# Probabilistic regression on outliers

I have a given data set $D = \{ x_i, y_i \}_{i=1}^n$ for a regression problem. When I plot the data, it looks like there is an underlying parabola (2nd order linear model) and some outliers.

I want to design an approach using a probabilistic model with a latent binary variable $\{ 0,1 \}$ indicating whether a data point is an outlier or not.

Currently I have no idea what I could do, what would the parameters be in this cause and how are they optimized? Is Expectation Maximization an idea?

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Are there known outliers in your data? Why isn't using the $\frac{3}{2} IQR$ cutoff sufficient? –  user17794 Jun 16 '12 at 22:41

My recommendation is to use robust regression. It is simpler and downweights the outliers.

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But this doesn't involve a probabilistic model, does it? –  Mahoni Jun 16 '12 at 22:02
Why do you want a probabilistic model for outliers? –  Michael Chernick Jun 16 '12 at 22:23
@MichaelChernick : Your suggestion makes sense only if outliers are bad. What if the whole purpose is to find outliers? The outliers may be the places where you should drill for oil. –  Michael Hardy Jun 16 '12 at 22:38
@MichaelHardy Mahoni said that the model fit a quadratic function except for a few outliers. That indicates that the outliers were hurting the fit. But if you want to detect the outliers the larger residuals from a robust regression fit will be the outliers. –  Michael Chernick Jun 16 '12 at 22:50