Initialisation

Model Initialisation

To initialise a model for profile likelihood evaluation we use initialise_LikelihoodModel which returns a struct of type LikelihoodModel. This struct contains all the information we require for the PWA workflow and will also contain computed profiles and profile-wise predictions.

LikelihoodBasedProfileWiseAnalysis.initialise_LikelihoodModel — Function

initialise_LikelihoodModel(loglikefunction::Function,
    predictfunction::Union{Function, Missing},
    errorfunction::Union{Function, Missing}
    data::Union{Tuple, NamedTuple},
    θnams::Vector{<:Symbol},
    θinitialguess::AbstractVector{<:Real},
    θlb::AbstractVector{<:Real},
    θub::AbstractVector{<:Real},
    θmagnitudes::AbstractVector{<:Real}=Float64[];
    <keyword arguments>)

Initialises a LikelihoodModel struct, which contains all model information, profiles, samples and predictions. Solves for the maximum likelihood estimate of loglikefunction.

Arguments

loglikefunction: a log-likelihood function to maximise which takes two arguments, θ and data, in that order, where θ is a vector containing the values of each parameter in θnames and data is a Tuple or NamedTuple - see data below. Set up to be used in a maximisation objective.
predictfunction: a prediction function to generate model predictions from that is paired with the loglikefunction. Requirements for the prediction function can be seen in add_prediction_function!. It can also be missing if no function is provided to initialise_LikelihoodModel, because predictions are not required when evaluating parameter profiles. The function can be added at a later point using add_prediction_function!.
errorfunction: an error function used to predict realisations from predictions generated with predictfunction. Requirements for the error function can be seen in add_error_function!. It can also be missing if no function is provided to initialise_LikelihoodModel, because predictions are not required when evaluating parameter profiles. The function can be added at a later point using add_error_function!.
data: a Tuple or a NamedTuple containing any additional information required by the log-likelihood function, such as the time points to be evaluated at.
θnames: a vector of symbols containing the names of each parameter, e.g. [:λ, :K, :C0].
θinitialguess: a vector containing the initial guess for the values of each parameter. Used to find the MLE point.
θlb: a vector of lower bounds on parameters.
θub: a vector of upper bounds on parameters.
θmagnitudes: a vector of the relative magnitude of each parameter. If not provided, it will be estimated using the difference of θlb and θub with LikelihoodBasedProfileWiseAnalysis.calculate_θmagnitudes. Can be updated after initialisation using setmagnitudes!.

Keyword Arguments

optimizationsettings: optimization settings used to optimize the log-likelihood function using Optimization.jl. Default is default_OptimizationSettings() (see default_OptimizationSettings).
uni_row_prealloaction_size: number of rows of uni_profiles_df to preallocate. Default is missing (a single row).
biv_row_preallocation_size: number of rows of biv_profiles_df to preallocate. Default is missing (a single row).
dim_row_preallocation_size: number of rows of dim_samples_df to preallocate. Default is missing (a single row).
find_zero_atol: a Real number greater than zero for the absolute tolerance of the log-likelihood function value from the target value to be used when searching for confidence intervals/boundaries. Default is 0.001.
show_progress: Whether to show the progress of profiling and predictions.

Array initialisation within a log-likelihood function

If you initialise an array within the provided log-likelihood function, e.g. using zeros, then for automatic differentiation methods to work you need to also initialise the type of the array to be based on the type of the input values of θ. Otherwise, zeros will by default create an array with element types Float64 which will likely return errors. For example, use:

my_new_array = zeros(eltype(θ), dimensions)

where eltype passes the element type of the θ vector into the zeros function.