  In recent years, local differential privacy (LDP) has emerged as a technique
of choice for privacy-preserving data collection in several scenarios when the
aggregator is not trustworthy. LDP provides client-side privacy by adding noise
at the user's end. Thus, clients need not rely on the trustworthiness of the
aggregator.
  In this work, we provide a noise-aware probabilistic modeling framework,
which allows Bayesian inference to take into account the noise added for
privacy under LDP, conditioned on locally perturbed observations. Stronger
privacy protection (compared to the central model) provided by LDP protocols
comes at a much harsher privacy-utility trade-off. Our framework tackles
several computational and statistical challenges posed by LDP for accurate
uncertainty quantification under Bayesian settings. We demonstrate the efficacy
of our framework in parameter estimation for univariate and multi-variate
distributions as well as logistic and linear regression.
