Module pointprocesses::likelihood

Utility functions to compute the log-likelihood of the data under the models. The general form is given by $$ \ell(\Theta) = \sum_i \log(\lambda_{t_i}) - \int_0^T \lambda_t dt $$

Structs

HawkesLikelihood

Log-likelihood of the given event data under the Hawkes model. $$ \ell = \sum_{i=1}^N \log\left( \lambda_0 + \sum_{j < i} \alpha e^{-\beta(t_i-t_j)} \right) - \lambda_0 T - \sum_{i=1}^N \frac\alpha\beta \left(1 - e^{-\beta(T - t_i)}\right) $$

Functions

hawkes_likelihood	Log-likelihood of the given event data under the Hawkes model. $$ \ell = \sum_{i=1}^N \log\left( \lambda_0 + \sum_{j < i} \alpha e^{-\beta(t_i-t_j)} \right) - \lambda_0 T - \sum_{i=1}^N \frac\alpha\beta \left(1 - e^{-\beta(T - t_i)}\right) $$
poisson_likelihood	Log-likelihood of the data under the given Poisson model $$ \ell(\lambda) = N\ln\lambda - \lambda T $$