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thinking-probabilistic

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Probabilistic Thinking

概率思维

Core rule: State beliefs as numbers and ranges, not vibes. Anchor on a base rate, update with an explicit likelihood, and bound unknowns by factoring them — never invent false precision.
核心原则： 将信念以数字和范围的形式呈现，而非模糊感觉。以基准率为锚点，结合明确的似然概率进行更新，并通过考量未知因素设定边界——绝不要捏造虚假的精确性。

When to Use

适用场景

  • Timeline, effort, or outcome forecasts where the true value is uncertain.
  • Risk sizing for a change, migration, deploy, or launch.
  • Any moment you are about to state a confident single number you cannot actually know.
  • New evidence arrives and a prior estimate should move.
  • 真实数值不确定的时间线、工作量或结果预测。
  • 变更、迁移、部署或发布的风险评估。
  • 任何你即将给出一个无法确定的绝对精确数字的场景。
  • 出现新证据，需要更新先前估算的情况。

When NOT to Use

不适用场景

  • The quantity is measurable or look-up-able — measure or look it up.
  • The decision is invariant across the whole plausible range — skip the estimate and act.
  • There is no real reference class and you would invent a base rate — label it a guess, not a calibrated forecast.
  • You only need a binary gate and already have a decisive observation — do not pad with ceremony.
  • 该数值可测量或可查询——直接测量或查询即可。
  • 在整个合理范围内决策不会发生变化——跳过估算直接行动。
  • 没有真实的参考类别，需要凭空捏造基准率——将其标注为猜测，而非校准后的预测。
  • 只需要二元判断且已有决定性观测结果——无需多余流程。

Procedure

操作步骤

  1. Define a checkable claim: outcome + timeframe + unit. Prefer a falsifiable statement over vague language ("likely").
  2. Lock a prior and challenge it: name a reference-class base rate and at least one credible alternative path/hypothesis with its rate. Pull the prior toward the base rate unless you write a concrete reason for deviation. Then state the strongest evidence-based case that your chosen prior or range is wrong, what estimate it supports, and revise if that countercase survives. Convert vague words to numbers (e.g. "likely" ≈ 65–80%).
  3. Express a range, not a point: give at least one confidence interval (50% and 80% preferred). Assume overconfidence; widen intervals when the outside view is thin.
  4. Update prior → likelihood → posterior when evidence arrives:
    • Prior odds = p / (1 − p).
    • Likelihood ratio LR = P(E|H) / P(E|¬H). LR > 1 supports H; LR = 1 is noise; LR < 1 undermines H.
    • Posterior odds = prior odds × LR (multiply even when LR < 1); p = odds / (1 + odds).
    • Strength bands for distance from 1: weak ~1.5–3×, moderate 3–10×, strong 10–100×, definitive 100×+.
    • Yesterday's posterior is today's prior for the next evidence. For rare events, start from the base rate — vivid positives still leave most mass on false alarms.
  5. Fermi-bound unmeasured quantities (only when you need a magnitude you cannot measure/look up):
    • Decompose: Quantity = Factor₁ × Factor₂ × … (or sum of components).
    • Bound each factor with a range; use one-significant-figure geometric means for order-of-magnitude.
    • Multiply; report "~X within 3–5×"; sanity-check whether a 10× error would change the decision; replace any factor that is actually lookup-able.
    • Skip Fermi when the number is cheaply measurable, when the decision needs tighter than ~3–5× precision, or when every factor is pure invention.
  6. State the final estimate for checking: claim, range/CIs, key uncertainties, and the observation that would prove it wrong. Stop when the decision is stable across the remaining range or the next update needs new evidence you do not have.
  1. 定义可验证的断言： 包含结果+时间范围+单位。优先使用可证伪的陈述，而非模糊表述（如“可能”）。
  2. 锁定先验概率并提出质疑： 指定参考类别的基准率，以及至少一个具有对应概率的可信替代路径/假设。除非能写出偏离基准率的具体理由，否则先验概率应向基准率靠拢。然后陈述基于最强证据的反驳观点（即你所选先验概率或范围错误的理由）、该观点支持的估算值，若反驳成立则进行修正。将模糊词汇转换为数字（例如“可能”≈65–80%）。
  3. 给出范围而非单点值： 至少提供一个置信区间（推荐50%和80%置信区间）。假设存在过度自信，当外部参考信息不足时，扩大区间范围。
  4. 出现证据时更新先验→似然→后验概率：
    • 先验赔率 = p / (1 − p)。
    • 似然比 LR = P(E|H) / P(E|¬H)。LR > 1 支持假设H；LR = 1 为无关信息；LR < 1 削弱假设H。
    • 后验赔率 = 先验赔率 × LR（即使LR < 1 也需相乘）；p = 赔率 / (1 + 赔率)。
    • 与1的距离对应的强度等级：弱~1.5–3倍，中等3–10倍，强10–100倍，决定性100倍以上。
    • 前一天的后验概率即为次日新证据的先验概率。对于罕见事件，从基准率开始——生动的正面案例仍大概率是误报。
  5. 对不可量化因素进行费米估算边界设定（仅当你需要一个无法测量/查询的数量级时使用）：
    • 分解：数值 = 因子₁ × 因子₂ × …（或各组成部分之和）。
    • 为每个因子设定范围；使用一位有效数字的几何均值来确定数量级。
    • 相乘计算；报告“约X，误差在3–5倍以内”；检查10倍误差是否会改变决策；替换任何实际可查询的因子。
    • 若数值可低成本测量、决策需要比~3–5倍更精确的结果，或所有因子均为凭空捏造，则跳过费米估算。
  6. 给出用于验证的最终估算： 包含断言、范围/置信区间、关键不确定性，以及可证伪该估算的观测结果。当决策在剩余范围内保持稳定，或下一次更新需要的新证据尚未获取时，停止估算。

