How to Utilize the Outputs of Functions

When users execute some functions, the output is Vector{<:PosteriorSample}. The examples of Vector{<:PosteriorSample} are

• Vector{Parameter}: output of posterior_sampler
• Vector{ReducedForm}: output of reducedform
• Vector{LatentSpace}: output of latentspace
• Vector{YieldCurve}: output of fitted_YieldCurve
• Vector{TermPremium}: output of term_premium
• Vector{Forecast}: outputs of conditional_forecasts and scenario_analysis

Each entry of the above vectors is a posterior sample and takes the form of a struct, which is one of the following: Parameter, ReducedForm, LatentSpace, YieldCurve, TermPremium, Forecast. The above six struct have their unique fields. See the API section to see what fields each struct contains. Section Notations explains the specific meanings of the fields.

Extract Posterior Samples of the fields

Vector{<:PosteriorSample} contains posterior samples of the fields of the corresponding struct. You can call posterior samples of a specific field by using getindex. For example, if we want to get posterior samples of phi in Parameter, run

samples_phi = saved_params[:phi]

for saved_params::Vector{Parameter}. Then, samples_phi is a vector, and samples_phi[i] is the i-th posterior sample of phi. Note that samples_phi[i] is a matrix in this case. (Julialang allows Vector to have Array elements.)

Descriptive Statistics of the Posterior Distributions

We extend mean, var, std, median, and quantile from Statistics.jl to Vector{<:PosteriorSample}. These five functions can be conveniently used to calculate descriptive statistics of the posterior distribution, such as the posterior mean or posterior variance. For example, the posterior mean of phi can be calculated by

mean_phi = mean(saved_params)[:phi]

mean_phi[i,j] is the posterior mean of the entry in the i-th row and j-th column of phi. Outputs of all functions(mean, var, std, median, and quantile) have the same shapes as their corresponding parameters. quantile needs the second input. For example, in the case of

q_phi = quantile(saved_params, 0.4)[:phi]

40% of posterior samples of phi[i,j] are less than q_phi[i,j].