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.