Working definition
Information theory measures uncertainty and dependence through quantities such as entropy, cross-entropy, and mutual information. Estimates depend on distributions, sample size, discretization, and conditioning; apparent information can arise from leakage or shared trends.
Notation
H(X) = −Σ p(x) log p(x)I(X;Y) = H(Y) − H(Y|X)Assumptions
- Probability distributions are defined.
- Sampling supports the estimator.
- Conditioning variables prevent obvious confounding where possible.
Invariants
- Entropy is nonnegative for discrete variables.
- Mutual information is symmetric and nonnegative.
- Deterministic invertible recoding preserves information.
Reproducible procedure
- Define variables and estimation method.
- Estimate against shuffled and simple baselines.
- Use held-out data and report estimator bias.
Error and boundary controls
- High-dimensional estimates are sample hungry.
- Binning changes estimates.
- Mutual information does not identify causal direction.
What this does not establish
Statistical dependence between planetary features and outcomes does not establish a causal celestial mechanism or robust future utility.
Explicit applications
1 cross-domain bridges
Incremental rule information audit
Measure whether a rule pack adds out-of-sample information beyond base rates and ordinary covariates.
Inputs
- locked rule features
- outcomes
- baseline predictions
Outputs
- incremental information
- uncertainty
- null comparison
Transformation: Estimate held-out score or information gain with leakage controls.
Limit: Dependence does not identify cause and must replicate prospectively.
Open connected system →Authoritative references
- [1]NIST/SEMATECH e-Handbook of Statistical Methods · National Institute of Standards and Technology
Establishes: Methods for uncertainty analysis, calibration, time-series modeling, process monitoring, experimental design, reliability, and statistical comparison.
Boundary: Statistical procedures quantify evidence under a design and model; they do not repair biased sampling, outcome leakage, post-hoc hypotheses, or unmeasured confounding.
Direct answer
- Information theory measures uncertainty and dependence through quantities such as entropy, cross-entropy, and mutual information. Estimates depend on distributions, sample size, discretization, and conditioning; apparent information can arise from leakage or shared trends.
Mechanism and method
- Define variables and estimation method.
- Estimate against shuffled and simple baselines.
- Use held-out data and report estimator bias.
What is measured
- Entropy is nonnegative for discrete variables.
- Mutual information is symmetric and nonnegative.
- Deterministic invertible recoding preserves information.
Limitations
- High-dimensional estimates are sample hungry.
- Binning changes estimates.
- Mutual information does not identify causal direction.
- Probability distributions are defined.
- Sampling supports the estimator.
- Conditioning variables prevent obvious confounding where possible.
What this does not establish
- Statistical dependence between planetary features and outcomes does not establish a causal celestial mechanism or robust future utility.
Bridge: Incremental rule information audit
- Measure whether a rule pack adds out-of-sample information beyond base rates and ordinary covariates.
- Input: locked rule features
- Input: outcomes
- Input: baseline predictions
- Output: incremental information
- Output: uncertainty
- Output: null comparison
- Limit: Dependence does not identify cause and must replicate prospectively.