With likelihood weighting, we fix the evidence variables.

And this weighting is relatively straightforward to apply in Gaussian fitting.

Likelihood weighting is a great technique, but it doesn't solve all our problems.

And because of this left weighting, the average is actually here, way to the left.

And then the next routine just implements the simple addition with the measurement_noise as the inverse weighting factor.

So, we're going to introduce a new method called likelihood weighting that generates samples so that we can keep every one.

In likelihood weighting, we're going to be collecting samples just like before, but we're going to add a probabilistic weight to each sample.

It ignores measurements, because the measurement sets the weighting factor in this resampling process, but with only 1 particle the same particle will be resampled no matter what.

When we include the weights, counting this sample that was forced to have a s and a w with a weight of 0.099, instead of counting it as a full one sample, we find that likelihood weighting is also consistent.

I now want you to implement the function smooth, which takes as an input the path, our two weighting factors, and a small tolerance variable, which I'll explain to you in a second, and it creates the new path, which are the y's in our equations so far from the old path.