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In the last two decades, Bayesian inference has become commonplace in astronomy. At the same time, the choice of algorithms, terminology, notation, and interpretation of Bayesian inference varies from one sub-field of astronomy to the next, which can lead to confusion to both those learning and those familiar with Bayesian statistics. Moreover, the choice varies between the astronomy and statistics literature, too. In this paper, our goal is two-fold: (1) provide a reference that consolidates and clarifies terminology and notation across disciplines, and (2) outline practical guidance for Bayesian inference in astronomy. Highlighting both the astronomy and statistics literature, we cover topics such as notation, specification of the likelihood and prior distributions, inference using the posterior distribution, and posterior predictive checking. It is not our intention to introduce the entire field of Bayesian data analysis -- rather, we present a series of useful practices for astronomers who already have an understanding of the Bayesian "nuts and bolts" and wish to increase their expertise and extend their knowledge. Moreover, as the field of astrostatistics and astroinformatics continues to grow, we hope this paper will serve as both a helpful reference and as a jumping off point for deeper dives into the statistics and astrostatistics literature.

Bayesian adaptive clinical trials offer a flexible and efficient alternative to traditional fixed-design trials, but their implementation is often hindered by the complexity of Bayesian computations and the need for advanced statistical programming expertise. The authors introduce a custom fine-tuned LLM designed to assist with this and lower barriers to adoption of Bayesian methods for adaptive clinical trials. This paper describes the development and fine-tuning of BACTA-GPT, a Large Language Model (LLM)-based tool designed to assist in the implementation of Bayesian Adaptive Clinical Trials. This engine uses GPT-3.5 as the underlying model and takes in Natural Language input from the Statistician or the Trialist. The fine-tuned model demonstrates a viable proof-of-concept in its objectives. Test case evaluations show that the model is capable of generating a fit-for-purpose Bayesian model for an adaptive trial and evaluate its operating characteristics via simulations using R and JAGS. The integration of AI code generation has significant potential to lower technical barriers for the design and implementation of Bayesian Adaptive trials. But they also require attention to important considerations regarding validation and quality control.