Fit!(X::AbstractArray{T}, y::AbstractVector{U}, R; η=1.01,V=30,ζ=1.0,ι=1.0,aΔ=1.0,bΔ=1.0, 
     ν=10, nburn=30000, nsamples=20000, maxburn=50000, mingen=0, maxgen=0, psrf_cutoff=1.01, x_transform=true, suppress_timer=false, 
     num_chains=2, seed=nothing, purge_burn=nothing, filename="parameters.log") where {T,U}

Fit the Bayesian Network Regression model. There are two alternative schemes governing the number of generations.

• In the "traditional" scheme, the algorithm generates nsamp Gibbs samples after nburn burn-in are discarded.
• In the "doubling generation" scheme, the algorithm generates mingen samples and discards the first half. If the Gelman-Rubin PSRF cutoff is not achieved, mingen additional samples will be generated (now considering the first half of all generations as burn-in) until either convergence is achieved or maxgen samples are generated.

By default, the traditional scheme is used. If valid values for mingen and maxgen are supplied then then "doubling generation" scheme will be used.

Road map of fit!:

• Calls generate_samples! for "traditional" scheme or generate_samples_dbl! for "doubling generation" scheme directly
• generate_samples! calls initialize_and_run! on every chain
• initialize_and_run! calls initialize_variables! and gibbs_sample!

Arguments

• X: matrix, required, matrix of unweighted symmetric adjacency matrices to be used as predictors. Two options: 2D matrix with each row the upper triangle of the adjacency matrix associated with one sample 1D matrix with each row the adjacency matrix relating the nodes to one another
• y: vector, required, vector of response variables
• R: integer, required, the dimensionality of the latent variables u, a hyperparameter
• η: float, default=1.01, hyperparameter used for sampling the 0 value of the πᵥ parameter, must be > 1
• ζ: float, default=1.0, hyperparameter used for sampling θ
• ι: float, default=1.0, hyperparameter used for sampling θ
• aΔ: float, default=1.0, hyperparameter used for sampling Δ
• bΔ: float, default=1.0, hyperparameter used for sampling Δ
• ν: integer, default=10, hyperparameter used for sampling M, must be > R
• nburn: integer, default=30000, number of burn-in samples to generate and discard
• nsamples: integer, default=20000, number of Gibbs samples to generate after burn-in
• mingen: integer, default 0, for "doubling generation" the minimum total number of samples to generate (burn-in + retained)
• maxgen: integer, default 0, for "doubling generation" the maximum total number of samples to generate (burn-in + retained)
• psrf_cutoff: float, defalut=1.2, value at which convergence is determined to have been achieved
• x_transform: boolean, default=true, set to false if X has been pre-transformed into one row per sample. Otherwise the X will be transformed automatically.
• suppress_timer: boolean, default=false, set to true to suppress "progress meter" output
• num_chains: integer, default=2, number of separate sampling chains to run (for checking convergence)
• seed: integer, default=nothing, random seed used for repeatability
• purge_burn: integer, default=nothing, if set must be less than the number of burn-in samples (and ideally burn-in is a multiple of this value). After how many burn-in samples to delete previous burn-in samples.
• filename: logfile with the parameters used for the fit, default="parameters.log". The file will be overwritten if a new name is not specified.

Returns

Results object with the state table from the first chain and PSRF r-hat values for γ and ξ

Summary(results::Results;interval::Int=95,digits::Int=3)

Generate summary statistics for results: point estimates and credible intervals for edge coefficients, probabilities of influence for individual nodes

Arguments

• results: a Results object, returned from running Fit!
• interval: (optional) Integer, level for credible intervals. Default is 95%.
• digits: (optional) Integer, number of digits (after the decimal) to round results to. Default is 3.

Returns

A BNRSummary object containing a matrix of edge coefficient point estimates (coef_matrix), a matrix of edge coefficient credible intervals (ci_matrix), and a DataFrame containing the probability of influence of each node (pi_nodes).