+ Parameter estimation
+ The main function for Bayesian parameter estimation,
+ stan_igbm, allows for specification of a
+ joint distribution for the outcomes (in this case, the age-specific
+ mortality counts) and the unknown quantities, which is expressed by
+ the likelihood for the outcomes conditional on the unknowns
+ multiplied by a marginal prior distribution for the unknowns. This
+ joint distribution is proportional to the posterior distribution of
+ the unknowns conditional on the observed data. Prior beliefs for the
+ unknown model parameters can be expressed by a selection of
+ appropriate distributions available to the end-user.
+ Bernadette uses the framework offered by the
+ probabilistic programming language Stan
+ (Carpenter
+ et al., 2017) to specify a model and draw from the posterior
+ distribution using MCMC. The user-specified model is internally
+ translated into data that are passed to a precompiled
+ Stan program and then it is fit using
+ sampling methods from rstan
+ (Stan
+ Development Team, 2023).
+
+
+ Post-processing
+ The output of stan_igbm contains draws
+ from the posterior distribution, which can be post-processed and
+ visualized to extract insights about the mechanism of disease
+ transmission over a given period.
+
+
+ plot_posterior_cm: Density plots of
+ the posterior distribution of the random contact matrix.
+
+
+ posterior_infections: Summarizes the
+ posterior distribution of the infection counts over time
+ (age-specific and aggregated). It is accompanied by the plotting
+ function plot_posterior_infections.
+
+
+ posterior_mortality: Summarizes the
+ posterior distribution of the mortality counts over time
+ (age-specific and aggregated). It is accompanied by the plotting
+ function plot_posterior_mortality.
+
+
+ posterior_transmrate: Summarizes the
+ posterior distribution of the age-specific transmission rate. It
+ is accompanied by the plotting function
+ plot_posterior_transmrate.
+
+
+ posterior_rt: Summarizes the posterior
+ distribution of the time-varying reproduction number. The
+ posterior trajectory is visualized with
+ plot_posterior_rt.
+
+
+ The output of stan_igbm can additionally
+ be used to compute approximate leave-one-out cross-validation with
+ the loo R package
+ (Vehtari
+ et al., 2023). This enables estimation of information
+ criteria which are considered when comparing among a set of
+ alternative models for the same data.
+
+