Robert Kohn

Bayesian Inference Using Synthetic Likelihood: Asymptotics and Adjustments

Journal of the American Statistical Association · 2022-06-07 · 34 citations

Implementing Bayesian inference is often computationally challenging in complex models, especially when calculating the likelihood is difficult. Synthetic likelihood is one approach for carrying out inference when the likelihood is intractable, but it is straightforward to simulate from the model. The method constructs an approximate likelihood by taking a vector summary statistic as being multivariate normal, with the unknown mean and covariance estimated by simulation. Previous research demons…

Dynamic linear regression models for forecasting time series with semi long memory errors

ArXiv.org · 2024-08-17 · 2 citations

Dynamic linear regression models forecast the values of a time series based on a linear combination of a set of exogenous time series while incorporating a time series process for the error term. This error process is often assumed to follow a stationary autoregressive integrated moving average (ARIMA) model, or its seasonal variants, which are unable to capture a long-range dependence structure (long memory) of the error process. We propose a novel dynamic linear regression model that incorpora…

Calibrated Generalized Bayesian Inference

arXiv (Cornell University) · 2023-11-27 · 2 citations

We propose a simple approach that provides accurate uncertainty quantification for Bayesian inference in misspecified or approximate models, and for generalized (Gibbs) posteriors. While existing solutions in this context are based on explicit Gaussian approximations or post-processing procedures, we demonstrate that correct uncertainty quantification can be achieved by substituting the usual posterior with an intuitively appealing alternative that conveys the same information. This solution app…

A Beta Cauchy-Cauchy (BECCA) shrinkage prior for Bayesian variable selection

arXiv (Cornell University) · 2025-01-13

This paper introduces a novel Bayesian approach for variable selection in high-dimensional and potentially sparse regression settings. Our method replaces the indicator variables in the traditional spike and slab prior with continuous, Beta-distributed random variables and places half Cauchy priors over the parameters of the Beta distribution, which significantly improves the predictive and inferential performance of the technique. Similar to shrinkage methods, our continuous parameterization of…

Fast Variational Boosting for Latent Variable Models

ArXiv.org · 2025-02-27

We consider the problem of estimating complex statistical latent variable models using variational Bayes methods. These methods are used when exact posterior inference is either infeasible or computationally expensive, and they approximate the posterior density with a family of tractable distributions. The parameters of the approximating distribution are estimated using optimisation methods. This article develops a flexible Gaussian mixture variational approximation, where we impose sparsity in…