deletions | additions       diff --git a/Hidden Markov Models.tex b/Hidden Markov Models.tex  index 979423c..160f7cf 100644  --- a/Hidden Markov Models.tex  +++ b/Hidden Markov Models.tex 
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s_t =& \exp(\lambda_t) w(\theta_t) + B_t +\xi\\  \end{align*}  For the phase $\theta$ we used a mean period $T_1$ of $24$h and a phase diffusion coefficient $\sigma_{\theta}$ of $0.15 [(rad (rad  / h )^{1/2}]$. )^{1/2}$.  For the amplitude $\lambda$ we used a timescale $\gamma_{\lambda}^{-1}$ of $30$h a mean zero value $\mu_{\lambda}$ and a diffusion coefficient of $0.07$. For the background $B$ we used a timescale of $30$h, a zero mean and diffusion coefficient of $0.022$. These parameters were choosen such that the amplitude and the background smoothly follow the maximums and the minimums of the signal, without explaining variations in the shape of the signal, which we aim to capture in the phase. Finally the variance of the emmission was set to $0.1$.