Moments

Four classes have a moments method:

• Sample

• Marginals

• ImportanceSample

• ExtendedImportanceSample

They all work the same way, computing posterior moments using some reweighting strategy. Specifically, * importance weighting for Sample and Marginals * importance sampling for ImportanceSample and ExtendedImportanceSample)

Note that computing moments using importance weighting (i.e. from Sample and Marginals) is always going to be more accurate than computing moments from importance samples (i.e. from ImportanceSample).

There are several different ways to call obj.moments:

obj.moments(varname: str, moment: alan.Moment)

The most basic form of the moments function, which computes a single, univariate moment.

Example:

sample.moments('a', alan.mean)

Arguments:

varname (str):

the name of the variable to compute the moment.

moment (alan.Moment):

the moment to compute.

Returns:

the moment represented an named torch.Tensor, where the names correspond to the plates.

obj.moments(varnames: tuple[str], moment: alan.Moment)

Some moments (such as a covariance) depend on two random variables. This form admits tuples of random variable names, allowing you to compute a single, multivariate moment.

Example:

sample.moments(('a', 'b'), alan.cov)

Arguments:

varname (tuple[str]):

a tuple of names of the variable.

moment (alan.Moment):

the moment to compute.

Returns:

the moment represented an named torch.Tensor, where the names correspond to the plates.

obj.moments(moment_list: list[tuple[varname(s), alan.Moment]])

If you’re computing moments from Sample, then it is far more efficient to pass in a whole bunch of moments at once. This form of the moments function allows you to do that.

Example:

sample.moments([
    ('a', mean),
    ('b', mean),
])

Arguments:

moment_list (list[tuple[varname(s), alan.Moment]]):

A list of tuples with two elements. The first element is the variable name (str) or the variable names (tuple[str]), and the second element is an alan.Moment.

Returns:

A list of moments represented an named torch.Tensor, where the names correspond to the plates.

When we’re specifying the moment using an alan.Moment class, we have a few options: * mean: computes the mean * mean2: computes the raw second moment * var: computes the variance