EM Algorithm: Expectation Step (E-step)

This function calculates the posterior distribution of the latent variables and computes the expected values for different model configurations. It approximates expectations using methods like Gaussian-Legendre (GL), Monte Carlo (MC), or Trapezoidal (TI) methods.

Usage

E_z(
  serial,
  model,
  method = "gl",
  period = c(0, 1),
  par1,
  gamma_par = c(2, 0.1),
  data,
  n_samples = NULL,
  n_intervals = NULL,
  n_points = NULL
)

Arguments

serial: Integer, specifies the expected value to calculate (e.g., 1 to 6).
model: Character, specifies the model type ("M0", "M1", "M2", etc.).
method: Character, specifies the numerical method for approximation ("gl", "mc", or "ti").
period: Numeric vector of length 2, defines the integration limits (e.g., `c(0, 1)`).
par1: List, model parameters for each variable. Includes `delta_Lambda` and `delta_Lambda0`.
gamma_par: Numeric vector, parameters for the gamma distribution, used for specific models (e.g., `c(2, 0.1)`).
data: Matrix, observed data where rows represent samples and columns represent variables.
n_samples: Integer, the number of random samples for Monte Carlo integration. Default is NULL.
n_intervals: Integer, the number of intervals for Trapezoidal integration. Default is NULL.
n_points: Integer, the number of points for Gaussian-Legendre integration. Default is NULL.

Value

Numeric matrix, expected values for the latent variables based on the provided `serial` and `model`. The result varies depending on the type of expectation (e.g., posterior mean, variance, etc.).