cedalion.math package

Submodules

cedalion.math.ar_irls module

cedalion.math.ar_irls.ar_irls_GLM(
y,
x,
pmax: int | None = 40,
M=<statsmodels.robust.norms.TukeyBiweight object>,
)[source]

This function implements the AR-IRLS GLM model.

The autoregressive iteratively reweighted least squares GLM model is described in Barker et al. [BAH13]. By estimating prewhitening filters it addresses serial correlations and confounding noise components in the signal and avoids the inflated false positive rates observed when fitting the GLM with ordinary least squares.

Parameters:

  • y – Dependent variable time series (pandas Series or NDTimeSeries with a "time" dimension).

  • x – Design matrix (pandas DataFrame).

  • pmax – Maximum AR model order to consider. If None, set to 2 × ceil(sampling_rate). A value of 4–5× the sampling rate is sufficient; do not set it excessively high as it reduces the number of usable time points.

  • M – Robust norm for the IRLS step (default: Tukey bi-weight, c=4.685). Tuning constant reference values: 4.685 → 95% efficiency, 4.00 → ~90%, 3.55 → ~85%.

Returns:

Fitted statsmodels.RLM results object containing betas, t-stats, and residuals after prewhitening.

Note

Do not low-pass filter before calling this function — the AR step needs access to the full spectrum to estimate stable prewhitening filters. High-pass filtering is acceptable; prefer Legendre polynomials or discrete cosine terms in the design matrix over regular polynomials.

Initial Contributors:

Ted Huppert | huppert1@pitt.edu | 2024

cedalion.math.ar_model module

cedalion.math.ar_model.bic_arfit(dd, pmax=30)[source]

This function computes the ar coefficients up to a max model order.

BIC is used to select the model

Parameters:

  • dd – pd.Series

  • pmax – int (default 30)

Returns:

sm.tsa.AutoReg results class (includes intercept term)

cedalion.math.ar_model.fit_ar_coefs(data, pmax=12)[source]

This function loops over a timeseries and computs the AR-coefficients.

Parameters:

  • data – xr.DataArray time course

  • pmax – int (default 12)

Returns:

Array[channels,types] of lists of AR stats results classes

cedalion.math.ar_model.ar_filter(data, pmax=12)[source]

This function computes and applies an AR filter on a data time series.

Parameters:

  • data – xr.DataArray

  • pmax – int (default=12)

cedalion.math.resample module

cedalion.math.resample.resample(data: DataArray, Fs: float = 4)[source]

Function for temporally resampling (up or down) a time series.

Parameters:

  • data – xr.DataArray

  • Fs – new sample rate (as float)

Returns:

resampled data

cedalion.math.stats_helpers module

cedalion.math.stats_helpers.BenjaminiHochberg(p: ndarray)[source]

Apply Benjamini-Hochberg FDR correction for multiple comparisons.

See http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3530395/

Parameters:

p – Array of uncorrected p-values, arbitrary shape.

Returns:

Array of FDR-corrected q-values, same shape as p, clipped to [0, 1].

Module contents

Autoregressive Modeling, Stats Helpers and (Re-)Sampling.