In the second part, observations of deterministic chaos are presented and characterized by the time trace, spectral density, phase portrait, Poincaré section and return map.
Convergence was assessed by trace and density plots, the autocorrelation of model parameters from posterior distributions and diagnostic tests [ 36] with none indicating non-convergence.
Convergence detection is done using standard graphic tools (trace and density plots) and the commonly used Gelman and Rubin diagnostic (Gelman and Rubin, 1992).
Eight independent MCMC chains of the Bayesian multi-trait animal model for the 14 bovine milk fatty acids converged to similar estimates of the variance components, which was confirmed by trace and density plots.
Combined log files were analyzed in Tracer v.1.6 [ 68] to check, if the effective sample sizes (ESS) of parameters represent the posterior distribution adequately; further trace and density plots were checked for convergence of the MCMC and posterior probability distributions in different runs.
From the recorded spectra trace gas densities and temperature fields were derived on a very dense spatial grid.
Traces and densities of body length (X1) and growth rate in length (X2) for repeatabilities (above) and heritabilities (below).
First we check that our truncated set of equations (6) and (8) conserves the trace of the density operator tr = 1 (conservation of probability).
Time trace, power spectral density (PSD), phase-plane plot and Poincaré map are used to characterize the motion of the tube.
Band density trace and quantification were determined using ImageJ National Institutes of Healthh).
The authors should show clear examples of how an alternative trace violates the density.
