Calculate Batch Size for Bookend Strategy

Predicts the number of simulations needed to reach a target ESS based on the observed ESS trajectory. Fits sqrt and linear models to the cumulative (n_sims, threshold_ESS) data and predicts from the sqrt model unless the linear model fits clearly better. A log model is also fitted, but only as a diagnostic (a warning when it fits best); it is never used for prediction.

Usage

calc_bookend_batch_size(
  ess_history,
  target_ess,
  max_total_sims,
  target_r_squared = 0.95
)

Arguments

ess_history

ESS measurements from calibration phase

target_ess

Target ESS value

max_total_sims

Maximum total simulations allowed

target_r_squared

Target R-squared for ESS regression (default: 0.95)

Value

List with batch size recommendation. phase is one of "complete", "low_confidence", "no_progress" or "predictive".

Details

The extrapolation is only defined when the chosen model's ESS increases with the number of simulations. When its slope is zero or negative the target is unreachable on the fitted trajectory, and the function returns phase = "no_progress" with batch_size = 0 instead of squaring a negative root into a positive requirement.