API reference

PointProcesses

A package for temporal point process modeling, simulation and inference.

History{M,T<:Real}

Linear event histories with marks of type M and temporal locations of type T.

Fields

• times::Vector{T}: sorted vector of event times
• marks::Vector{M}: associated vector of event marks
• tmin::T: start time
• tmax::T: end time

event_marks(h)

Return the vector of event marks for h, sorted according to their event times.

event_times(h)

Return the sorted vector of event times for h.

min_time(h)

Return the starting time of h (not the same as the first event time).

max_time(h)

Return the end time of h (not the same as the last event time).

nb_events(h)

Count events in h.

nb_events(h, tmin, tmax)

Count events in h during the interval [tmin, tmax).

has_events(h)

Check the presence of events in h.

has_events(h, tmin, tmax)

Check the presence of events in h during the interval [tmin, tmax).

length(h)

Alias for nb_events(h).

duration(h)

Compute the difference h.tmax - h.tmin.

min_mark(h; [init])

Return the smallest event mark if it is smaller than init, and init otherwise.

max_mark(h; [init])

Return the largest event mark if it is larger than init, and init otherwise.

push!(h, t, m)

Add event (t, m) at the end of history h.

append!(h1, h2)

Add all the events of h2 at the end of h1.

time_change(h, Λ)

Apply the time rescaling t -> Λ(t) to history h.

split_into_chunks(h, chunk_duration)

Split h into a vector of consecutive histories with individual duration chunk_duration.

AbstractPointProcess{M}

Common interface for all temporal point processes with mark type M.

BoundedPointProcess{M,P,T} <: AbstractPointProcess{M}

Temporal point process P with pre-defined start and end times.

Implements some fallbacks for the AbstractPointProcess interface which accept fewer arguments.

Fields

• pp::P: underlying point process
• tmin::T: start time
• tmax::T: end time

intensity(pp, m, t, h)

Compute the conditional intensity for a temporal point process pp applied to history h and event (t, m).

The conditional intensity function λ(t,m|h) quantifies the instantaneous risk of an event with mark m occurring at time t after history h.

ground_intensity(pp, h, t)

Compute the ground intensity for a temporal point process pp applied to history h at time t.

The ground intensity quantifies the instantaneous risk of an event with any mark occurring at time t after history h:

λg(t|h) = Σₘ λ(t,m|h)

log_intensity(pp, m, t, h)

Compute the logarithm of the conditional intensity for a temporal point process pp applied to history h and event (t, m).

mark_distribution(pp, t, h)

Compute the distribution of marks for a temporal point process pp knowing that an event takes place at time t after history h.

simulate_ogata(rng, pp, tmin, tmax)

Simulate a temporal point process pp on interval [tmin, tmax) using Ogata's algorithm.

rand([rng,] pp, tmin, tmax)

Alias for simulate_ogata.

rand([rng,], bpp::BoundedPointProcess)

Simulate a point process on a predefined time interval.

logdensityof(pp, h)

Compute the log probability density function for a temporal point process pp applied to history h:

ℓ(h) = Σₖ log λ(tₖ|hₖ) - Λ(h)

The default method uses a loop over events combined with integrated_ground_intensity, but it should be reimplemented for specific processes if faster computation is possible.

integrated_ground_intensity(pp, h, a, b)

Compute the integrated ground intensity (or compensator) Λ(t|h) for a temporal point process pp applied to history h on interval [a, b):

Λ(h) = ∫ λg(t|h) dt

ground_intensity_bound(pp, t, h)

Compute a local upper bound on the ground intensity for a temporal point process pp applied to history h at time t.

Return a tuple of the form (B, L) satisfying λg(t|h) ≤ B for all u ∈ [t, t+L).

fit(::Type{PP}, h)
fit(::Type{PP}, histories)

Fit a point process of type PP to one or several histories.

Not implemented by default.

fit_map(::Type{PP}, h, prior)
fit_map(::Type{PP}, histories, prior)

Fit a point process of type PP to one or several histories using maximum a posteriori with a prior.

Not implemented by default.

AbstractPoissonProcess{M} <: AbstractPointProcess{M}

Common interface for all temporal Poisson processes, that is, temporal point processes for which the intensity is not a function of past history.

Implements some fallbacks for the AbstractPointProcess interface which accept fewer arguments.

MultivariatePoissonProcess{R}

Multivariate homogeneous temporal Poisson process.

Fields

• λ::Vector{R}: event rates.

MultivariatePoissonProcessPrior{R1,R2}

Gamma prior on all the event rates of a MultivariatePoissonProcess.

Fields

• λ_α::Vector{R1}
• λ_β::R2

MarkedPoissonProcess{M,R,D}

Homogeneous temporal Poisson process with arbitrary mark distribution.

Fields

• λ::R: event rate.
• mark_dist::D: mark distribution with sample type M.

Constructor

MarkedPoissonProcess{M}(λ, mark_dist)