A comparison of frequentist and Bayesian inference: Searching for low-frequency p modes and g modes in Sun-as-a-star data

TL;DR

This paper compares frequentist and Bayesian statistical methods for detecting low-frequency solar oscillations in Sun-as-a-star data, highlighting Bayesian approach's effectiveness in reducing false detections.

Contribution

The study demonstrates that Bayesian inference provides more reliable detection of solar oscillation modes compared to frequentist methods in Sun-as-a-star data.

Findings

Frequentist approach results in many false detections.

Bayesian approach reduces false positives significantly.

Bayesian detections can be validated with prior knowledge.

Abstract

We describe and use two different statistical approaches to try and detect low-frequency solar oscillations in Sun-as-a-star data: a frequentist approach and a Bayesian approach. We have used frequentist statistics to search contemporaneous Sun-as-a-star data for coincident, statistically-prominent features. However, we find that this approach leads to numerous false detections. We have also used Bayesian statistics to search for evidence of low-frequency p modes and g modes in Sun-as-a-star data. We describe how Bayesian statistics can be used to search near-contemporaneous data for coincident prominent features. Near-contemporaneous data were used to circumvent the difficulties in deriving probabilities that occur when common noise is present in the data. We find that the Bayesian approach, which is reliant on the assumptions made when determining the posterior probability, leads to significantly fewer false detections and those that are observed can be discredited using a priori knowledge. Therefore, we have more confidence in the mode candidates found with Bayesian statistics.