Path sampling

Abstract

In sampling spatial populations, one part of the cost is due to the distance travelled to observe all of the units in a sample. Cluster sampling is one such sampling design which is often used specifically to address this issue. Even in cluster sampling, the researcher may have to travel great distances from the cluster to cluster selected. In an optimal setting, when sampling costs are mainly a function of distance travelled, researchers could sample all of the units in the path travelled during the sampling. For this reason, the authors are introducing a new sampling design, called “path sampling,” which offers exactly the latter ability to sample all of the units in the researcher’s path traversed during the sampling. Path sampling is a design in which the researcher selects a path or paths from start to finish, as opposed to selecting units. By applying the Horvitz-Thompson estimator, path sampling offers unbiased estimators for both mean and variance. This dissertation covers the pros and cons of path sampling in comparison to simple random sampling, cluster sampling, and random walk sampling. The simulation results show that path sampling gives the smallest value of the expected number of units traveled for the same sample size among four sampling designs. Thus, path sampling has less traveling or less cost. However, path sampling is less efficient than cluster sampling, simple random sampling without replacement, and random walk sampling in the population with low variation of y-values among clusters. On the other hand, path sampling is more efficient than random walk sampling in a population with high variation of y-values among clusters. Moreover, path sampling is more efficient than cluster sampling and SRSWOR in a population with high variation of y-values among clusters with the path starting or ending point on high y-values.