Probability of direction¶
Summarize a posterior effect's sign certainty as the larger of Pr(θ>0) and Pr(θ<0), ranging from one-half to one for continuous posteriors while deliberately not measuring magnitude or practical importance.
Core Idea¶
Probability of direction (pd) is max{Pr(θ>0|data),Pr(θ<0|data)}, with special care for discrete mass at zero and alternative scaling conventions. Posterior mass is partitioned by sign; the majority side becomes the reported direction and its mass the certainty index. Estimation from draws counts samples sharing the posterior median's sign under continuous 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¶
Probability of direction belongs to bayesian statistics and is useful where the analyst can specify a posterior distribution for a scalar effect θ, a null point, sign probabilities, Monte Carlo draws or analytic probabilities, and a reporting convention, then evaluate the posterior, parameter orientation, null point, zero-mass handling, Monte Carlo error, and one- or two-sided reporting convention are stated. The scope is broad within that domain but bounded by the need for the posterior, parameter orientation, null point, zero-mass handling, Monte Carlo error, and one- or two-sided reporting convention are stated. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the posterior, parameter orientation, null point, zero-mass handling, Monte Carlo error, and one- or two-sided reporting convention are stated the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Probability of direction can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
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 Probability of direction. Probability of direction 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: a posterior distribution for a scalar effect θ, a null point, sign probabilities, Monte Carlo draws or analytic probabilities, and a reporting convention. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the posterior, parameter orientation, null point, zero-mass handling, Monte Carlo error, and one- or two-sided reporting convention are stated independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of bayesian statistics because they reuse a posterior distribution for a scalar effect θ, a null point, sign probabilities, Monte Carlo draws or analytic probabilities, and a reporting convention, Posterior mass is partitioned by sign; the majority side becomes the reported direction and its mass the certainty index.
Transfer outside the home domain is weaker. The skeletal pattern—type the carrier, apply the defining mechanism of Probability of direction, preserve its invariant, and derive only consequences licensed by the stated boundary—may suggest an analogy, but the domain-specific mechanisms, admissible evidence, and consequences do not come along automatically.
Relationships to Other Abstractions¶
Current abstraction Probability of direction Domain-specific
Parents (1) — more general patterns this builds on
-
Probability of direction is a kind of Measurement Prime
The proposed strict upward parent is
prime:measurement.
Hierarchy path (1) — routes to 1 parentless root
- Probability of direction → Measurement
Neighborhood in Abstraction Space¶
Probability of direction sits in a crowded region of the domain-specific corpus (25th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Bayesian Inference & Probabilistic Models (23 abstractions)
Nearest neighbors
- Widely applicable information criterion — 0.93
- Bayesian linear regression — 0.92
- Posterior probability — 0.91
- Jeffreys prior — 0.91
- Normal-inverse-gamma distribution — 0.91
Computed from structural-signature embeddings · 2026-09-08