Why is a wider prediction interval viewed as more informative compared to a narrower one?

A wider prediction interval is considered more informative primarily because it represents more variability in the data. In the context of predictive modeling, a prediction interval provides a range within which we expect future observations to fall, given a certain level of confidence. When the interval is wider, it indicates that the underlying data exhibits more variability or uncertainty. This variability can arise from factors such as the natural fluctuations in the data, measurement errors, or unaccounted influences affecting the predictions.

By capturing a broader range of possible outcomes, a wider prediction interval gives users insight into the potential risks and uncertainties associated with the predictions. It allows stakeholders to make more informed decisions by acknowledging the range of possible scenarios rather than just a single point estimate, which may overlook significant risks or overestimate precision.

In contrast, a narrower prediction interval suggests less variability and might imply a stronger confidence in a specific outcome. However, this could be misleading if it does not reflect the true uncertainty present in the underlying data. Therefore, while narrower intervals may seem appealing due to their precision, they may lack the informative quality necessary for comprehensive decision-making under risk conditions.