The mean field variational Bayes (VB) algorithm implemented in Stan is relatively fast and efficient, making it feasible to produce model-estimated official statistics on a rapid timeline. Yet, while consistent point estimates of parameters are achieved for continuous data models, the mean field approximation often produces inaccurate uncertainty quantification to the extent that parameters are correlated a posteriori. In this paper, we propose a simulation procedure that calibrates uncertainty intervals for model parameters estimated under approximate algorithms to achieve nominal coverages. Our procedure detects and corrects biased estimation of both first and second moments of approximate marginal posterior distributions induced by any estimation algorithm that produces consistent first moments under specification of the correct model. The method generates replicate data sets using parameters estimated in an initial model run. The model is subsequently re-estimated on each replicate data set, and we use the empirical distribution over the re-samples to formulate calibrated confidence intervals of parameter estimates of the initial model run that are guaranteed to asymptotically achieve nominal coverage. We demonstrate the performance of our procedure in Monte Carlo simulation study and apply it to real data from the Current Employment Statistics survey.

Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited attention in massive data applications, mainly due to the prohibitively slow posterior computations using Markov chain Monte Carlo (MCMC) algorithms. We address this problem using a divide-and-conquer Bayesian approach. We first create a large number of data subsamples with much smaller sizes. Then, we formulate the VCM as a linear mixed-effects model and develop a data augmentation algorithm for obtaining MCMC draws on all the subsets in parallel. Finally, we aggregate the MCMC-based estimates of subset posteriors into a single Aggregated Monte Carlo (AMC) posterior, which is used as a computationally efficient alternative to the true posterior distribution. Theoretically, we derive minimax optimal posterior convergence rates for the AMC posteriors of both the varying coefficients and the mean regression function. We provide quantification on the orders of subset sample sizes and the number of subsets. The empirical results show that the combination schemes that satisfy our theoretical assumptions, including the AMC posterior, have better estimation performance than their main competitors across diverse simulations and in a real data analysis.

We propose a Bayesian pseudo posterior mechanism to generate record-level synthetic databases equipped with an $(\epsilon,\pi)-$ probabilistic differential privacy (pDP) guarantee, where $\pi$ denotes the probability that any observed database exceeds $\epsilon$. The pseudo posterior mechanism employs a data record-indexed, risk-based weight vector with weight values $\in [0, 1]$ that surgically downweight the likelihood contributions for high-risk records for model estimation and the generation of record-level synthetic data for public release. The pseudo posterior synthesizer constructs a weight for each datum record by using the Lipschitz bound for that record under a log-pseudo likelihood utility function that generalizes the exponential mechanism (EM) used to construct a formally private data generating mechanism. By selecting weights to remove likelihood contributions with non-finite log-likelihood values, we guarantee a finite local privacy guarantee for our pseudo posterior mechanism at every sample size. Our results may be applied to any synthesizing model envisioned by the data disseminator in a computationally tractable way that only involves estimation of a pseudo posterior distribution for parameters, $\theta$, unlike recent approaches that use naturally-bounded utility functions implemented through the EM. We specify conditions that guarantee the asymptotic contraction of $\pi$ to $0$ over the space of databases, such that the form of the guarantee provided by our method is asymptotic. We illustrate our pseudo posterior mechanism on the sensitive family income variable from the Consumer Expenditure Surveys database published by the U.S. Bureau of Labor Statistics. We show that utility is better preserved in the synthetic data for our pseudo posterior mechanism as compared to the EM, both estimated using the same non-private synthesizer, due to our use of targeted downweighting.

Government surveys of business establishments receive a large volume of submissions where a small subset contain errors. Analysts need a fast-computing algorithm to flag this subset due to a short time window between collection and reporting. We offer a computationally-scalable optimization method based on non-parametric mixtures of hierarchical Dirichlet processes that allows discovery of multiple industry-indexed local partitions linked to a set of global cluster centers. Outliers are nominated as those clusters containing few observations. We extend an existing approach with a new merge step that reduces sensitivity to hyperparameter settings. Survey data are typically acquired under an informative sampling design where the probability of inclusion depends on the surveyed response such that the distribution for the observed sample is different from the population. We extend the derivation of a penalized objective function to use a pseudo-posterior that incorporates sampling weights that undo the informative design. We provide a simulation study to demonstrate that our approach produces unbiased estimation for the outlying cluster under informative sampling. The method is applied for outlier nomination for the Current Employment Statistics survey conducted by the Bureau of Labor Statistics.