Bayes.outlier {BAS} R Documentation

## Bayesian Outlier Detection

### Description

Calculate the posterior probability that the absolute value of error exceeds more than k standard deviations P(|epsilon_j| > k sigma | data) under the model Y = X B + epsilon, with epsilon ~ N(0, sigma^2 I) based on the paper by Chaloner & Brant Biometrika (1988). Either k or the prior probability of there being no outliers must be provided. This only uses the reference prior p(B, sigma) = 1; other priors and model averaging to come.

### Usage

Bayes.outlier(lmobj, k, prior.prob)


### Arguments

 lmobj An object of class 'lm' k number of standard deviations used in calculating probability of an individual case being an outlier, P(|error| > k sigma | data) prior.prob The prior probability of there being no outliers in the sample of size n

### Value

Returns a list of three items:

 e residuals hat leverage values prob.outlier posterior probabilities of a point being an outlier prior.prob prior probability of a point being an outlier

### References

Chaloner & Brant (1988) A Bayesian Approach to Outlier Detection and Residual Analysis Biometrika (1988) 75, 651-659

### Examples

data("stackloss")
stack.lm <- lm(stack.loss ~ ., data = stackloss)
stack.outliers <- Bayes.outlier(stack.lm, k = 3)
plot(stack.outliers$prob.outlier, type = "h", ylab = "Posterior Probability") # adjust for sample size for calculating prior prob that a # a case is an outlier stack.outliers <- Bayes.outlier(stack.lm, prior.prob = 0.95) # cases where posterior probability exceeds prior probability which(stack.outliers$prob.outlier > stack.outliers\$prior.prob)


[Package BAS version 1.6.4 Index]