Bayesian dynamic borrowing strategies with power priors and quantifying prior information for circular priors.

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This dissertation concerns two problems in Bayesian prior construction. One is the development of a dynamic historical borrowing strategy tailored for settings with small current or historical data samples. The second concerns strategies for the assessment of circular priors. Chapter two introduces a novel dynamic borrowing method that can be applied in both clinical and non-clinical settings. Recent approaches such as that in Thompson et al. (2021) do not accommodate situations with limited current sample sizes. Our approach integrates data amplification techniques specifically for small data sets. We assess the effectiveness of this method through simulation. In Chapter three, we explore the bioassay validation process, which necessitates borrowing from previous studies. We apply the method introduced in Chapter two to a case study for bioassay validation. The outcomes are then contrasted with results derived from another dynamic borrowing method we present in this chapter. Chapter four shifts focus to the quantification of information contained in a circular prior. Circular data are measurements on a unit circle, with the von Mises model being the most widely used model for such data. We gauge the information contained in priors for the von Mises data model using prior equivalent sample size.

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