The ABC algorithm is a Bayesian method which simulates samples from the posterior distribution. In this thesis, the method is applied on both synthetic and observed data of a regression model. Under normal error distribution a conjugate prior and the likelihood function are used in the algorithm. Additionally, a bootstrap method is implemented in a modified algorithm to provide an alternative method, without requiring normal error distribution. The results of both methods are thereafter presented and compared with the analytic posterior under a conjugate prior, to evaluate their performances. Lastly, advantages and possible issues are discussed.

Yes / We compare the performance of logistic regression with several alternative machine learning methods to estimate the risk of death for patients following an emergency admission to hospital based on the patients’ first blood test results and physiological measurements using an external validation approach. We trained and tested each model using data from one hospital (n=24696) and compared the performance of these models in data from another hospital (n=13477). We used two performance measures – the calibration slope and area under the curve (AUC). The logistic model performed reasonably well – calibration slope 0.90, AUC 0.847 compared to the other machine learning methods. Given the complexity of choosing tuning parameters of these methods, the performance of logistic regression with transformations for in-hospital mortality prediction was competitive with the best performing alternative machine learning methods with no evidence of overfitting. / Health Foundation; National Institute for Health Research (NIHR) Yorkshire and Humberside Patient Safety Translational Research Centre (NIHR YHPSTRC)