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without further ado please take it away stephen all right thanks will so were going to be talking today about inference for prediction problems or uncertainty quantification for prediction problems and in particular were going to be able to use kind of complex machine learning models along the way so predictive inference for black box machine learning models before i go farther id like to say thank you and acknowledge my um my co-authors here so anastasios and liwa who are both on hand to answer questions in the chat and jatendra and mike so its been great to work with these guys so to start the conversation today i want to introduce kind of a classification problem that were going to think about so this is a real classification problem um its medical images and theyre each one of three classes some of these chest x-rays are from class normal some are from class covet 19 and some are from class pneumonia all right and then what i did here this is real data i fit kind of a deep