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Univariate Multiple Independent Change-Point (MICH) Model

Source: R/mich_vector.R
mich_vector.Rd

Fits the univariate version of the MICH model for mean and variance change-points. Number of change-points can either be fixed or mich_vector() will search for the number of changes that maximizes the ELBO when (L_auto | K_auto | J_auto) == TRUE.

Usage

mich_vector(
  y,
  fit_intercept,
  fit_scale,
  standardize,
  J,
  L,
  K,
  J_auto,
  L_auto,
  K_auto,
  J_max,
  L_max,
  K_max,
  pi_j_weighted,
  pi_l_weighted,
  pi_k_weighted,
  tol,
  verbose,
  max_iter,
  reverse,
  detect,
  merge_level,
  merge_prob,
  restart,
  n_search,
  increment,
  omega_j,
  u_j,
  v_j,
  log_pi_j,
  omega_l,
  log_pi_l,
  u_k,
  v_k,
  log_pi_k
)

Arguments

y

A numeric vector. Length \(T\) vector of observations.

fit_intercept

A logical. If fit_intercept == TRUE, then an intercept is estimated, otherwise it is assumed that \(\mu_0 = 0\).

fit_scale

A logical. If fit_scale == TRUE, then the initial precision is estimated, otherwise it is assumed that \(\lambda_0 = 1\).

standardize

A logical. If standardize == TRUE, then y is centered and rescaled before fitting.

L, K, J

Integers. Respective number of mean-scp, var-scp, and meanvar-scp components included in the model. If L_auto == TRUE, K_auto == TRUE, or J_auto == TRUE then L, K, and J lower bound the number of each kind of change-point in the model.

L_auto, K_auto, J_auto

Logicals. If L_auto == TRUE, K_auto == TRUE, and/or J_auto == TRUE, then mich_vector() returns the \(L\) between L and L_max, the \(K\) between K and K_max, and/or the \(J\) between J and J_max that maximize the ELBO (see Appendix C.4 of Berlind, Cappello, Madrid Padilla (2025)).

L_max, K_max, J_max

Integers. If L_auto == TRUE, K_auto == TRUE, or J_auto == TRUE then L_max, K_max, and J_max upper bound the number of each kind of change-point in the model.

pi_l_weighted, pi_k_weighted, pi_j_weighted

Logicals. If TRUE, then the weighted priors specified in Appendix C.2 of Berlind, Cappello, Madrid Padilla (2025) are used.

tol

A scalar. Convergence tolerance for relative increase in ELBO.

verbose

A logical. If verbose == TRUE and L_auto == FALSE, K_auto == FALSE, and J_auto == FALSE then the value of the ELBO is printed every 5000th iteration. If verbose == TRUE and any of L_auto, K_auto, or J_auto are TRUE, then the value of the ELBO is printed for each combinatin of \((L,K,J)\) as mich_vector() searches for the parameterization that maximized the EBLO.

max_iter

An integer. Maximum number of iterations. If ELBO does not converge before max_iter is reached, then converged == FALSE in the returned fit object.

reverse

A logical. If reverse == TRUE then MICH is fit to \(\mathbf{y}_{T:1}\) and the model parameters are reversed in post-processing.

detect

A scalar. The detection criteria. The \(i^{\text{th}}\) component of the model detects a change-point only if the posterior credible set for that component contains fewer than detect indices.

merge_level

A scalar. A value between (0,1) for the significance level to construct credible sets at when merging. A model component is only considered to be a candidate for merging if its merge_level-level credible set contains fewer than detect indices.

merge_prob

A scalar. A value between (0,1) indicating the merge criterion. If the posterior probability that two components identify the same change is greater than merge_level, then those components are merged (see Appendix C.3 of Berlind, Cappello, Madrid Padilla (2025)).

restart

A logical. If restart == TRUE and L_auto, K_auto, or J_auto are TRUE, then after n_search increments of L, K, and/or J, if the ELBO has not increased, mich_vector() will restart by setting the L, K, and J components to the null model initialization (except for the components with maximum posterior probabilities > 0.9) then refit and begin the search again.

