Sunrise problem¶
The problem of assigning predictive probability to the next recurrence of a repeatedly observed event, exposing how induction depends on prior assumptions.
Core Idea¶
The historical sun example is illustrative, not an astronomical model; the rule of succession follows from a particular exchangeable Bernoulli model and prior, so repeated observations alone do not uniquely determine the probability. A prior over an unknown recurrence rate is updated by observed successes, yielding a posterior predictive probability whose value changes with the prior, likelihood, independence and stationarity assumptions. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Sunrise problem belongs to bayesian epistemology and is useful where the analyst can specify the typed bayesian epistemology carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the recurring event and prediction horizon, observed success and failure counts, sampling and exchangeability assumptions, likelihood, prior over recurrence rate, posterior and posterior predictive probability, Laplace rule of succession, model misspecification and induction-versus-deduction boundary are explicit. The scope is broad within that domain but bounded by the need for the recurring event and prediction horizon, observed success and failure counts, sampling and exchangeability assumptions, likelihood, prior over recurrence rate, posterior and posterior predictive probability, Laplace rule of succession, model misspecification and induction-versus-deduction boundary are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the recurring event and prediction horizon, observed success and failure counts, sampling and exchangeability assumptions, likelihood, prior over recurrence rate, posterior and posterior predictive probability, Laplace rule of succession, model misspecification and induction-versus-deduction boundary are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Sunrise problem. Sunrise problem compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed bayesian epistemology carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the recurring event and prediction horizon, observed success and failure counts, sampling and exchangeability assumptions, likelihood, prior over recurrence rate, posterior and posterior predictive probability, Laplace rule of succession, model misspecification and induction-versus-deduction boundary are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of bayesian epistemology because they reuse the typed bayesian epistemology carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, A prior over an unknown recurrence rate is updated by observed successes, yielding a posterior predictive probability whose value changes with the prior, likelihood, independence and stationarity assumptions., and type the carrier, state every parameter and convention in the definition, test that the recurring event and prediction horizon, observed success and failure counts, sampling and exchangeability assumptions, likelihood, prior over recurrence rate, posterior and posterior predictive probability, Laplace rule of succession, model misspecification and induction-versus-deduction boundary are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Sunrise problem Domain-specific
Parents (1) — more general patterns this builds on
-
Sunrise problem is a kind of Inference Prime
The proposed strict upward parent is
prime:inference.
Hierarchy path (1) — routes to 1 parentless root
- Sunrise problem → Inference → Rationality → Normativity → Constraint
Neighborhood in Abstraction Space¶
Sunrise problem sits in a crowded region of the domain-specific corpus (26th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Epistemic Measurement & Causal Reasoning (19 abstractions)
Nearest neighbors
- Bayesian epistemology — 0.93
- Information field theory — 0.91
- Radical probabilism — 0.91
- Widely applicable information criterion — 0.91
- Recursive Bayesian estimation — 0.91
Computed from structural-signature embeddings · 2026-09-08