Volcanic records are often incomplete and vary in detail, making it hard to draw conclusions about Earth's internal processes. This is a common challenge across Earth Sciences for many natural events that unfold over long timescales. Our research introduces a new method to tackle this by identifying how much reliable information can be extracted from these sparse volcanic histories. We call this defining 'inference-driven scales'—essentially, determining what can and cannot be learned from a record.

Our approach involves grouping eruption events over time. We use a statistical technique to find the ideal level of detail for each record, ensuring we're not over-interpreting data. We then transform these grouped events into a standardized measure of eruption intensity, complete with an uncertainty range, allowing comparisons even between records with different levels of detail.

This framework enables three types of comparisons:

1. Standardized Rates: We can compare absolute eruption rates consistently across different records.


2. Pattern Analysis: We can test simple hypotheses, like whether eruptions tend to be clustered or spread out randomly.


3. Cross-Scale Comparisons: We can even compare records of vastly different quality or age by adjusting for how densely events are recorded.

We show that, despite gaps, these records contain valuable, recoverable information.