We describe how aggregation is handled in the Trio system for uncertain and probabilistic data. Because "exact" aggregation in uncertain databases can produce exponentially-sized results, we provide three alternatives: a low bound on the aggregate value, a high bound on the value, and the expected value. These variants return a single result instead of a set of possible results, and they are generally efficient to compute for both full-table and grouped aggregation queries. We provide formal

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... initions and semantics and a description of our open-source implementation for single-table aggregation queries. We study the performance and scalability of our algorithms through experiments over a large synthetic data set. We also provide some preliminary results on aggregations over joins. Note to referees: Our initial results were published as a workshop paper [17] . This paper includes the following additional material: (1) More algorithms for different aggregate variants (Section IV). (2) Proofs of the key lemmas and theorem for approximating expected-average (Section V and Appendix). (3) Performance experiments (Section VI) (4) Preliminary results on aggregation over joins (Section VII)