Bayesian learning of models for estimating uncertainty in alert systems: application to air traffic conflict avoidance

Alert systems detect critical events which can happen in the short term. Uncertainties in data and in the models used for detection cause alert errors. In the case of air traffic control systems such as Short-Term Conflict Alert (STCA), uncertainty increases errors in alerts of separation loss. Statistical methods that are based on analytical assumptions can provide biased estimates of uncertainties. More accurate analysis can be achieved by using Bayesian Model Averaging, which provides estimates of the posterior probability distribution of a prediction. We propose a new approach to estimate the prediction uncertainty, which is based on observations that the uncertainty can be quantified by variance of predicted outcomes. In our approach, predictions for which variances of posterior probabilities are above a given threshold are assigned to be uncertain. To verify our approach we calculate a probability of alert based on the extrapolation of closest point of approach. Using Heathrow airport flight data we found that alerts are often generated under different conditions, variations in which lead to alert detection errors. Achieving 82.1% accuracy of modelling the STCA system, which is a necessary condition for evaluating the uncertainty in prediction, we found that the proposed method is capable of reducing the uncertain component. Comparison with a bootstrap aggregation method has demonstrated a significant reduction of uncertainty in predictions. Realistic estimates of uncertainties will open up new approaches to improving the performance of alert systems

Prediction of survival probabilities with Bayesian Decision Trees

Practitioners use Trauma and Injury Severity Score (TRISS) models for predicting the survival probability of an injured patient. The accuracy of TRISS predictions is acceptable for patients with up to three typical injuries, but unacceptable for patients with a larger number of injuries or with atypical injuries. Based on a regression model, the TRISS methodology does not provide the predictive density required for accurate assessment of risk. Moreover, the regression model is difficult to interpret. We therefore consider Bayesian inference for estimating the predictive distribution of survival. The inference is based on decision tree models which recursively split data along explanatory variables, and so practitioners can understand these models. We propose the Bayesian method for estimating the predictive density and show that it outperforms the TRISS method in terms of both goodness-of-fit and classification accuracy. The developed method has been made available for evaluation purposes as a stand-alone application

Bayesian averaging over Decision Tree models for trauma severity scoring

Health care practitioners analyse possible risks of misleading decisions and need to estimate and quantify uncertainty in predictions. We have examined the “gold” standard of screening a patient's conditions for predicting survival probability, based on logistic regression modelling, which is used in trauma care for clinical purposes and quality audit. This methodology is based on theoretical assumptions about data and uncertainties. Models induced within such an approach have exposed a number of problems, providing unexplained fluctuation of predicted survival and low accuracy of estimating uncertainty intervals within which predictions are made. Bayesian method, which in theory is capable of providing accurate predictions and uncertainty estimates, has been adopted in our study using Decision Tree models. Our approach has been tested on a large set of patients registered in the US National Trauma Data Bank and has outperformed the standard method in terms of prediction accuracy, thereby providing practitioners with accurate estimates of the predictive posterior densities of interest that are required for making risk-aware decisions

Essays on Tree-based Methods for Prediction and Causal Inference

The first chapter of this thesis contains an application of causal forests to a residential electricity smart meter trial dataset. Household specific estimates are obtained for the effect of a Time-of-Use pricing scheme on peak demand. The most and least responsive households differ across education, age, employment status, and past electricity consumption. The results suggest that past consumption information is more useful than pre-trial survey information, which includes building characteristics, household characteristics, and responses to appliance usage questions. The second chapter explores new variations of Bayesian tree-based machine learning algorithms. Bayesian Additive Regression Trees (BART) (Chipman et al. 2010) and Bayesian Causal Forests (BCF) (Hahn et al. 2020) are state-of-the-art machine learning methods for prediction and causal inference. A number of existing implementations of BART make use of Markov Chain Monte Carlo algorithms, which can be computationally expensive when applied to high-dimensional datasets, do not always perform well in terms of mixing of chains, and have limited parallelizability. The second chapter introduces four variations of BART that do not rely on MCMC: 1. An improved implementation of the existing method BART-BMA (Hernandez et al. 2018), which averages over sum-of-tree models found by a model search algorithm, performs well on high-dimensional datasets, and produces more interpretable output than other BART implementations because the output includes a comparatively small number of sum-of-tree models. %, each of which contains (under the default settings) 5 trees. Improvements are made to the model search algorithm, calculation of predictions, and credible intervals.% The algorithm is entirely deterministic. 2. A treatment effect estimation algorithm that combines the model structure of BCF with the implementation of BART-BMA (BCF-BMA). This method successfully accounts for confounding on observables using the BCF parameterization, while retaining the parsimonious model selection approach of BART-BMA. 3. A simple alternative BART implementation algorithm that uses importance sampling of models (BART-IS). This approach contrasts with existing MCMC and model-search based approaches in that BART-IS makes fast data-independent draws of many sum-of-tree models. The advantages of this approach are that it is straightforward to implement, fast, and trivially parallelizable. 4. Bayesian Causal Forests using Importance Sampling (BCF-IS). This is a combination of the BCF model framework with the BART-IS implementation. BART-IS and BCF-IS exhibit comparable performance to BART-MCMC and BCF across a large number of simulated datasets. The second chapter also includes some illustrative applications. The methods are extendable to multiple treatments, multivariate outcomes, and panel data methods. The third chapter of this thesis describes how the methods introduced in the second chapter can be generalized from regression and treatment effect estimation for continuous outcomes, to a range of models with various link functions and outcome variables. As examples of how to apply the general approach, Logit-BART-BMA and Logit-BART-IS are introduced with illustrative applications

Customer profile classification using transactional data

Customer profiles are by definition made up of factual and transactional data. It is often the case that due to reasons such as high cost of data acquisition and/or protection, only the transactional data are available for data mining operations. Transactional data, however, tend to be highly sparse and skewed due to a large proportion of customers engaging in very few transactions. This can result in a bias in the prediction accuracy of classifiers built using them towards the larger proportion of customers with fewer transactions. This paper investigates an approach for accurately and confidently grouping and classifying customers in bins on the basis of the number of their transactions. The experiments we conducted on a highly sparse and skewed real-world transactional data show that our proposed approach can be used to identify a critical point at which customer profiles can be more confidently distinguished