mcquad

xitorch.integrate.mcquad(ffcn: Union[Callable[[…], torch.Tensor], Callable[[…], Sequence[torch.Tensor]]], log_pfcn: Callable[[…], torch.Tensor], x0: torch.Tensor, fparams: Sequence[Any] = [], pparams: Sequence[Any] = [], bck_options: Mapping[str, Any] = {}, method: Optional[Union[str, Callable]] = None, **fwd_options) → Union[torch.Tensor, Sequence[torch.Tensor]][source]

Performing monte carlo quadrature to calculate the expectation value:

\[\mathbb{E}_p[f] = \frac{\int f(\mathbf{x},\theta_f) p(\mathbf{x},\theta_p) \ \mathrm{d}\mathbf{x} }{ \int p(\mathbf{x},\theta_p)\ \mathrm{d}\mathbf{x} }\]
Parameters

  • ffcn (Callable) – The function with to be integrated. Its outputs is a tensor or a list of tensors. To call the function: ffcn(x, *fparams)

  • log_pfcn (Callable) – The natural logarithm of the probability function. The output should be a one-element tensor. To call the function: log_pfcn(x, *pparams)

  • x0 (torch.Tensor) – Tensor with any size as the initial position. The call ffcn(x0,*fparams) must work.

  • fparams (list) – Sequence of any other parameters for ffcn.

  • pparams (list) – Sequence of any other parameters for gfcn.

  • bck_options (dict) – Options for the backward mcquad operation. Unspecified fields will be taken from fwd_options.

  • method (str or callable or None) – Monte Carlo quadrature method. If None, it will choose "mh".

  • **fwd_options (dict) – Method-specific options (see method section below).

Returns

The expectation values of the function ffcn over the space of x. If the output of ffcn is a list, then this is also a list.

Return type

torch.Tensor or a list of torch.Tensor

method="mh"
mcquad(..., method="mh", *, nsamples=10000, nburnout=5000, step_size=1.0)

Perform Metropolis-Hasting steps to collect samples

Keyword Arguments

  • nsamples (int) – The number of samples to be collected

  • nburnout (int) – The number of initial steps to be performed before collecting samples

  • step_size (float) – The size of the steps to be taken

method="mhcustom"
mcquad(..., method="mhcustom", *, nsamples=10000, nburnout=5000, custom_step=None)

Perform Metropolis sampling using custom_step

Keyword Arguments

  • nsamples (int) – The number of samples to be collected

  • nburnout (int) – The number of initial steps to be performed before collecting samples

  • custom_step (callable or None) – Callable with call signature custom_step(x, *pparams) to produce the next samples (already decided whether to accept or not). This argument is required. If None, it will raise an error