Computing path functionals

This package uses the Euler-Maruyama solvers implemented in DiffusionDefinition.jl to sample diffusion trajectories. Consequently, in the same way that in the latter package it has been possible to compute path functionals whilst sampling, it is possible to do so for the conditioned trajectories of guided proposals sampled with this package as well.

Sampling over a single interval

To compute a functional when sampling over a single interval simply pass a named argument f=... with a function you wish to evaluate. The function that you pass must have the following methods defined for it:

# called at the very start of solve!
f_accum = foo(P, y)
# called at the beginning of every iteration of the Euler-Maruyama scheme
f_accum = foo(f_accum, P, y, t, dt, dW, i)
# called at the very end, just before return statement
f_accum = foo(f_accum, P, y, Val(:final))

For in-place computations these three functions must have a slightly different form

# called at the very start of solve!
f_accum = foo(buffer, P, y) # the buffer needs to accommodate the needs of function f
# called at the beginning of every iteration of the Euler-Maruyama scheme
foo(buffer, P, y, tt[i-1], dt, i-1)
# called at the very end, just before return statement
foo(buffer, P, y, _FINAL)

You may pass it to rand or rand! so long as Val(:ll) is not passed (i.e. so long as you are not calling optimized sampler that already computes the log-likelihood for you).

Sampling over multiple intervals

To compute functionals when sampling over multiple intervals, instead of passing a single method as a named argument f=... pass a list of methods, say f=[foo₁,foo₂,foo₃], one for each interval. Additionally, pass an extra container to a named argument f_out. The results of method evaluation on each interval are going to be saved there.

Computing gradients of path functionals

Just as it was described in DiffusionDefinition.jl, it is possible to compute gradients while sampling.