Code to perform point estimation with neural Bayes estimators and censored input data based on the methodology described in "Neural Bayes estimators for censored inference with peaks-over-threshold models" (Richards et al., 2023+). See also Sainsbury-Dale et al. (2023+) for a general overview of neural Bayes estimation.
The scripts in this repository are based primarily on the Julia package NeuralEstimators and its accompanying R interface.
First, download this repository and navigate to its top-level directory within terminal.
Before installing the software dependencies, users may wish to setup a conda environment, so that the dependencies of this repository do not affect the user's current installation. To create a conda environment, run the following command in terminal:
conda create -n CensoredNeuralEstimators -c conda-forge julia=1.8.0 r-base nlopt
Then activate the conda environment with:
conda activate CensoredNeuralEstimators
The above conda environment installs Julia and R automatically. If you do not wish to use a conda environment, you will need to install Julia and R manually if they are not already on your system:
Once Julia and R are setup, install package dependencies by running:
julia --project=. -e 'using Pkg; Pkg.instantiate(); Pkg.precompile()'. This will install all Julia package dependencies given inProject.tomlandManifest.toml.Rscript Dependencies.R. This will install all R package dependencies.
The code in src reproduces training and assessment of two of the estimators used by Richards et al. (2023+):
HW_cNBE.jl: this script constructs estimators for the random scale mixture process used by Richards et al. (2023+) to model extreme Arabian PM2.5 concentrations. Training is conducted using "simulation-on-the-fly", and is done solely via this Julia script. Due to GitHub's requirement that individual files do not exceed 50MB in size, we only provide here the standardised data withG=4used in the application. Whilst the code will run for the other values ofGconsidered by Richards et al. (2023+), the required data must be downloaded from Zenodo and placed indata/. The original PM2.5 concentrations data are provided indata/PM25_original.Rdata.simulate_IMSP_random_tau.R, followed byIMSP_random_tau_cNBE.jl: reproduces the "random-tau" estimator for the inverted max-stable process (IMSP; see Section 4.3 of Richards et al., 2023+). Simulation of the IMSP is first carried out in R usingsimulate_IMSP_random_tau.R. We then pass these replicates to Julia and train the estimator usingIMSP_random_tau_cNBE.jl.
Note that the scripts are designed to run quickly using a very small number of sampled parameter vectors during training (i.e., setting 'K' in the manuscript to be very small); to fully replicate the estimators used by Richards et al. (2023+), this value must be changed (detailed comments are included in the scripts). Note that we have not included code to reproduce the likelihood-based inference for the simulation study in Section 4 of Richards et al. (2023+) as i) this methodology is not pat of the novel contributions of this paper and ii) reproducing these results is not computationally feasible without access to substantial computational resources.
Julia must be started with the command julia --project=. in order to load an environment with the correct package dependencies. Users wishing to run the scripts from the terminal may enter the following commands:
julia --project=. --threads=auto src/HW_cNBE.jlRscript src/simulate_IMSP_random_tau.Rjulia --project=. --threads=auto src/IMSP_random_tau_cNBE.jlor run all scripts in succession usingbash all.sh.
- Richards, J., Sainsbury-Dale, M., Zammit-Mangion, A., and Huser, R. (2023+). Neural Bayes estimators for censored inference with peaks-over-threshold models. arxiv.org/2306.15642
- Sainsbury-Dale, M., Zammit-Mangion, A., and Huser, R. (2023+). Likelihood-free parameter estimation with neural Bayes estimators. The American Statistician (to appear). arxiv.org/2208.12942