bcad 1.0.1

Bootstrap Comparison of Attractor Dimensions

Code and data for running "bootstrap comparison of attractor dimension" (BCAD). BCAD is a method for refuting the existence of causal relations between two observables of a (noisy dynamical) system.

See the paper: Refuting causal relations for synchronized pathogen dynamics.

Installation

pip install bcad

Command line usage

bcad    # Runs BCAD on New York state data

Python usage example

import pandas as pd
from bcad.helpers import load_state, infer, decisions
from bcad.rypdal_sugihara import transform
from bcad.ssa import denoise

# Load bundled data for a single state
df = load_state("New_York")
df = (df - df.mean()) / df.std()

# Parameters
M = int(365 * 3 / 7)  # SSA window: 3 years, weekly data
tau = 12               # time delay for embedding
window = 12            # window for reproduction number
shift = -1             # time shift for R calculation
n_bootstrap = 200      # number of bootstrap resamples

# Denoise with Singular Spectrum Analysis with automatic optimal hard thresholding via Gavish and Donoho's method
dd = denoise(df, M=M)

# Compute reproduction number from pneumonia/influenza incidence
dd = dd.assign(R=transform(dd.pi_inc, window=window, shift=shift)).dropna()

# Run BCAD
res = infer(dd, n_bootstrap=n_bootstrap, tau=tau, predictors=['R', 'AH'])
aggd = decisions(res)

# BCAD refutes a causal relation X -> Y when dim(X) > dim(Y) significantly
aggd = aggd[['pval', 'theta_hat', 0.95, 0.99]].assign(refute=aggd[0.95] < 0)
print(aggd)