Application of Kalman Filtering with Bayesian formulation in adaptive sampling

Abstract

An extensive amount of research is emphasized on survey designs and estimation procedures related to rare and clustered characteristics of a population. Adaptive Sampling design is the most applicable probabilistic technique to estimate the mean or total of the variable of interest, bearing rarity and clustered characteristics. Since rarity is regarded as a time-dependent feature, such surveys need to be organized constantly over time. No studies so far have investigated the effect of time in the estimation context of Adaptive Sampling. This research therefore captures the need to synthesize this periodic information when conducting a survey using Adaptive Sampling design. A recursive process is employed here that improves the estimate of the population parameter from a practical perspective. “Kalman Filtering” is a well known recursive procedure to use past data. Later, statisticians were able to use that Kalman Filtering technique with the Bayesian formulation. This Bayesian approach is proposed to employ here to improve the estimation in the context of Adaptive Sampling design, utilizing the past data. A simulation study is carried out and it is concluded that the suggested approach substantially improves the estimation accuracy.