main effects is being small we could rely on that we can do many other things so we imagined higher dimensional X take on many many values but somehow an efficiently incurring a single component and mixture that we're using to represent P of X ok let's see what we can do now our running example is going to be a mixture model P of X has a weighted sum this is choosing the mode there's different modes index by I there is a distribution of x given I so supposed to I think is down maybe when we sample X we first sample a mode and