Global sampler

Link to the source files:

Path

The path.jl file exports a type Path and a few functions that apply on such an object.

A Path object encapsulates

xs a matrix of size $p \times N_e$ where $p$ is the dimension and $N_e$ are the number of events recorded
ts a vectof of times associated with the events
p the dimension
nseg the number of segments

Auxiliary type

The type Segment is useful to encapsulate the information contained between two events. It contains:

ta, tb the times at the two events
xa, xb the positions
tau (implicit) the travel time corresponding to the segment or $(t_b-t_a)$
v (implicit) the velocity along the segment

Auxiliary functions

getsegment retrieves a segment starting at time Path.ts[j]
samplepath takes a time or a list of times and returns the position along the Path object at those times
quadpathpoly does a simple analytical integration along the path for simple test functions of the form $\varphi(x)=P(x)$ where $P$ is a polynomial (for each dimension)
pathmean computes the mean using quadpathpoly where the polynomial is just $x$
esspath computation of the ESS corresponding to a number of samples equally spaced along the path. It tries to achieve a specific ratio and increases the number of samples until it achieves it.

The simulate.jl file is the main file for the Global Sampler. It contains one main immutable object which contains all of the parameters of the simulation. This is convenient if multiple parameters need to be tested.

A number of default parameters are pre-encoded but some parameters are essential (starting point, starting velocity, etc).

Simulate function

This function should mimic rather closely the original paper. Note in the main loop:

tau = min(bounce.tau, taubd, tauref)

corresponds to finding which action needs to be executed (normal bounce, boundary bounce or refreshment). After this one of three branches is executed:

if tau==bounce.tau
    ...
elseif tau==taubd
    ...
else
    ...
end

The first branch corresponds to a bounce against the level set of the log-likelihood, the second to a boundary bounce and third a refreshment.

In the first branch, an explicit call to bounce.dobounce checks whether to thin the event or not. If the time is accepted then the velocity is refreshed otherwise the whole loop is ignored.