ETAS conditional intensity - used by inlabru

Function to calculate the value of the ETAS model conditional intensity at a specified time given the history of the process.

Usage

cond_lambda(theta, t, th, mh, M0)

Arguments

theta

ETAS parameters as list with names mu, K, alpha, c, p

t

Time at which the conditional intensity is evaluated, scalar

th

Time of the events in the history of the process, vector

mh

Magnitudes of the events in the history of the process, vector

M0

Minimum magnitude threshold

Value

Value of the ETAS conditional intensity calculated at t with history th, mh, scalar

Details

The function takes a single value t and returns the ETAS conditional intensity calculated at t with history th, mh. The ETAS conditional intensity is given by $$\lambda(t | \mathcal H_t) = \mu + \sum_{h: (t_h,m_h) \in \mathcal H_t} K e^{\alpha(m_h - M_0)} \left( \frac{t - t_h}{c} + 1\right)^{-p}$$

Do not use when t is a vector.