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