## 2 Eruption Forecasting Algorithm
### Training Data  
A database comprised of monitoring data, source modeling results, and historic eruption information from a series of volcanic unrest episodes is required for deriving the logistic model coefficients. Unfortunately, no such database existed in the public domain at the time of this study. Therefore, one had to be constructed for this research. Ideally, a large and diversified set of data is desired for identifying the set of explanatory variables that will produce the most robust logistic model. Moreover, it is also desirable to identify a large number of events that either culminate or fail to culminate into an eruption. However, published accounts of volcanic unrest events vary greatly in detail and do not contain a consistent set of observations. This problem is exasperated by the fact that events which eventually result in an eruption tend to be published, while those that fail are not. This has artificially biased the open literature toward eruptive events as opposed to those that eventually fail [61]. As a result, only a small set of unrest events with known sources and a consistent set of explanatory variables could be identified for this research. The database constructed for this work is listed in Table 1. It is a collection of unrest events with a consistent set of observations whose causes were identified through source modeling. The 40 events in the database were gathered from various volcanoes in Northern America, Iceland, and Italy. For an event to be included in the database, a seismic catalog and modeling results that identify the source of the unrest must be available. These data were acquired from a combination of journal articles, technical reports, conference papers, and open seismic catalogs that are made freely available to the public by a number of organizations (e.g., USGS, ANSS, Icelandic Meteorological Institute) via the internet. It is assumed that this collection of events represent a random sample of volcanic activity in the northern hemisphere and is representative of this population. Table 1 consists of eleven columns. The first two columns list the episode year and volcano of origin. Column three is the event's \((VEI)\). The fourth column, \((Er)\), specifies whether the event culminated in an eruption, where true (eruption) and false (no eruption) outcomes are represented by a 1 or 0. The cause of the unrest is listed in column five, \((In)\), where a value of 1 or 0 states whether the source is a magmatic intrusion or not. Source modeling results are listed in column six, \((MM)\), where a value of 1 or 0 states if the source of the unrest can be modeled as a magmatic intrusion or not. The total number of earthquakes occurring over the course of the episode is listed in column seven, \((TNE)\). An estimate of the total cumulative seismic moment generated throughout the episode, \((TCSM)\), is listed in column eight. The duration of each episode in terms of days is listed in column nine, \((Days)\). The total number of eruptions at a particular site over the last 211 years is listed in column ten, \((TEH)\). This time span represents the extent of the Smithsonian Institute (SI) global volcanism database of eruptions that are known to have occurred in modern history (post 1800) [62]. It is meant to prevent overestimation of the probability of eruption at sites that typically display high levels of geologic activity but rarely erupt. The Yellowstone caldera is a prime example of where such a term is necessary. If historic eruption activity is not accounted for at Yellowstone, forecasts would show that an eruption is imminent (probability of eruption = 1.0) inside the caldera on an almost continuous basis. When historic eruptive activity is taken into consideration, the probability of eruption is adjusted to account for long periods of non-eruptive behavior. Finally the source of the information listed in each row is referenced in column eleven.