How to Utilize the Outputs of Functions

When you execute some functions, the output is Vector{<:PosteriorSample}. Examples of Vector{<:PosteriorSample} include

• 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_forecast and conditional_expectation

Each entry in the vectors above is a posterior sample and takes the form of a struct: Parameter, ReducedForm, LatentSpace, YieldCurve, TermPremium, or Forecast. The above six structs have unique fields. See the API section for the fields each struct contains. The Notations section 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 access posterior samples of a specific field by using getindex. For example, if you 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. (Julia allows vectors to have array elements.)

Descriptive Statistics of the Posterior Distributions

The package extends mean, var, std, median, and quantile from Statistics.jl to Vector{<:PosteriorSample}. These five functions can be 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. The outputs of all functions (mean, var, std, median, and quantile) have the same shapes as their corresponding parameters. quantile needs a 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].