Poisson Approximation for Count Variance Method

A Poisson Approximation for Count Variance Method is a variance approximation method that models true positive counts, false positive counts, and false negative counts as Poisson-distributed variables with variance equal to mean.

• AKA: Poisson Count Variance Method, Mean-Equals-Variance Approximation, Poisson Variance Assumption Method, Count Data Poisson Model.
• Context:
  • It can typically assume count variance equals count mean for classification counts.
  • It can typically simplify variance calculations in Delta-Method F1 Standard Error Estimation Methods.
  • It can typically enable analytical solutions for performance metric variances.
  • It can often provide reasonable approximations for large sample sizes.
  • It can often underestimate variance when overdispersion exists.
  • It can often support Normal Approximation for P-Value Methods through central limit theorem.
  • It can range from being a Simple Poisson Approximation for Count Variance Method to being a Overdispersion-Adjusted Poisson Approximation for Count Variance Method, depending on its dispersion parameter.
  • It can range from being a Independent Poisson Approximation for Count Variance Method to being a Correlated Poisson Approximation for Count Variance Method, depending on its independence assumption.
  • It can range from being a Homogeneous Poisson Approximation for Count Variance Method to being a Heterogeneous Poisson Approximation for Count Variance Method, depending on its rate parameter variation.
  • It can range from being a Exact Poisson Approximation for Count Variance Method to being a Approximate Poisson Approximation for Count Variance Method, depending on its approximation quality.
  • ...
• Example(s):
  • TP Count Variance Estimations, such as:
    • Var(TP) = TP for true positive counts.
    • Var(FP) = FP for false positive counts.
  • Aggregated Count Variances, such as:
    • Total variance from sum of Poisson variables.
    • Group-level variance aggregation.
  • Delta Method Applications, such as:
    • Variance propagation through F1 formula.
    • SE estimation for harmonic mean.
  • ...
• Counter-Example(s):
  • Binomial Variance Method, which uses n*p*(1-p) formula.
  • Negative Binomial Variance Method, which allows overdispersion.
  • Empirical Variance Method, which uses observed variance.
• See: Poisson Distribution, Variance Approximation Method, Count Data Model, Delta-Method F1 Standard Error Estimation Method, Binomial Approximation for Count Variance Method, Variance Estimation, Mean-Variance Relationship, Overdispersion, Count Data, Statistical Assumption, Moment Matching Method, Maximum Likelihood Estimation.

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