Surveys often present responders with answer options formatted as intervals/bins when asking sensitive questions, to preserve privacy, or to simplify cognitive load. Instead of asking for exact age, survey designer may ask for an age group; instead of asking for exact income, the designer may ask for a range; instead of asking how much time a task took, the options may be "5-15 minutes" and "1-2 days" to make it easier for the survey taker to answer the question and to make the analysis of responses easier. In this post we present a simple model which may be used to infer a latent, potentially skewed continuous distribution which can only be observed indirectly through discretized realizations.

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