Fig. 3: Accurate estimation of timescales and uncertainty quantification with the aABC algorithm.
From: A flexible Bayesian framework for unbiased estimation of timescales
The same synthetic data as in Fig. 1 for T = 1 s. a, Data are generated from an OU process with τ = 20 ms. Left: the shape of the data autocorrelation is accurately reproduced by the autocorrelation of synthetic data from the generative model with the MAP estimate parameters (τMAP = 20.2 ms), but it cannot be captured by the direct exponential fit. Middle: the marginal posterior distributions (histograms overlaid with Gaussian kernel smoothing) include the ground-truth timescales, whereas direct exponential fits underestimate the ground-truth timescales. The width of the posteriors indicates the estimation uncertainty. Right: the convergence of the aABC algorithm is defined based on accR, which decreases together with ε over the iterations of the algorithm. Data are plotted from the second iteration. The initial error threshold for all fits was set to 1. b, Same as a for data from a linear mixture of an OU process with τ = 20 ms and an oscillation with f = 2 Hz; τMAP = 60.5 ms. c, Same as a for data from an inhomogeneous Poisson process with two timescales: τ1 = 5 ms and τ2 = 80 ms. τ1,MAP = 4.7 ms and τ2,MAP = 80 ms. Other parameters are provided in Supplementary Tables 1 and 2.
