# Continuous gravitational wave searches with pulsar timing arrays: Maximization versus marginalization over pulsar phase parameters

## TL;DR

This paper compares two statistical methods for detecting gravitational waves from supermassive black hole binaries using pulsar timing arrays, finding that marginalization improves localization accuracy for weaker signals.

## Contribution

It introduces and evaluates the effectiveness of marginalization over pulsar phase parameters versus maximization in gravitational wave searches with pulsar timing arrays.

## Key findings

- Marginalization (AvPhase) outperforms maximization (MaxPhase) for weak/moderate signals.
- Both methods perform similarly for strong signals.
- Simulation with 17 pulsars demonstrates the comparative advantages.

## Abstract

Resolvable Supermassive Black Hole Binaries are promising sources for Pulsar Timing Array based gravitational wave searches. Search algorithms for such targets must contend with the large number of so-called pulsar phase parameters in the joint log-likelihood function of the data. We compare the localization accuracy for two approaches: Maximization over the pulsar phase parameters (MaxPhase) against marginalization over them (AvPhase). Using simulated data from a pulsar timing array with 17 pulsars, we find that for weak and moderately strong signals, AvPhase outperforms MaxPhase significantly, while they perform comparably for strong signals.