# Drift Kernels¶

## Introduction¶

The default behavior of MH based inference algorithms is to generate proposals by sampling from the prior. This strategy is generally applicable, but can be inefficient when the prior places little mass in areas where the posterior mass in concentrated. In such situations the algorithm may make many proposals before a move is accepted.

An alternative is to sample proposals from a distribution centered on the previous value of the random choice to which we are proposing. This produces a random walk that allows inference to find and explore areas of high probability in a more systematic way. This type of proposal distribution is called a drift kernel.

This strategy has the potential to perform better than sampling from the prior. However, the width of the proposal distribution affects the efficiency of inference, and will often need tuning by hand to obtain good results.

## Specifying drift kernels¶

A drift kernel is represented in a WebPPL program as a function that maps from the previous value taken by a random choice to a distribution.

For example, to propose from a Gaussian distribution centered on the previous value we can use the following function:

```var gaussianKernel = function(prevVal) {
return Gaussian({mu: prevVal, sigma: .1});
};
```

This function can be used to specify a drift kernel at any `sample` statement using the `driftKernel` option like so:

```sample(dist, {driftKernel: kernelFn});
```

To use our `gaussianKernel` with a Cauchy random choice we would write:

```sample(Cauchy(params), {driftKernel: gaussianKernel});
```

## Helpers¶

A number of built-in helpers provide sensible drift kernels for frequently used distributions. These typically take the same parameters as the distribution from which they sample, plus an extra parameter to control the width of the proposal distribution.

`gaussianDrift`({mu: ..., sigma: ..., width: ...})
`dirichletDrift`({alpha: ..., concentration: ...})
`uniformDrift`({a: ..., b: ..., width: ...})