forecasting-ch02-belieflisted

# Chapter 2: The Mathematics of Belief ## Scope and intake Use when binary success evidence must update a base rate or a selected sample needs a survivorship audit. Do not use for a causal claim from regression toward the mean or exchangeability that cannot be defended. Ask only for unresolved material inputs: What counts as a trial and success? Are trials independent and comparable? Why this prior? Which failures or nonrespondents are missing? ## Input contract and additional evidence CSV successes,trials with integer 0 <= successes <= trials and trials > 0; rows must represent disjoint comparable batches. Config prior_alpha and prior_beta are positive. Record population, sampling window and observation/selection rules. Minimal **format illustration**, not sufficient training data: ```csv successes,trials 7,10 ``` ## Executable interface Exact CLI columns: `successes,trials`. Supported method controls: `as_of, frequency, horizon, prior_alpha, prior_beta, season, seed`. The three rows use .25×, 1× and 4× prior strength, with 95% posterior credible bounds. They hold the prior mean fixed. There is no future-count interval in this output. ## Applied procedure 1. Define the trial population and observation process. Identify exclusions and whether repeating customers or clustered trials violate simple binomial assumptions. 2. Choose and document Beta prior alpha,beta before inspecting the batch. Sum only disjoint exchangeable observations. 3. Update to Beta(alpha+succe