the single most likely path in state space that was followed based on the observations I had that's maximum a-posteriori estimation it's about finding the max instead of the distribution now we won't work through the math on the board for this one but it is a bit exercise to try it on your own and the results are on the slides but effectively you'll see happen in these slides is that instead of looking at a summation over the variables we look at a max over two variables and a max will interact with this whole set of