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SOMA: a novel sampler for exchangeable variables

The problem of sampling exchangeable random variables arises in many Bayesian inference tasks, especially in data imputation given a privatized summary statistics. These permutation-invariant joint distributions often have dependency structures that …

Statistical Inference for Privatized Data with Unknown Sample Size

We develop both theory and algorithms to analyze privatized data in the unbounded differential privacy(DP), where even the sample size is considered a sensitive quantity that requires privacy protection. We show that the distance between the sampling …

Sequential Monte Carlo algorithms for agent-based models of disease transmission

A simple Markov chain for independent Bernoulli variables conditioned on their sum

We consider a vector of $N$ independent binary variables, each with a different probability of success. The distribution of the vector conditional on its sum is known as the conditional Bernoulli distribution. Assuming that $N$ goes to infinity and …