Application of the BLE to the Simple Random Sample design

(From Section 2.3.1 of the “Gonçalves, Moura and Migon: Bayes linear estimation for finite population with emphasis on categorical data”)

In a simple model, where there is no auxiliary variable, and a Simple Random Sample was taken from the population, we can calculate the Bayes Linear Estimator for the individuals of the population with the BLE_SRS() function, which receives the following parameters:

Vague Prior Distribuition

Letting \(v \to \infty\) and keeping \(\sigma^2\) fixed, that is, assuming prior ignorance, the resulting estimator will be the same as the one seen in the disgn-based context for the simple random sampling case. 

This can be achieved using the BLE_SRS() function by omitting either the prior mean and/or the prior variance, that is:


  1. We will use the TeachingSampling’s BigCity dataset for this example (actually we have to take a sample of size \(10000\) from this dataset so that R can perform the calculations). Imagine that we want to estimate the mean or the total Expenditure of this population, after taking a simple random sample of only 20 individuals, but applying a prior information (taken from a previous study or an expert’s judgment) about the mean expenditure (a priori mean = \(300\)).

Our design-based estimator for the mean will be the sample mean:

Applying the prior information about the population we can get a better estimate, especially in cases when only a small sample is available:

  1. Example from the help page