Non-representative surveys are commonly used and widely available but suffer from selection bias that generally cannot be entirely eliminated using weighting techniques. Instead, we propose a Bayesian method to synthesize longitudinal representative unbiased surveys with non-representative biased surveys by estimating the degree of selection bias over time. We show using a simulation study that synthesizing biased and unbiased surveys together out-performs using the unbiased surveys alone, even if the selection bias may evolve in a complex manner over time. Using COVID-19 vaccination data, we are able to synthesize two large sample biased surveys with an unbiased survey to reduce uncertainty in now-casting and inference estimates while simultaneously retaining the empirical credible interval coverage. Ultimately, we are able to conceptually obtain the properties of a large sample unbiased survey if the assumed unbiased survey, used to anchor the estimates, is unbiased for all time-points.

翻译：非代表性调查虽常用且广泛可得，但存在选择性偏差，且该偏差通常无法通过加权技巧完全消除。为此，我们提出一种贝叶斯方法，通过随时间估计选择性偏差程度，将纵向代表性无偏调查与非代表性有偏调查进行综合。模拟研究表明，即使选择性偏差随时间呈现复杂演化，综合有偏与无偏调查的效果仍优于仅使用无偏调查。我们利用COVID-19疫苗接种数据，成功将两个大样本有偏调查与一个无偏调查相综合，在降低即时预测与推断估计不确定性的同时，保持了经验可信区间覆盖率。最终，若用于锚定估计的无偏调查在所有时间点均保持无偏性，我们即可在概念上获得大样本无偏调查的特性。