Probability Paths and the Structure of Predictions over Time
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概率路径与预测随时间演化的结构
- 研究问题
- 对于未来二元事件的概率预测，如何刻画信息到达导致的动态更新，并量化未来概率路径的不确定性以支持决策时点选择？
- 方法与思路
- 作者提出贝叶斯高斯潜在信息鞅框架，以历史数据推断潜在信息流，建模概率预测轨迹并保留概率路径的鞅结构。
- 材料陈述的贡献
- 摘要称该框架更好量化未来概率路径的不确定性，并在三种评价指标下优于三个常用基线的后验路径分布估计。
- 阅读关注点
- 应核对概率路径满足鞅结构的条件、潜在信息过程与观测概率的关系，以及后验估计、指标选择和基线比较设计。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收均未核实；摘要未说明数据、具体指标和适用条件，不能确认一般预测场景中的优势。
原文摘要
In settings ranging from weather forecasts to political prognostications to financial projections, probability estimates of future binary outcomes often evolve over time. For example, the estimated likelihood of rain on a specific day changes by the hour as new information becomes available. Given a collection of such probability paths, we introduce a Bayesian framework -- which we call the Gaussian latent information martingale, or GLIM -- for modeling the structure of dynamic predictions over time. Suppose, for example, that the likelihood of rain in a week is 50 %, and consider two hypothetical scenarios. In the first, one expects the forecast to be equally likely to become either 25 % or 75 % tomorrow; in the second, one expects the forecast to stay constant for the next several days. A time-sensitive decision-maker might select a course of action immediately in the latter scenario, but may postpone their decision in the former, knowing that new information is imminent. We model these trajectories by assuming predictions update according to a latent process of information flow, which is inferred from historical data. In contrast to general methods for time series analysis, this approach preserves important properties of probability paths such as the martingale structure and appropriate amount of volatility and better quantifies future uncertainties around probability paths. We show that GLIM outperforms three popular baseline methods, producing better estimated posterior probability path distributions measured by three different metrics. By elucidating the dynamic structure of predictions over time, we hope to help individuals make more informed choices.