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Those values result of a trade off between sparsity and precision of the model.  \subsubsection{A first approach: histogram}  The easiest way to approximate the probability distribution i.e. all $p(x,y)$ for $(x,y)$ one of  the bin's coordinates of the discretized field (we will come to that later) is to use histogram. $p(x,y)$ is then the occurence ratio of $(x,y)$ among the whole set of positions traveled by the trajectory $T$. in another words $p(x,y)$ is given by:  \[P_{hist}((x,y),T) = \sum_{(x',y')\in T}\mathbb{1}_{(x=x',y=y')}\]  Similarly the histogram of joint distribution of two trajectories $T$ and $S$ will be given by:  \[P_{hist}((x_{1},y_{1},x_{2},y_{2}),TxS) = \sum_{(x'_{1},y'_{1},x'_{2},y'_{2})\in TxS}\mathbb{1}_{((x_{1}=x'_{1},y_{1}=y'_{1},x_{2}=x'_{2},y_{2}=y'_{2}))}\]