An integer. Grid search parameter. Number of times to increment L, K, and/or J before terminating automatic procedure when L_auto, K_auto, or J_auto are TRUE.

increment

An integer. Number of components to increment L, K and J by when L_auto, K_auto, or J_auto are TRUE.

omega_j

A scalar. Prior precision parameter for meanvar-scp components of the model.

u_j

A scalar. Prior shape parameter for meanvar-scp components of the model.

v_j

A scalar. Prior rate parameter for meanvar-scp components of the model.

log_pi_j

A numeric matrix. A \(T \times J\) matrix of prior log change-point location probabilities for each of the \(J\) mean-variance change-points.

omega_l

A scalar. Prior precision parameter for mean-scp components of the model.

log_pi_l

A numeric matrix. A \(T \times L\) matrix of prior log change-point location probabilities for each of the \(L\) mean change-points.

u_k

A scalar. Prior shape parameter for var-scp components of the model.

v_k

A scalar. Prior rate parameter for var-scp components of the model.

log_pi_k

A numeric matrix. A \(T \times K\) matrix of prior log change-point location probabilities for each of the \(K\) variance change-points.

Value

A list. Parameters of the variational approximation the MICH posterior distribution, including:

  • y: A numeric vector. Original data.

  • L,K,J: Integers. Number of mean-scp, var-scp, and meanvar-scp components included in the model.

  • residual: A numeric vector. Residual \(\tilde{\mathbf{r}}_{1:T}\) (see (B.4) of Berlind, Cappello, Madrid Padilla (2025)).

  • mu: A numeric vector. Posterior estimate of \(\Sigma_{\ell=1}^L E[\mu_{\ell,1:T}|\mathbf{y}_{1:T}] + \Sigma_{j=1}^J E[\mu_{j,1:T}|\mathbf{y}_{1:T}]\).

  • lambda: A numeric vector. Posterior estimate of \(\Pi_{k=1}^K E[\lambda_{k,1:T}|\mathbf{y}_{1:T}] \times \Pi_{j=1}^J E[\lambda_{j,1:T}|\mathbf{y}_{1:T}]\).

  • delta: A numeric vector. Posterior estimate of equation (B.4) of Berlind, Cappello, Madrid Padilla (2025).

  • mu_0: A scalar. Estimate of the intercept.

  • lambda_0: A scalar. Estimate of the initial precision.

  • elbo: A numeric vector. Value of the ELBO after each iteration.

  • converged: A logical. Indicates whether relative increase in the ELBO is less than tol.

  • meanvar_model: A list. List of meanvar-scp posterior parameters:

    • pi_bar: A numeric matrix. A \(T \times J\) matrix of posterior change-point location probabilities.

    • b_bar: A numeric matrix. A \(T \times J\) matrix of posterior mean parameters.

    • omega_bar: A numeric matrix. A \(T \times J\) matrix of posterior precision parameters.

    • v_bar: A numeric matrix. A \(T \times J\) matrix of posterior rate parameters.

    • u_bar: A numeric vector. A length \(T\) vector of posterior shape parameters.

    • mu_lambda_bar: A numeric matrix. A \(T \times J\) matrix of scaled posterior mean signals \(E[\lambda_{jt}\mu_{jt}|\mathbf{y}_{1:T}]\).

    • mu2_lambda_bar: A numeric matrix. A \(T \times J\) matrix of scaled posterior squared mean signals \(E[\lambda_{jt}\mu^2_{jt}|\mathbf{y}_{1:T}]\).

    • lambda_bar: A numeric matrix. A \(T \times J\) matrix of posterior precision signals \(E[\lambda_{jt}|\mathbf{y}_{1:T}]\).

  • mean_model: A list. List of mean-scp posterior parameters:

    • pi_bar: A numeric matrix. A \(T \times L\) matrix of posterior change-point location probabilities.

    • b_bar: A numeric matrix. A \(T \times L\) matrix of posterior mean parameters.

    • omega_bar: A numeric matrix. A \(T \times L\) matrix of posterior precision parameters.

    • mu_bar: A numeric matrix. A \(T \times L\) matrix of posterior mean signals \(E[\mu_{\ell t}|\mathbf{y}_{1:T}]\).

    • mu2_bar: A numeric matrix. A \(T \times L\) matrix of posterior squared mean signals \(E[\mu_{\ell t}^2|\mathbf{y}_{1:T}]\).

  • var_model: A list. List of var-scp posterior parameters:

    • pi_bar: A numeric matrix. A \(T \times K\) matrix of posterior change-point location probabilities.

    • v_bar: A numeric matrix. A \(T \times K\) matrix of posterior rate parameters.

    • u_bar: A numeric vector. A length \(T\) vector of posterior shape parameters.

    • lambda_bar: A numeric matrix. A \(T \times K\) matrix of posterior precision signals \(E[\lambda_{kt}|\mathbf{y}_{1:T}]\).