SequentialPointProcesses

This package defines a few sequential point processes and implements logpdf and rand for them. The models are special cases models proposed in

Penttinen, A., & Ylitalo, A.-K. (2016). Deducing self-interaction in eye movement data using sequential spatial point processes. Spatial Statistics, 17, 1-21. doi:10.1016/j.spasta.2016.03.005

Installation

import Pkg
Pkg.add(url="https://github.com/mikkoku/PointPatternStatistics.jl")
Pkg.add(url="https://github.com/mikkoku/SequentialPointProcesses.jl")

Softcore model

The Softcore model is parametrised by a kernel $f$. The density for the point $y$ given the $k$ earlier points is proportional to $$ \exp(\sum_{i=0}^k f(|x_i - y|)$$. See https://arxiv.org/abs/2005.01517 for more details.

using SequentialPointProcesses
using Distributions
M1(theta) = Softcore(d -> (2.3/d)^(theta))
pp = rand(M1(4.5), (x=(0,10), y=(0,10)), 10)
logpdf(M1(4.5), pp, 100)

Other models

Mixture and Uniform.

Implementation of Softcore model

The method for rand uses simple rejection algorithm with uniform proposals and thus may fail if the density is generally low.

The method for logpdf uses grid based numerical integration and the grid size has to be specified logpdf(model, pointpattern, N) where N is the number of integration points in the first dimension.

Multithreading

It is possible to use threads by using

logpdf(M1(4.5), pp, SequentialPointProcesses.Options(nx=100, parallel=:threads))

and CUDA by using

using CUDA
M1cuda(theta::T) where T = Softcore(d -> (2.3/d)^(theta), d -> CUDA.pow((T(2.3)/d), theta))
logpdf(M1cuda(4.5), pp, SequentialPointProcesses.Options(nx=100, parallel=:cuda))
logpdf(M1cuda(4.5f0), pp, SequentialPointProcesses.Options(nx=100, parallel=:cuda, cudatype=Float32))

where cudatype can Float32 or Float64 and cudabatchsize can be increased to decrease the amount of GPU memory required. Using CUDA might require specifying a CUDA friendly kernel.