for the training signals that are known to belong to that particular class. Note that in practice, the Gaussian distribution will be an approximation to the true distribution of the (finite sample) Fisher z-transformed coherence estimates. We recommend that, as for any such analysis, this assumption is validated for any data set analysed.

As in [@Krz], classification is performed using a subset of wavelet coefficients that show the largest difference between the classes in terms of the transformed coherence. The subset, denoted by $\mathcal{M}$, consists of the scale and channel indices $(j,p,q)$ for $p<q$. $\mathcal{M}$ is made up of the coefficients that have the largest values of the discrepancy measure $\bigtriangleup_{j}^{(p,q)}$ given by $$\bigtriangleup_{j}^{(p,q)}=\displaystyle\sum\limits_{c=1}^{N_{c}} \displaystyle\sum\limits_{g=c+1}^{N_{c}} \Biggl\lvert \frac{\widehat{\zeta}_{j}^{(p,q)(c)}-\widehat{\zeta}_{j}^{(p,q)(g)}}{\sqrt{\text{var}\big(\widehat{\zeta}_{j}^{(p,q)(c)}\big)+\text{var}\big(\widehat{\zeta}_{j}^{(p,q)(g)}\big) }} \Biggr\rvert. \label{disind}$$ In practice, a proportion $\wp$ is typically chosen and the subset $\mathcal{M}$ are those $\wp$% of time-scale indices with the largest discrepancies [@Krz]. In order to estimate the probability that the signal $\mathbf{X}_{t}$ belongs to a particular class at a given time, the transformed coherence $\widehat{\zeta}_{jk;X}$ is first estimated, before using Bayes’ theorem to obtain $$\label{eq:bayes}
\text{Pr}\Big[C(k)=c \bigl\lvert\widehat{\zeta}_{jk;X}\Big] \propto \text{Pr}\big[C(k)=c\big]\mathcal{L}\Big(\widehat{\zeta}_{jk;X}\bigl\lvert\zeta_{j}(k/T)=\xi_{j}^{(c)} \quad \forall j \Big),$$ where $\mathcal{L}(\theta |x)$ is the likelihood and $ \text{Pr}\big[C(k)=c\big]$ is a prior probability [@ParkDC]. Due to 