Calculated Probability Value

A Calculated Probability Value is a numeric value between 0 and 1 that represents the probability of an event or outcome computed through mathematical calculations or statistical procedures.

• AKA: Computed Probability, Derived Probability, Probability Calculation Result, Statistical Probability Value, Probability Estimate.
• Context:
  • It can typically be produced by probability functions applied to data or theoretical distributions.
  • It can typically represent likelihoods, chances, or relative frequencies of events.
  • It can typically be bounded between 0 (impossible event) and 1 (certain event) by definition.
  • It can typically be expressed as decimal values, percentages, or fractions depending on context.
  • It can typically serve as input to statistical decision procedures and risk assessments.
  • It can often be derived from empirical data through frequency calculations or statistical models.
  • It can often be computed from theoretical distributions using probability density functions or probability mass functions.
  • It can often be combined using probability rules such as addition rules and multiplication rules.
  • It can often be updated through Bayesian methods incorporating prior information and new evidence.
  • It can often require assumptions about independence, distributions, or sampling methods.
  • It can range from being an Exact Calculated Probability Value to being an Approximate Calculated Probability Value, depending on its computation method.
  • It can range from being a Marginal Calculated Probability Value to being a Conditional Calculated Probability Value, depending on its conditioning context.
  • It can range from being a Frequentist Calculated Probability Value to being a Bayesian Calculated Probability Value, depending on its interpretive framework.
  • It can range from being a Discrete Calculated Probability Value to being a Continuous Calculated Probability Value, depending on its event space.
  • It can range from being a Simple Calculated Probability Value to being a Compound Calculated Probability Value, depending on its event complexity.
  • It can be interpreted within probability theory frameworks and statistical paradigms.
  • It can be validated through calibration tests and probability assessment methods.
  • It can be visualized using probability plots, distribution curves, or probability trees.
  • It can be subject to probability axioms including non-negativity, normalization, and additivity.
  • ...
• Example(s):
  • Statistical Test Probability Values, such as:
    • Observed p-Value = 0.03 from hypothesis testing procedure.
    • p-Value Score = 0.045 indicating evidence against null hypothesis.
    • Type I Error Probability = 0.05 as significance level.
    • Type II Error Probability = 0.20 as beta risk.
    • Statistical Power Value = 0.80 for effect detection.
  • Prediction Probability Values, such as:
    • Classification Probability = 0.92 for positive class membership.
    • Regression Prediction Interval Probability = 0.95 for coverage.
    • Forecast Probability = 0.70 for rain tomorrow.
    • Default Probability = 0.02 for loan risk assessment.
    • Churn Probability = 0.15 for customer retention.
  • Bayesian Probability Values, such as:
    • Prior Probability = 0.10 for disease prevalence.
    • Posterior Probability = 0.85 after positive test result.
    • Marginal Likelihood = 0.23 for model evidence.
    • Credible Interval Probability = 0.95 for parameter range.
  • Sampling Probability Values, such as:
    • Selection Probability = 0.001 in survey sampling design.
    • Inclusion Probability = 0.15 in stratified sample.
    • Bootstrap Probability = 0.632 for resampling procedure.
    • Capture Probability = 0.80 in capture-recapture study.
  • Distribution Probability Values, such as:
    • Cumulative Probability = 0.975 at z=1.96 in standard normal.
    • Tail Probability = 0.025 beyond critical value.
    • Quantile Probability = 0.50 at median value.
    • Exceedance Probability = 0.01 for extreme event.
    • Density Value = 0.3989 at mean of standard normal.
  • Reliability Probability Values, such as:
    • Survival Probability = 0.85 at 5-year mark.
    • Failure Probability = 0.001 per operational hour.
    • System Reliability = 0.999 for uptime requirement.
    • Component Reliability = 0.95 for critical part.
  • Game Theory Probability Values, such as:
    • Nash Equilibrium Probability = 0.33 for mixed strategy.
    • Win Probability = 0.48 in zero-sum game.
    • Cooperation Probability = 0.60 in prisoner's dilemma.
  • Information Theory Probability Values, such as:
    • Entropy Probability = 0.693 for binary uniform distribution.
    • Mutual Information Probability = 0.25 for channel capacity.
    • Error Probability = 0.01 in communication channel.
  • ...
• Counter-Example(s):
  • Test Statistic, which is a standardized measure rather than probability.
  • Effect Size, which measures magnitude rather than probability.
  • Correlation Coefficient, which measures association strength rather than probability.
  • Count Value, which is a frequency rather than probability.
  • Z-Score, which is a standardized value rather than probability.
  • Odds Ratio, which is a ratio rather than probability (though convertible).
  • Likelihood Value, which is not normalized to sum to 1.
  • Score Function, which is a derivative rather than probability.
  • Distance Measure, which quantifies separation rather than probability.
• See: Probability Theory, Probability Function, Statistical Probability, Observed p-Value, p-Value Score, Confidence Level, Bayesian Probability, Frequentist Probability, Probability Distribution, Random Variable, Statistical Inference, Probability Measure, Probability Space, Conditional Probability, Joint Probability, Probability Axioms.

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