(redirected from Marked Point Process)
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References in periodicals archive ?
The scan statistics introduced in this paper allow one to detect high-variance clusters in marked point processes without any parameter to set up.
Cucala, "A distribution-free spatial scan statistic for marked point processes," Spatial Statistics, vol.
Site-saturated nucleation processes and space-time dependent nucleation processes can be modeled by point processes and marked point processes, respectively.
and Andreas Brandt, 1995, Marked Point Processes on the Real Line: The Dynamic Approach (New York: Springer).
Thus, the statement of the theorem follows from the definition of the Palm mark distribution of the stationary marked point process [X.sup.T] = {([X.sub.n], [v.sub.1]([T.sub.sub]([X.sub.n])))}.
Proof Consider the two jointly stationary marked point processes [X.sup.H] = {([X.sub.H,n],[L.sup.o.sub.H,n])} and [X.sup.T].
we can apply Neveu's exchange formula (Neveu, 1976; Maier et al., 2004) for stationary marked point processes which yields Eq.
Let [[PSI].sub.d] = {[[X.sub.i], [R.sub.i]] : i [greater than or equal to] 1} be a stationary, independently marked point process in [R.sup.d] with generic non-negative mark [R.sub.0] having the df [F.sub.d] (r), r [greater than or equal to] 0.
The system of non-empty s-spheres [B.sub.s]([[bar.X].sub.i],[[bar.R].sub.i]) is completely described by the stationary marked point process [[bar.PSI].sub.s] = {[[[bar.Y].sub.i], [[bar.R].sub.i]] : i [greater than or equal to] 1} in [R.sup.s] with intensity measure [[bar.[LAMBDA].sub.s] (A x (0, r]) = [[lambda].sub.s] [v.sub.s] (A) [bar.F].sub.s](r), where [[bar.F].sub.s] denotes the df of the 'typical radius' [[bar.R].sub.0].
A birth-and-growth process is made of two main ingredients, a birth process modelled as a marked point process. and a growth process.
It is well known (Bremaud, 1981, Last and Brandt, 1995) that, under general conditions, a marked point process is characterized by its compensator (or stochastic intensity), say v(dt x dx), with respect to the internal history [F.sub.t], of the process.
"Modeling and detection of wrinkles in aging human faces using marked point processes," in Proc.