  Providing provenance in scientific workflows is essential for reproducibility
and auditability purposes. Workflow systems model and record provenance
describing the steps performed to obtain the final results of a computation. In
this work, we propose a framework that verifies the correctness of the
statistical test results that are conducted by a researcher while protecting
individuals' privacy in the researcher's dataset. The researcher publishes the
workflow of the conducted study, its output, and associated metadata. They keep
the research dataset private while providing, as part of the metadata, a
partial noisy dataset (that achieves local differential privacy). To check the
correctness of the workflow output, a verifier makes use of the workflow, its
metadata, and results of another statistical study (using publicly available
datasets) to distinguish between correct statistics and incorrect ones. We use
case the proposed framework in the genome-wide association studies (GWAS), in
which the goal is to identify highly associated point mutations (variants) with
a given phenotype. For evaluation, we use real genomic data and show that the
correctness of the workflow output can be verified with high accuracy even when
the aggregate statistics of a small number of variants are provided. We also
quantify the privacy leakage due to the provided workflow and its associated
metadata in the GWAS use-case and show that the additional privacy risk due to
the provided metadata does not increase the existing privacy risk due to
sharing of the research results. Thus, our results show that the workflow
output (i.e., research results) can be verified with high confidence in a
privacy-preserving way. We believe that this work will be a valuable step
towards providing provenance in a privacy-preserving way while providing
guarantees to the users about the correctness of the results.
