The goal of muscadet is to provide ways of simulating and estimating planar point patterns according to various two-mark DPP models. It currently provides support for Gaussian and Bessel DPPs. Estimation can be performed either by minimizing the pair correlation function contrast or by maximizing the likelihood.
Installation
You can install the development version of muscadet from GitHub with:
# install.packages("devtools")
devtools::install_github("LMJL-Alea/muscadet")Example
The typical way of using muscadet for studying two-mark planar DPPs is to use the TwoMarkDPP class:
library(muscadet)
mod <- TwoMarkDPP$new(model = "Gauss")
mod
#>
#> ── Two-mark planar Gauss determinantal point process ───────────────────────────
#> • Intensity of the 1st marginal DPP: ?
#> • Intensity of the 2nd marginal DPP: ?
#> • Repulsion rate of the 1st marginal DPP: ?
#> • Repulsion rate of the 2nd marginal DPP: ?
#> • Repulsion rate between marks: ?
#> • Correlation between marks: ?
#> • Window size: ?As one can see, the model is initially empty, in the sense that no parameter is provided. You can start setting them manually one at a time:
mod$first_intensity <- 100
mod
#>
#> ── Two-mark planar Gauss determinantal point process ───────────────────────────
#> • Intensity of the 1st marginal DPP: 100
#> • Intensity of the 2nd marginal DPP: ?
#> • Repulsion rate of the 1st marginal DPP: (0, 0.056)
#> • Repulsion rate of the 2nd marginal DPP: ?
#> • Repulsion rate between marks: ?
#> • Correlation between marks: ?
#> • Window size: ?You can notice how the model gets updated and gives you intervals of feasible values for some parameters as soon as it is able to compute this information given the set of already known parameters.
mod$second_intensity <- 100
mod$first_repulsion_rate <- 0.03
mod$second_repulsion_rate <- 0.03
mod
#>
#> ── Two-mark planar Gauss determinantal point process ───────────────────────────
#> • Intensity of the 1st marginal DPP: 100
#> • Intensity of the 2nd marginal DPP: 100
#> • Repulsion rate of the 1st marginal DPP: 0.03
#> • Repulsion rate of the 2nd marginal DPP: 0.03
#> • Repulsion rate between marks: [0.03, Inf)
#> • Correlation between marks: ?
#> • Window size: ?
mod$cross_repulsion_rate <- 0.035
mod
#>
#> ── Two-mark planar Gauss determinantal point process ───────────────────────────
#> • Intensity of the 1st marginal DPP: 100
#> • Intensity of the 2nd marginal DPP: 100
#> • Repulsion rate of the 1st marginal DPP: 0.03
#> • Repulsion rate of the 2nd marginal DPP: 0.03
#> • Repulsion rate between marks: 0.035
#> • Correlation between marks: [0, 0.735)
#> • Window size: ?
mod$between_mark_correlation <- 0.5
mod$window_size <- 1
mod
#>
#> ── Two-mark planar Gauss determinantal point process ───────────────────────────
#> • Intensity of the 1st marginal DPP: 100
#> • Intensity of the 2nd marginal DPP: 100
#> • Repulsion rate of the 1st marginal DPP: 0.03
#> • Repulsion rate of the 2nd marginal DPP: 0.03
#> • Repulsion rate between marks: 0.035
#> • Correlation between marks: 0.5
#> • Window size: 1Now the model is fully specified and you can simulate a point pattern from it via the $random() method:
progressr::handlers("rstudio")
withr::with_seed(1234, {
progressr::with_progress({
df <- mod$random(n = 1)
})
})Note that the computations are parallelized over the sample size using the futureverse framework.
If you have an observed two-mark planar point pattern, you can also use it to fit the model which automatically adjusts the parameter set and bounds. This is achieved via the $fit() method:
mod$fit(df[[1]])
mod
#>
#> ── Two-mark planar Gauss determinantal point process ───────────────────────────
#> • Intensity of the 1st marginal DPP: 105
#> • Intensity of the 2nd marginal DPP: 102
#> • Repulsion rate of the 1st marginal DPP: 0.034
#> • Repulsion rate of the 2nd marginal DPP: 0.037
#> • Repulsion rate between marks: 0.036
#> • Correlation between marks: 0.71
#> • Window size: 1If you want finer control over the estimation methods, you can use the functions fit_via_pcf() and fit_via_mle() from outside the model class.