errorrate: Error rate of the Bayes rule for two-class Gaussian...

In EMMIXSSL: Semi-Supervised Gaussian Mixture Model with a Missing-Data Mechanism

Error rate of the Bayes rule for two-class Gaussian homoscedastic model

Description

The optimal error rate of Bayes rule for two-class Gaussian homoscedastic model

Usage

errorrate(beta0, beta, pi, mu, sigma)

Arguments

beta0	An n\times p matrix where each row represents an individual observation
beta	Number of observations.
pi	A g-dimensional vector for the initial values of the mixing proportions.
mu	A p \times g matrix for the initial values of the location parameters.
sigma	A p\times p covariance matrix if ncov=1, or a list of g covariance matrices with dimension p\times p \times g if ncov=2.

Details

The optimal error rate of Bayes rule for two-class Gaussian homoscedastic model can be expressed as

err(y_j;θ)=π_1φ\{-\frac{β_0+β_1^Tμ_1}{(β_1^TΣβ_1)^{\frac{1}{2}}}\}+π_2φ\{\frac{β_0+β_1^Tμ_2}{(β_1^TΣβ_1)^{\frac{1}{2}}}\}

where φ is a normal probability function with mean μ_i and covariance matrix Σ_i.

Value

errval

A vector of error rate.

EMMIXSSL documentation built on Oct. 18, 2022, 5:08 p.m.