Population-sample regression in the estimation of population proportions

A method comprising:

• specifying a desired margin of error for a Bayesian point estimate of an actual population mean of the measurements of individuals in each of two or more distinctly different groups on a single specified real-number scale on which the mean measurement of the combined groups is equal to zero;
• determining an equal sample size for each of the groups needed to achieve the desired margin of error by simulating for one of the groups samples of different sizes, each having a Bayesian point estimate equal to the desired margin of error plus zero, which is the population mean as well as the sample mean of the combined groups, the determined sample size being the one yielding the desired margin of error;
• and
• obtaining from each of the populations of individuals an independent random sample of the size determined to yield the desired margin of error;
• and estimating the actual population mean of individuals in each group separately from a simple Bayesian regression of the actual population mean for the group on the computed mean of measurements of individuals in the sample obtained from the group using a classical, non-Bayesian estimator of a square of the correlation between the population means and the sample means of the two groups as the regression coefficient, wherein said sample size is less than a sample size required to achieve said desired margin of error.

A non-transitory computer-readable medium having instructions stored thereon that, responsive to execution by an electronic system, cause said electronic system to perform operations, the operations comprising:

• specifying a desired margin of error for a Bayesian point estimate of an actual population proportion of individuals choosing a particular one of a plurality of options;
• determining a sample size needed to achieve the desired margin of error by simulating samples of different sizes, each yielding a Bayesian point estimate equal to the desired margin of error plus a number equal to one divided by the number of the plurality of options, the determined sample size being the one yielding the desired margin of error;
• obtaining from a population of individuals each choosing one of the plurality of options an independent random sample of the size determined to yield the desired margin of error;
• and
• estimating the actual population proportion of individuals choosing the particular one of the plurality of options from a simple Bayesian regression of the estimated population proportion on the computed proportion of individuals in the sample choosing the particular one of the plurality of options using an unbiased classical, non-Bayesian estimator of a square of the correlation between the population proportions and the sample proportions over the plurality of options as the regression coefficient, wherein said sample size is less than a sample size required to achieve said desired margin of error determined without said simulating and said estimating.

A non-transitory computer-readable medium having instructions stored thereon that, responsive to execution by an electronic system, cause said electronic system to perform operations, the operations comprising:

• specifying a desired margin of error for a Bayesian point estimate of an actual population mean of the measurements of individuals in each of two or more distinctly different groups on a single specified real-number scale on which the mean measurement of the combined groups is equal to zero;
• determining an equal sample size for each of the groups needed to achieve the desired margin of error by simulating for one of the groups samples of different sizes, each having a Bayesian point estimate equal to the desired margin of error plus zero, which is the population mean as well as the sample mean of the combined groups, the determined sample size being the one yielding the desired margin of error;
• obtaining from each of the populations of individuals an independent random sample of the size determined to yield the desired margin of error;
• and
• estimating the actual population mean of individuals in each group separately from a simple Bayesian regression of the actual population mean for the group on the computed mean of measurements of individuals in the sample obtained from the group using a classical, non-Bayesian estimator of a square of the correlation between the population means and the sample means of the two groups as the regression coefficient, wherein said sample size is less than a sample size required to achieve said desired margin of error.