draw_intensity_step

Sample NHPPP times using the thinning method

internal

Simulates events from one dimensional nonhomogeneous Poisson point processes (NHPPPs) as per Trikalinos and Sereda (2024, <doi:10.48550/arXiv.2402.00358> and 2024, <doi:10.1371/journal.pone.0311311>). Functions are based on three algorithms that provably sample from a target NHPPP: the time-transformation of a homogeneous Poisson process (of intensity one) via the inverse of the integrated intensity function (Cinlar E, "Theory of stochastic processes" (1975, ISBN:0486497996)); the generation of a Poisson number of order statistics from a fixed density function; and the thinning of a majorizing NHPPP via an acceptance-rejection scheme (Lewis PAW, Shedler, GS (1979) <doi:10.1002/nav.3800260304>).

Thomas Trikalinos

nhppp

Simulating Nonhomogeneous Poisson Point Processes

Yuliia Sereda

draw_intensity_step function

<dl><dt>lambda</dt>
<dd>(function) the instantaneous rate of the NHPPP.
A continuous function of time.</dd>
<dt>majorizer_vector</dt>
<dd>(scalar, double) <code>K</code> constant majorizing rates, one per interval</dd>
<dt>time_breaks</dt>
<dd>(vector, double) <code>K+1</code> time points defining <code>K</code> intervals
of constant rates:
<code>[t_1 = range_t[1], t_2)</code>: the first interval
<code>[t_k, t_{k+1})</code>: the <code>k</code>-th interval
<code>[t_{K}, t_{K+1} = range_t[2])</code>: the <code>K</code>-th (last) interval</dd>
<dt>atmost1</dt>
<dd>boolean, draw at most 1 event time</dd></dl>

Arguments

Simulate from a non homogeneous Poisson Point Process (NHPPP) from
(t0, t_max) (thinning method) with piecewise constant_majorizer — draw_intensity_step

<dl>

<dt>lambda</dt>
<dd>(function) the instantaneous rate of the NHPPP.
A continuous function of time.</dd>


<dt>majorizer_vector</dt>
<dd>(scalar, double) <code>K</code> constant majorizing rates, one per interval</dd>


<dt>time_breaks</dt>
<dd>(vector, double) <code>K+1</code> time points defining <code>K</code> intervals
of constant rates:
<code>[t_1 = range_t[1], t_2)</code>: the first interval
<code>[t_k, t_{k+1})</code>: the <code>k</code>-th interval
<code>[t_{K}, t_{K+1} = range_t[2])</code>: the <code>K</code>-th (last) interval</dd>


<dt>atmost1</dt>
<dd>boolean, draw at most 1 event time</dd>

</dl>

draw_intensity_step: Simulate from a non homogeneous Poisson Point Process (NHPPP) from (t0, t_max) (thinning method) with piecewise constant_majorizer

Description

Usage

Value

Arguments