Model Selection Reference

SimulatedModelSelection

Perform model selection using simulation-based ABC.

Arguments

• reference_data::AbstractArray{Float64,2}: The observed data to which the simulated model output will be compared. Size: (nmodeltrajectories, ntimepoints)
• threshold_schedule::AbstractArray{Float64}: A set of maximum distances from the summarised model output to summarised observed data for a parameter vector to be included in the posterior. Each distance will be used in a single run of the ABC-SMC algorithm.
• parameter_priors::AbstractArray{AbstractArray{ContinuousUnivariateDistribution},1}: Priors for the parameters of each model. The length of the outer array is the number of models.
• summary_statistic::Union{String,AbstractArray{String,1},Function}: Either: 1. A String or 1D Array of strings that Or 2. A function that outputs a 1D Array of Floats that summarises model output. Defaults to keep_all. See detailed documentation of summary statistics.
• simulator_functions::AbstractArray{Function,1}: An array of functions that take a parameter vector as an argument and outputs model results (one per model).
• 'model_prior::DiscreteUnivariateDistribution': The prior from which models are sampled. Default is a discrete, uniform distribution.
• distance_function::Function: Any function that computes the distance between 2 1D Arrays. Optional argument (default is to use the Euclidean distance).
• max_iter::Int: The maximum number of simulations that will be run. The default is 1000*n_particles. Each iteration samples a single model and performs ABC using a single particle.

Returns

A ModelSelectionOutput object that contains which models are supported by the observed data.

EmulatedModelSelection

Perform model selection using emulation-based ABC.

Arguments

• n_design_points::Int64: The number of parameter vectors used to train the Gaussian process emulator.
• reference_data::AbstractArray{Float64,2}: The observed data to which the simulated model output will be compared. Size: (nmodeltrajectories, ntimepoints)
• n_particles::Int64: The number of parameter vectors (particles) that will be included in the final posterior.
• threshold_schedule::AbstractArray{Float64}: A set of maximum distances from the summarised model output to summarised observed data for a parameter vector to be included in the posterior. Each distance will be used in a single run of the ABC-SMC algorithm.
• parameter_priors::AbstractArray{AbstractArray{ContinuousUnivariateDistribution},1}: Priors for the parameters of each model. The length of the outer array is the number of models.
• summary_statistic::Union{String,AbstractArray{String,1},Function}: Either: 1. A String or 1D Array of strings that Or 2. A function that outputs a 1D Array of Floats that summarises model output. Defaults to keep_all. See detailed documentation of summary statistics.
• simulator_functions::AbstractArray{Function,1}: An array of functions that take a parameter vector as an argument and outputs model results (one per model).
• 'model_prior::DiscreteUnivariateDistribution': The prior from which models are sampled. Default is a discrete, uniform distribution.
• distance_function::Function: Any function that computes the distance between 2 1D Arrays. Optional argument (default is to use the Euclidean distance).
• max_iter::Int: The maximum number of simulations that will be run. The default is 1000*n_particles. Each iteration samples a single model and performs ABC using a single particle.
• max_batch_size::Int: The maximum batch size for the emulator when making predictions.

Returns

A ModelSelectionOutput object that contains which models are supported by the observed data.

ModelSelectionOutput

Contains results of a model selection computation, including which models are best supported by the observed data and the parameter poseteriors at each population for each model.

Fields

• M::Int64: The number of models.
• n_accepted::AbstractArray{AbstractArray{Int64,1},1}: The number of parameters accepted by each model at each population. n_accepted[i][j] contains the number of acceptances for model j at population i.
• threshold_schedule::AbstractArray{Float64,1}: A set of maximum distances from the summarised model output to summarised observed data for a parameter vector to be included in the posterior.
• smc_outputs::AbstractArray{ABCSMCOutput,1}: A ['SimulatedABCSMCOutput']@(ref) or ['EmulatedABCSMCOutput']@(ref) for each model. Use to find details of the ABC results at each population.
• completed_all_populations::Bool: Indicates whether the algorithm completed all the populations successfully. A successful population is one where at least one model accepts at least one particle.