In the wake of the 2016 election, the polling industry has no shortage of critics. While these are difficult times for the industry as a whole, there are exciting innovations happening that will serve to benefit and revitalize the industry for years. One of these exciting innovations is Probability Proportional to Size (PPS) sampling. I will elaborate on what PPS sampling is and provide a mathematical foundation for its use in polling. I also discuss what some of the myriad of issues plaguing the polling industry are and then show how PPS sampling can be used to remedy many of these ills. Finally, I look at a real-world application of PPS sampling. The Mia Love internal polling team, Y2 Analytics, granted me access to their PPS data. I use it to show that we can accurately model the electorate using PPS samples and that polls conducted by this method are at least as accurate as other polls using simple random samples.

Pfeffermann, Krieger e Rinott (1998) apresentaram uma metodologia para modelar processos de amostragem que pode ser utilizada para avaliar se este processo de amostragem é informativo. Neste cenário, as probabilidades de seleção da amostra são aproximadas por uma função polinomial dependendo das variáveis resposta e concomitantes. Nesta abordagem, nossa principal proposta é investigar a aplicação do teste de significância FBST (Full Bayesian Significance Test), apresentado por Pereira e Stern (1999), como uma ferramenta para testar a ignorabilidade amostral, isto é, para avaliar uma relação de significância entre as probabilidades de seleção da amostra e a variável resposta. A performance desta modelagem estatística é testada com alguns experimentos computacionais. / Pfeffermann, Krieger and Rinott (1998) introduced a framework for modeling sampling processes that can be used to assess if a sampling process is informative. In this setting, sample selection probabilities are approximated by a polynomial function depending on outcome and auxiliary variables. Within this framework, our main purpose is to investigate the application of the Full Bayesian Significance Test (FBST), introduced by Pereira and Stern (1999), as a tool for testing sampling ignorability, that is, to detect a significant relation between the sample selection probabilities and the outcome variable. The performance of this statistical modelling framework is tested with some simulation experiments.

We have considered the problem in which a biased sample is selected from a finite population, and this finite population itself is a random sample from an infinitely large population, called the superpopulation. The parameters of the superpopulation and the finite population are of interest. There is some information about the selection mechanism in that the selection probabilities are linearly related to the measurements. This is typical of establishment surveys where the selection probabilities are taken to be proportional to the previous year's characteristics. When all the selection probabilities are known, as in our problem, inference about the finite population can be made, but inference about the distribution is not so clear. For continuous measurements, one might assume that the the values are normally distributed, but as a practical issue normality can be tenuous. In such a situation a transformation to normality may be useful, but this transformation will destroy the linearity between the selection probabilities and the values. The purpose of this work is to address this issue. In this light we have constructed two models, an ignorable selection model and a nonignorable selection model. We use the Gibbs sampler and the sample importance re-sampling algorithm to fit the nonignorable selection model. We have emphasized estimation of the finite population parameters, although within this framework other quantities can be estimated easily. We have found that our nonignorable selection model can correct the bias due to unequal selection probabilities, and it provides improved precision over the estimates from the ignorable selection model. In addition, we have described the case in which all the selection probabilities are unknown. This is useful because many agencies (e.g., government) tend to hide these selection probabilities when public-used data are constructed. Also, we have given an extensive theoretical discussion on Poisson sampling, an underlying sampling scheme in our models especially useful in the case in which the selection probabilities are unknown.

Pfeffermann, Krieger e Rinott (1998) apresentaram uma metodologia para modelar processos de amostragem que pode ser utilizada para avaliar se este processo de amostragem é informativo. Neste cenário, as probabilidades de seleção da amostra são aproximadas por uma função polinomial dependendo das variáveis resposta e concomitantes. Nesta abordagem, nossa principal proposta é investigar a aplicação do teste de significância FBST (Full Bayesian Significance Test), apresentado por Pereira e Stern (1999), como uma ferramenta para testar a ignorabilidade amostral, isto é, para avaliar uma relação de significância entre as probabilidades de seleção da amostra e a variável resposta. A performance desta modelagem estatística é testada com alguns experimentos computacionais. / Pfeffermann, Krieger and Rinott (1998) introduced a framework for modeling sampling processes that can be used to assess if a sampling process is informative. In this setting, sample selection probabilities are approximated by a polynomial function depending on outcome and auxiliary variables. Within this framework, our main purpose is to investigate the application of the Full Bayesian Significance Test (FBST), introduced by Pereira and Stern (1999), as a tool for testing sampling ignorability, that is, to detect a significant relation between the sample selection probabilities and the outcome variable. The performance of this statistical modelling framework is tested with some simulation experiments.