Narrow Results

Numerically estimating the integral of functions in high dimensional spaces is a nontrivial task. A oft-encountered example is the calculation of the marginal likelihood in Bayesian inference, in a context where a sampling algorithm such as a Markov Chain Monte Carlo provides samples of the function. We present an Adaptive Harmonic Mean Integration (AHMI) algorithm. Given samples drawn according to a probability distribution proportional to the function, the algorithm will estimate the integral of the function and the uncertainty of the estimate by applying a harmonic mean estimator to adaptively chosen regions of the parameter space. We describe the algorithm and its mathematical properties, and report the results using it on multiple test cases.

The proliferation of sequencing technologies in biomedical research has raised many new privacy concerns. These include concerns over the publication of aggregate data at a genomic scale (e.g. minor allele frequencies, regression coefficients). Methods such as differential privacy can overcome these concerns by providing strong privacy guarantees, but come at the cost of greatly perturbing the results of the analysis of interest. Here we investigate an alternative approach for achieving privacy-preserving aggregate genomic data sharing without the high cost to accuracy of differentially private methods. In particular, we demonstrate how other ideas from the statistical disclosure control literature (in particular, the idea of disclosure risk) can be applied to aggregate data to help ensure privacy. This is achieved by combining minimal amounts of perturbation with Bayesian statistics and Markov Chain Monte Carlo techniques. We test our technique on a GWAS dataset to demonstrate its utility in practice. An implementation is available at https://github.com/seanken/PrivMCMC.