidity in automated market maker based prediction markets.
A mechanism-consistent model is developed in which price responsiveness is governed
by a composite risk--liquidity parameter reflecting both market design and trader
risk tolerance. Window-level estimators are used to characterise how this parameter
varies across markets and over time.

Together, the thesis provides a unified statistical perspective on belief dynamics in forecasting and prediction-market environments.