The advancement of technology has led to rampant growth in data collection across almost every field, including astrophysics, with researchers turning to machine learning to process and analyze this data. One prominent example of this data in astrophysics is the atmospheric retrievals of exoplanets. In order to help bridge the gap between machine learning and astrophysics domain experts, the 2023 Ariel Data Challenge was hosted to predict posterior distributions of 7 exoplanetary features. The procedure outlined in this paper leveraged a combination of two deep learning models to address this challenge: a Multivariate Gaussian model that generates the mean and covariance matrix of a multivariate Gaussian distribution, and a Uniform Quantile model that predicts quantiles for use as the upper and lower bounds of a uniform distribution. Training of the Multivariate Gaussian model was found to be unstable, while training of the Uniform Quantile model was stable. An ensemble of uniform distributions was found to have competitive results during testing (posterior score of 696.43), and when combined with a multivariate Gaussian distribution achieved a final rank of third in the 2023 Ariel Data Challenge (final score of 681.57).

In this paper we demonstrate that tempering Markov chain Monte Carlo samplers for Bayesian models by recursively subsampling observations without replacement can improve the performance of baseline samplers in terms of effective sample size per computation. We present two tempering by subsampling algorithms, subsampled parallel tempering and subsampled tempered transitions. We provide an asymptotic analysis of the computational cost of tempering by subsampling, verify that tempering by subsampling costs less than traditional tempering, and demonstrate both algorithms on Bayesian approaches to learning the mean of a high dimensional multivariate Normal and estimating Gaussian process hyperparameters.