Heteroscedastic trees, ensembles, and other joint models for means and variances

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Predicting new outcomes based on data is an important part of any scientific, economic, or business endeavour. There are numerous statistical tools available today that allow people to predict mean, or average, responses to new situations. However, such tools are not yet designed to predict variability, which in some situations is just as important as predicting the average. In manufacturing, software design, chemistry, and economics, understanding how variable or volatile a future outcome may be is often the primary goal of a data analysis. Development of tools for performing this analysis has lagged behind that for predicting means. This proposal aims to develop methods of data analysis that can predict variability instead of, or in addition to, predicting an average. We will start from modern tools called "regression trees" that are already in heavy use for predicting means, and improve and adapt them to increase their capabilities. We will also assess how well the ordinary, unimproved tools can complete their task of prediction when faced with data that exhibit systematic changes in variablility, which is a situation that they are not meant to handle. If they are not already robust against these changes in variability, we will improve these tools in another way that will allow them to work better.