On a partially observed illness-death model. (English) Zbl 1006.62090
Summary: A biological population with \(N\) individuals assumed to be healthy is monitored over time. A portion of these individuals die from natural causes while other may get infected with a disease and become sick. A number of the sick individuals will then die from natural causes and other may die from the disease. A stochastic model for the various transitions ‘healthy, sick, death’, is studied where it is assumed that the only observed states are deaths. Based on this information, optimal filters for the number of individuals in each state are derived.
MSC:
62P10 | Applications of statistics to biology and medical sciences; meta analysis |
92C60 | Medical epidemiology |
62M20 | Inference from stochastic processes and prediction |
93E11 | Filtering in stochastic control theory |
60G35 | Signal detection and filtering (aspects of stochastic processes) |