Modelling Rare Events in an Adaptive Cluster Sampling Design with Heterogeneity among Networks and within the Network Units

Abstract

Rare events population (φ) is hard-to-reach, sparsely distributed and clustered; an Adaptive Cluster Sampling (ACS) is the design to collect information from φ. Researchers and Policy Makers have modelled φ in ACS design with homogeneity assumptions. This study modelled φ with heterogeneity among networks and within the network units. Data from the International Institute of Tropical Agriculture on Culcasia Scandens, an understory plant and simulation were used to validate the model. Estimators for total and average number of rare events were derived and their statistical properties were examined. Bayesian Model was embedded in the designed ACS to develop the model for predicting the total number of rare events. Parameters α, β and λ were used in the model to control the expected number of grid cells with rare events, the conditional expected number of sub-network and expected number of rare events in each sub-network respectively. Markov Chain Monte-Carlo Algorithm with R and Winbugs software were used to estimated these parameters. The robustness of the model was examined and its Sensitivity Analysis was carried out. Diagnostic checks were done and the proposed model was compared with the existing model. The samples converged and represented the target posterior and the total number of rare events estimated lies within the 95% HPD credible interval. The derived estimators were unbiased, consistent and efficient. The model was criterion and inference robust with a good fit. The results revealed that rare event was best modelled under heterogeneity assumptions.