Thomas Augustin — Page 2

arXiv2021

How to Guide Decisions with Bayes Factors

Some scientific research questions ask to guide decisions and others do not. By their nature frequentist hypothesis-tests yield a dichotomous test decision as result, rendering them rather inappropriate for latter types of research questions. Bayes factors, however, are argued to be both able to refrain from making decisions and to be employed in guiding decisions. This paper elaborates on how to use a Bayes factor for guiding a decision. In this regard, its embedding within the framework of Bayesian decision theory is delineated, in which a (hypothesis-based) loss function needs to be specified. Typically, such a specification is difficult for an applied scientist as relevant information might be scarce, vague, partial, and ambiguous. To tackle this issue, a robust, interval-valued specification of this loss function shall be allowed, such that the essential but partial information can be included into the analysis as is. Further, the restriction of the prior distributions to be proper distributions (which is necessary to calculate Bayes factors) can be alleviated if a decision is of interest. Both the resulting framework of hypothesis-based Bayesian decision theory with robust loss function and how to derive optimal decisions from already existing Bayes factors are depicted by user-friendly and straightforward step-by-step guides.

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arXiv2021

Towards a Paradigmatic Shift in Pre-election Polling Adequately Including Still Undecided Voters -- Some Ideas Based on Set-Valued Data for the 2021 German Federal Election

Within this paper we develop and apply new methodology adequately including undecided voters for the 2021 German federal election. Due to a cooperation with the polling institute Civey, we are in the fortunate position to obtain data in which undecided voters can state all the options they are still pondering between. In contrast to conventional polls, forcing the undecided to either state a single party or to drop out, this design allows the undecided to provide their current position in an accurate and precise way. The resulting set-valued information can be used to examine structural properties of groups undecided between specific parties as well as to improve election forecasting. For forecasting, this partial information provides valuable additional knowledge, and the uncertainty induced by the participants' ambiguity can be conveyed within interval-valued results. Turning to coalitions of parties, which is in the core of the current public discussion in Germany, some of this uncertainty can be dissolved as the undecided provide precise information on corresponding coalitions. We show structural differences between the decided and undecided with discrete choice models as well as elaborate the discrepancy between the conventional approach and our new ones including the undecided. Our cautious analysis further demonstrates that in most cases the undecideds' eventual decisions are pivotal which coalitions could hold a majority of seats. Overall, accounting for the populations' ambiguity leads to more credible results and paints a more holistic picture of the political landscape, pathing the way for a possible paradigmatic shift concerning the adequate inclusion of undecided voters in pre-election polls.

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