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Following the maximun likelihood estimation as done in Klavidko I would like to generalize this to more independent factors . In first istance I would use the transition function at time t as a sum of the non chi squared conditional distributions for each factor: \begin{equation} p_t = p_{1 t} +.. + p_{N t} \end{equation} then take the log of the product of all t times used in the data and optimize: \begin{equation} L = \sum_{t}log(p_t) \end{equation} On the other hand in the paper multi they just optimize the sum of each log product \begin{equation} L = \sum_{t,i}log(p_{i t}) \end{equation} Which one is correct? Thanks

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