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Conditional ACI specification

Source: R/aci-assimilation.R
aci_conditional.Rd

Describes which observed channels carry the causal question and which are conditioned out of it, and by which method. aci_conditional() describes conditional ACI masking; aci_conditional_reduce() is the model reduction method = "reduce" asks for.

Usage

aci_conditional(
  given = NULL,
  method = c("mask", "reduce"),
  target = NULL,
  first_step = c("uniform", "matlab")
)

Arguments

given

Integer or character vector naming the conditioning observed channels x_B. Supply this or target, not both.

method

Either "mask", which gives the conditioning channels' innovations zero weight in the filter, or "reduce", which substitutes them as known forcing.

target

Integer or character vector naming the target observed channels x_A. Supply this or given, not both.

first_step

Either "uniform", which masks the observation precision at every step, or "matlab", which leaves the first slice unmasked as the reference scripts do. "matlab" requires method = "mask".

Value

An object of class aci_conditional_spec.

Estimand

Split the observed process into target and conditioning channels, x = (x_A, x_B), with hidden process y. Conditional ACI is the estimand y(t) -> x_A | x_B: only the target channels x_A transfer information into the hidden posterior, and the conditioning channels x_B are conditioned upon rather than assimilated. "mask" realises it by giving the x_B innovations zero weight in the filter gain, the Riccati term and the online-smoother gain, through an observation-precision matrix supported only on the A block; "reduce" realises it by rewriting the model so x_B enters as a known time series (prescribed forcing). The two coincide when the A-B noise cross-block vanishes, which the reduction checks along the whole path.

target names x_A directly, which is how the reference scripts write the question (h_W(t) -> T_C | (u, T_E, tau, I), ENSO_model_cond_ACI_h_W_unobs.m:1199-1202). given names the complement x_B. Supply exactly one; the other side is derived.

First-slice convention

The reference scripts fill the first slice of the observation-precision array with the full Gram inverse before the target-only overwrite, and mask only the later slices (ENSO_model_cond_ACI_h_W_unobs.m:1197 against :1250). first_step selects between masking every slice, "uniform", and reproducing that asymmetry, "matlab". It is not a round-off-level choice: on a 4001-point ENSO path with h_W hidden and T_C the target it moves the step-2 filter mean by 0.108 and the peak ACI by 0.574, and the difference decays through the record rather than vanishing. It is inert wherever the mask itself is inert. "matlab" applies only to "mask", which is where a masked precision path exists.

See also

aci_conditional_reduce(), aci_filter()

Examples

aci_conditional(given = 2, method = "mask")
#> <aci_conditional_spec> x_B = {2}, method = mask
aci_conditional(target = 1, method = "mask")
#> <aci_conditional_spec> x_A = {1}, method = mask