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This page describes the operations needed to evaluate the posterior density and the likelihood function of a model

== LogPosteriorDensity ==
 * evaluate log-likelihood (!LogLikelihoodMain)
 * evaluate log prior density
 * returns the sum of log likelihood and log prior density

== LogPriorDensity ==
 * evaluate log prior density for each estimated parameter
 * returns the sum of the log prior densities
=== Data ===
 * stl::vector with prior density parameters for each estimated parameter (see EstimationModule)


== LogLikelihoodMain ==
 * evaluate log-likelihood for each subsample
 * returns the sum of the above
=== Data ===
 * stl::vector of pairs with initial period and number of periods for each subsample

== LogLikelihoodSubSample ==
 * update parameters (including covariance matrices)
 * detrend data
 * compute model solution
 * if first subsample
   * initialize Kalman filter
 * run Kalman filter
 * returns log likelihood
=== Data ===
 * observed data
 * detrended data
 * state space representation matrices

== UpdateParameters ==
 * for each estimated parameter, reset its value in model's data members, if it belongs to the estimated subsample
=== Data ===
 * stl::vector of a structure with type, position, and relevant subsample for each estimated parameter

== DetrendData (low priority) ==
 * remove possible constants and possible linear trends from observed data
=== Data ===
 * formulas for linear trends

== ComputeModelSolution ==
 * compute the steady state
 * computes first order approximation

== InitializeKalmanFilter ==
 * set <<latex($a_0=0$)>>
 * if model is declared stationary
   * compute covariance matrix of endogenous variables (<<latex($P^\star$)>>) by doubling algorithm
 * else (not prioritary)
   * compute Schur transformation of state space model
   * recover order of integration of the model (still need to determine exact algorithm)
   * recover list of stationary/non-stationary factors
   * compute covariance matrix of stationary endogenous variables (<<latex($P^\star$)>>) by doubling algorithm
   * set <<latex($P^\infty$)>>
   * compute diffuse Kalman filter for as many periods as order of integration

== KalmanFilter ==
 * vanilla Kalman filter without constant and with measurement error (use scalar 0 when no measurement error)
 * we still need to compare multivariate and univariate filter
 * if multivariate filter is faster, do as in Matlab: start with multivariate filter and switch to univariate filter only in case of singularity