Output

输出内容

  1. Claim — falsifiable statement with timeframe.
  2. Prior — base rate, alternative path, adjustment reason, strongest countercase, and resulting prior probability.
  3. Range — confidence intervals (not a lone point).
  4. Updates — each evidence row: prior, LR (or explicit heuristic Δ), posterior.
  5. Fermi bounds (if used) — factor product and "~X within N×".
  6. Decision implication — what changes if the true value is at the low vs high end of the range.
  1. 断言 —— 包含时间范围的可证伪陈述。
  2. 先验概率 —— 基准率、替代路径、调整理由、最强反驳观点，以及最终的先验概率。
  3. 范围 —— 置信区间（而非单点值）。
  4. 更新记录 —— 每条证据对应的行：先验概率、LR（或明确的启发式Δ）、后验概率。
  5. 费米边界（若使用）—— 因子乘积及“约X，误差在N倍以内”。
  6. 决策影响 —— 真实数值处于范围低端和高端时的决策变化。

Verification

验证环节

  • Falsify/stop: if you cannot name a base rate, alternative, or serious countercase, label the estimate as a guess rather than calibrated. If the decision is unchanged across the full range, stop estimating. If new evidence arrives and the number does not move (or moves without an LR/Δ), recompute.
  • Over-application guard: do not dress checkable facts as probabilities, invent reference classes, or Fermi-decompose quantities you can measure. Do not report three significant figures on a 5×-uncertain product. For rare events, refuse jumps from one vivid hit to near-certainty without the base-rate prior.
  • 证伪/停止： 若无法指定基准率、替代方案或严肃的反驳观点，则将估算标注为猜测而非校准后的结果。若在整个范围内决策均无变化，则停止估算。若出现新证据但数值未变化（或未基于LR/Δ进行调整），则重新计算。
  • 过度应用防范： 不要将可验证的事实包装成概率，不要凭空捏造参考类别，不要对可测量的数值进行费米分解。不要对误差在5倍以内的结果报告三位有效数字。对于罕见事件，拒绝仅凭一个生动的案例就从基准率跳跃到近乎确定的结论。