In statistical modeling, the act of “compare” is fundamental to understanding and validating our models. It’s not merely about noting differences; it’s about rigorously assessing which model better explains the observed data and is likely to perform better on new, unseen data. This comparison is crucial for making informed decisions based on statistical inference.
One powerful approach to define “compare” in this context is through the lens of Expected Log Predictive Density (ELPD). ELPD offers a framework to evaluate how well a model predicts future data. A higher ELPD generally indicates a model with superior predictive capabilities. This metric is deeply rooted in assessing the entire predictive distribution, not just point estimates. When we compare models using ELPD, we are essentially asking: which model is expected to be more accurate in predicting new observations?
However, the definition of “compare” extends beyond purely statistical metrics like ELPD. Utility and cost functions provide another critical dimension. These application-specific functions allow us to tailor the comparison to the practical implications of our models. For instance, in a medical context, the cost of misdiagnosis might be far more relevant than a generic measure of predictive accuracy. By incorporating these functions, we define “compare” in terms of real-world consequences and decision-making.
It’s important to recognize that traditional measures like RMSE or R^2, which focus on point estimates, offer an incomplete picture when we “compare” models. These metrics might be easily interpretable, but they often overlook the nuances of the entire predictive distribution. A comprehensive “comparison,” especially when guided by ELPD and supplemented by utility functions, provides a more robust and insightful evaluation. This holistic approach ensures that our model selection is not only statistically sound but also practically meaningful.
