the use of the Fisher-z transform in , the likelihood $\mathcal{L}(\theta |x)$ takes the form of a Gaussian likelihood with mean vector $\mu^{(c)}$ and covariance matrix $\Sigma^{(c)}$. The vector $\mu^{(c)}$ consists of the elements of $\widehat{\zeta}_{j}^{(p,q)(c)}$ $\forall~(j,p,q) \in \mathcal{M}$, whilst similarly $\widehat{\mu}_{k}$ contains the elements $\widehat{\zeta}_{jk;X}^{(p,q)}$ $\forall~j,p,q \in \mathcal{M}$. The Gaussian likelihood hence takes the form $$\mathcal{L} \Big(\hat{\zeta}_{jk;X}|\hat{\zeta_{j}}\big(k/T\big)=\zeta_{j}^{(c)}~\forall~j\Big)\propto \big|\Sigma^{(c)}\big|^{-\frac{1}{2}}\text{exp}\Big(-\tfrac{1}{2}\big\{\big(\hat{\mu}_{k}-\mu^{(c)}\big)^{\top}\big(\Sigma^{(c)}\big)^{-1}\big(\hat{\mu}_{k}-\mu^{(c)}\big)\big\}\Big).$$ In practice, the true mean vectors and covariance matrices of $\widehat{\zeta}_{jk;X}$ are unknown, and they are estimated using the training data. In the examples provided in Section \[sec:examples\], we use a flat (uninformative) prior. However, of course, many other prior specifications could be used in the formulation above to reflect beliefs from application-specific expert knowledge.

The dynamic classification method described here is an offline approach that calculates the probability of belonging to a particular class at each time point. Since we are interested in detecting stripes in DAS data in an online setting, we adapt the existing method to allow for classification of data streams. We describe our approach below.

Online dynamic classification of multivariate series {#sec:method}
====================================================

In order to adapt the existing dynamic classification method outlined in Section \[subsec:DC\] to an online setting, we make use of a moving 