TY - UNPB
T1 - Optimal decision rules for marked point process models
AU - van Lieshout, Marie-Colette
PY - 2023/9/7
Y1 - 2023/9/7
N2 - We study a Markov decision problem in which the state space is the set of finite marked point configurations in the plane, the actions represent thinnings, the reward is proportional to the mark sum which is discounted over time, and the transitions are governed by a birth-death-growth process. We show that thinning points with large marks is optimal when births follow a Poisson process and marks grow logistically. Explicit values for the thinning threshold and the discounted total expected reward over finite and infinite horizons are also provided. When the points are required to respect a hard core distance, upper and lower bounds on the discounted total expected reward are derived.
AB - We study a Markov decision problem in which the state space is the set of finite marked point configurations in the plane, the actions represent thinnings, the reward is proportional to the mark sum which is discounted over time, and the transitions are governed by a birth-death-growth process. We show that thinning points with large marks is optimal when births follow a Poisson process and marks grow logistically. Explicit values for the thinning threshold and the discounted total expected reward over finite and infinite horizons are also provided. When the points are required to respect a hard core distance, upper and lower bounds on the discounted total expected reward are derived.
U2 - 10.48550/arXiv.2309.03752
DO - 10.48550/arXiv.2309.03752
M3 - Working paper
SP - 1
EP - 14
BT - Optimal decision rules for marked point process models
PB - ArXiv.org
ER -