threshold_finder: Estimating the threshold for tpca changepoint detection
In Tveten/tpcaMonitoring: Simulation Study for Changepoint Detection by TPCA.

Description Usage Arguments Details Value

Description

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threshold_finder(x, mon_type, n, alpha, axes = NULL, p0 = NULL,
  w = 200, rel_tol = c(0.2, 0.1, 0.05, 0.025), thresh_alpha = 0.05,
  init_thresh = NULL, learning_coef = NULL, file_id = NULL)

`x`	The d x m training data matrix, where d is the dimension of the data and m the number of training samples
`mon_type`	Character string signifying which type of monitoring statistic to find the threshold for. Available options: "tpca" and "mixture".
`n`	The length of the segment to monitor for false alarms. See details.
`alpha`	Probability of type I error (false alarm) within the time window . See details.
`axes`	Indices of the principal axes to be used in simulations. MUST be supplied if mon_type == 'tpca'.
`p0`	The mixture probability of a dimension being affected by a change. MUST be supplied if mon_type == 'mixture'.
`w`	The window size (an integer).
`rel_tol`	A vector with the sequence of relative error tolerances allowed at each step towards convergence in the algorithm. See details.
`thresh_alpha`	1 - `thresh_alpha` is the confidence level. See details.
`init_thresh`	Use if a custom initial value for the threshold is wanted.
`learning_coef`	The learning rate is defined as `rel_tol` / `learning_coef`. The default `learning_coef` is 3, which has been found a good choice after a lot of experimenting.
`file_id`	A string that identifies the files associated with the particular threshold beyond the data dimension d, axes/p0, training size m or probability of false alarm alpha.

n and alpha governs the false alarm rate by the relation P(T < n | H_0) <= alpha. The corresponding average run length (arl) is approximately given by n / alpha.

rel_tol and thresh_alpha governs the number of simulations used in each step of the algorithm towards a more and more certain estimate. At each step, the number of simulations is chosen so that [(1 - rel_tol)arl, (1 + rel_tol)arl] approximately covers the true average run length at confidence level thresh_alpha. For example, when the last rel_tol is 0.025, it means that the final estimated threshold corresponds to an average run length of approximately arl +- 0.025 * arl at confidence level thresh_alpha. The algorithm should start with a large relative error tolerance, and then narrow it down for the quickest convergence.

A list with the following components:

threshold: The final estimate

tpca_threshold also creates a .txt file with each line showing summaries of each step in the estimation procedure. The last line corresponds to the final estimate.

Tveten/tpcaMonitoring documentation built on June 4, 2019, 4:04 p.m.