q_exp_marg_DZ: Marginal Exponential Method for Outlier Detection

In matthew-seth-smith/replicateOutliers: Outlier Detection Methods for Replicated Data

Description

This function implements the marginal exponential method for outlier detection among replicated data. It first fits the aboslute difference Delta between two replicates to an Asymmetric Laplace Distribution using MLE. It then determines whether Delta's Laplace Distribution is Asymmetric or Symmetric and whether it has a significant displacement parameter. Then among the points outside of some central band, we use the exponential parameters fitted to the Laplace Distribution for Delta (see the paper in the citation) to determine the marginal probability that Z will take a value greater than its observed value. We assign the probability 1 to points in the middle band.

Usage

q_exp_marg_DZ(D, Z, p_theta = 0.05, p_kappa = 0.05, k = 1)

Arguments

D	The absolute difference (Delta) between two vectors of (positive) replicated data: D = X_1 - X_2
Z	The coefficient of variation (Zeta) between two vectors of (positive) replicated data: Z = sqrt(2) * abs(X_1 - X_2) / (X_1 + X_2)
p_theta	We use the (1-p_theta)*100% two-sided confidence interval for theta in Delta = X_1 - X_2 + theta to determine if there is a significant translation of the absolute difference Delta. If this interval contains 0, then we set theta = 0. We set p_theta = 0.05 by default
p_kappa	We use the (1-p_kappa)*100% two-sided confidence interval for the asymmetry parameter kappa in the Asymmetric Laplace Distribution to which we fit Delta. If this interval for log(kappa) contains 0, then we set kappa = 0 and use a Symmetric Laplace Distribution for Delta. We set p_kappa = 0.05 by default
k	The number of standard deviations about the center (mean) of the Asymmetric Laplace Distribution for Delta that we use to define the "central band." We set k = 1 by default

Value

A numerical vector of equal length to the input D and Z vectors, with the outlier probability q = P(z <= Z <= sqrt(2)) if (d,z) is not in the middle band and the assigned value 1 if it is in the middle band

Examples

# Assume X_1 and X_2 are positive data vectors of the same length. These are the replicates
data(Sim_GG)
df <- data.frame(X_1=Sim_GG$X_1, X_2=Sim_GG$X_2)
df$D <- df$X_1 - df$X_2
df$Z <- sqrt(2) * abs(df$X_1 - df$X_2) / (df$X_1 + df$X_2)
df$q_exp_m <- q_exp_marg_DZ(df$D, df$Z)

matthew-seth-smith/replicateOutliers documentation built on Jan. 24, 2020, 9:34 p.m.