Table 7.

Overview of the proposed augmented GMMPP

Component	Description	Prior
Y	Observed Poisson process
$g_k$	kth functional form
V	States of the DTMC that determines the functional forms of the IF of Y
W	Times of the DTMC that determines the functional forms of the IF of Y
T	Non-virtual jump times of the DTMC—indicate an actual change in the IF
U	Virtual jump times of the DTMC
R	A set with the initial value of the IF at each of the non-virtual jump times	1. Continuous prior when the initial value is the same in all visits of each functional form. 2. Degenerate conditional prior to guarantee a continuous trajectory for the IF. 3. Continuous prior for the constant functional form and discrete prior for each of all the others when the initial value varies among visits to the same $g_k$
${\theta }_k$	Inverse of the mean waiting time of the IF at $g_k$	Gamma
’ ${\theta }_{k·}$	Vector of transition probabilities from $g_k$ to each of the K functional forms	Dirichlet
$\psi$	Parameters indexing the functional forms	Various