Matthias C.M. Troffaes’s research while affiliated with Durham University and other places

Causal effect estimation is a critical task in statistical learning that aims to find the causal effect on subjects by identifying causal links between a number of predictor (or, explanatory) variables and the outcome of a treatment. In a regressional framework, we assign a treatment and outcome model to estimate the average causal effect. Additionally, for high dimensional regression problems, variable selection methods are also used to find a subset of predictor variables that maximises the predictive performance of the underlying model for better estimation of the causal effect. In this paper, we propose a different approach. We focus on the variable selection aspects of high dimensional causal estimation problem. We suggest a cautious Bayesian group LASSO (least absolute shrinkage and selection operator) framework for variable selection using prior sensitivity analysis. We argue that in some cases, abstaining from selecting (or, rejecting) a predictor is beneficial and we should gather more information to obtain a more decisive result. We also show that for problems with very limited information, expert elicited variable selection can give us a more stable causal effect estimation as it avoids overfitting. Lastly, we carry a comparative study with synthetic dataset and show the applicability of our method in real-life situations.

Offshore wind farms are one of the major renewable energy resources that can help the UK to reach its net zero target. Under the 10 point plan of the green revolution, the UK is set to quadruple its wind energy production by increasing its offshore wind capacity to 40GW by 2030 [1]. Research needs to be conducted to study the failure and repair processes of wind turbines under various conditions as the current models make a simplifying assumption that the failure/repair rate remains constant over time. This research aims to create a more accurate model using SCADA data. In this research, different mathematical models are fitted to the time to failure and time to repair data of wind turbine components using frequentist methods (such as Maximum Likelihood Estimation) and Bayesian methods. Further analysis will be conducted using complex system analysis considering the failures of each electrical and mechanical component of the wind turbine. The aim of this project is to perform a more accurate reliability analysis that can help to further drive down costs of wind energy by potentially reducing the downtimes of the wind turbines.

Causal inference concerns finding the treatment effect on subjects along with causal links between the variables and the outcome. However, the underlying heterogeneity between subjects makes the problem practically unsolvable. Additionally, we often need to find a subset of explanatory variables to understand the treatment effect. Currently, variable selection methods tend to maximise the predictive performance of the underlying model, and unfortunately, under limited data, the predictive performance is hard to assess, leading to harmful consequences. To address these issues, in this paper, we consider a robust Bayesian analysis which accounts for abstention in selecting explanatory variables in the high dimensional regression model. To achieve that, we consider a set of spike and slab priors through prior elicitation to obtain a set of posteriors for both the treatment and outcome model. We are specifically interested in the sensitivity of the treatment effect in high dimensional causal inference as well as identifying confounder variables. However, confounder selection can be deceptive in this setting, especially when a predictor is strongly associated with either the treatment or the outcome. To avoid that we apply a post-hoc selection scheme, attaining a smaller set of confounders as well as separate sets of variables which are only related to treatment or outcome model. Finally, we illustrate our method to show its applicability.

Causal inference using observational data is an important aspect in many fields such as epidemiology, social science, economics, etc. In particular, our goal is to find the treatment effect on the subjects along with the causal links between the variables and the outcome. However, estimation for such problems are extremely difficult as the treatment effects may vary from subject to subject and modelling the underlying heterogeneity explicitly makes the problem practically unsolvable. Another issue we often face is the dimensionality of the problem and we need to find a subset of explanatory variables to initiate the treatment. However, currently variable selection methods tend to maximise the predictive performance of the outcome model only. This can be problematic in the case of limited information. As the consequence of mistreatment can be harmful. So, in this paper, we suggest a general framework with robust Bayesian analysis which accounts for abstention in deciding an explanatory variable in the high dimensional regression model. To achieve that, we consider a set of spike and slab priors through prior elicitation to obtain robust estimates for both the treatment and outcome model. We are specifically interested in the sensitivity of the treatment effect in the high dimensional causal inference as well as the identifying the confounder variables by means of variable selection. However, indicator based confounder selection can be deceptive in some cases. Especially, when the predictor is strongly associated with either the treatment or the outcome. This increases the posterior expectation of the selection indicators. To avoid that we apply a post-hoc selection scheme which successfully remove negligible non-zero effects from the model attaining a smaller set of confounders. Finally, we illustrate our result using synthetic dataset.