# A Metric Based on the Efficient Determination Criterion

## TL;DR

This paper introduces new metrics for model selection that improve the accuracy of DNA sequence analysis for dengue virus.

## Contribution

The paper introduces new efficient determination criteria metrics that enable strongly consistent estimation of partition Markov models.

## Key findings

- The efficient determination criteria (EDC) generalize the Bayesian information criterion (BIC) for model selection.
- The penalty ln(ln(n)) is identified as viable for maintaining strong consistency in PMM estimation.
- The new metrics were successfully applied to model DNA sequences of dengue virus type 3.

## Abstract

This paper extends the concept of metrics based on the Bayesian information criterion (BIC), to achieve strongly consistent estimation of partition Markov models (PMMs). We introduce a set of metrics drawn from the family of model selection criteria known as efficient determination criteria (EDC). This generalization extends the range of options available in BIC for penalizing the number of model parameters. We formally specify the relationship that determines how EDC works when selecting a model based on a threshold associated with the metric. Furthermore, we improve the penalty options within EDC, identifying the penalty ln(ln(n)) as a viable choice that maintains the strongly consistent estimation of a PMM. To demonstrate the utility of these new metrics, we apply them to the modeling of three DNA sequences of dengue virus type 3, endemic in Brazil in 2023.