Predicting legal judgments with reliable confidence is paramount for responsible legal AI applications. While transformer-based deep neural networks (DNNs) like BERT have demonstrated promise in legal tasks, accurately assessing their prediction confidence remains crucial. We present a novel Bayesian approach called BayesJudge that harnesses the synergy between deep learning and deep Gaussian Processes to quantify uncertainty through Bayesian kernel Monte Carlo dropout. Our method leverages informative priors and flexible data modelling via kernels, surpassing existing methods in both predictive accuracy and confidence estimation as indicated through brier score. Extensive evaluations of public legal datasets showcase our model's superior performance across diverse tasks. We also introduce an optimal solution to automate the scrutiny of unreliable predictions, resulting in a significant increase in the accuracy of the model's predictions by up to 27\%. By empowering judges and legal professionals with more reliable information, our work paves the way for trustworthy and transparent legal AI applications that facilitate informed decisions grounded in both knowledge and quantified uncertainty.

Models based on bidirectional encoder representations from transformers (BERT) produce state of the art (SOTA) results on many natural language processing (NLP) tasks such as named entity recognition (NER), part-of-speech (POS) tagging etc. An interesting phenomenon occurs when classifying long documents such as those from the US supreme court where BERT-based models can be considered difficult to use on a first-pass or out-of-the-box basis. In this paper, we experiment with several BERT-based classification techniques for US supreme court decisions or supreme court database (SCDB) and compare them with the previous SOTA results. We then compare our results specifically with SOTA models for long documents. We compare our results for two classification tasks: (1) a broad classification task with 15 categories and (2) a fine-grained classification task with 279 categories. Our best result produces an accuracy of 80\% on the 15 broad categories and 60\% on the fine-grained 279 categories which marks an improvement of 8\% and 28\% respectively from previously reported SOTA results.