Use Model Averaging instead of Model Selection in Pulsar Timing

Abstract

Over the past decade and a half, adoption of Bayesian inference in pulsar timing analysis has led to increasingly sophisticated models. The recent announcement of evidence for a stochastic background of gravitational waves by various pulsar timing array projects highlighted Bayesian inference as a central tool for parameter estimation and model selection. Despite its success, Bayesian inference is occasionally misused in the pulsar timing community. A common workflow is that the data is analyzed in multiple steps: a first analysis of single pulsars individually, and a subsequent analysis of the whole array of pulsars. A mistake that is then sometimes introduced stems from using the posterior distribution to craft the prior for the analysis of the same data in a second step, a practice referred to in the statistics literature as ``circular analysis.'' This is done to prune the model for computational efficiency. Multiple recent high-profile searches for gravitational waves by pulsar timing array (PTA) projects have this workflow. This letter highlights this error and suggests that Spike and Slab priors can be used to carry out model averaging instead of model selection in a single pass. Spike and Slab priors are proved to be equal to Log-Uniform priors.

arXiv comment6 pages, 2 figures

References in corpus (32)

• MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics
• The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
• Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array
• Searching for the nano-Hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I
• The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals
• The NANOGrav 15-year Data Set: Search for Signals from New Physics
• BayesWave: Bayesian Inference for Gravitational Wave Bursts and Instrument Glitches
• The NANOGrav 11-year Data Set: Pulsar-timing Constraints On The Stochastic Gravitational-wave Background
• The NANOGrav 15-year Data Set: Observations and Timing of 68 Millisecond Pulsars
• The second data release from the European Pulsar Timing Array I. The dataset and timing analysis
• Detecting the stochastic gravitational wave background using pulsar timing
• Optimal strategies for gravitational wave stochastic background searches in pulsar timing data
• On measuring the gravitational-wave background using Pulsar Timing Arrays
• TempoNest: A Bayesian approach to pulsar timing analysis
• The gravitational-wave background null hypothesis: Characterizing noise in millisecond pulsar arrival times with the Parkes Pulsar Timing Array
• Hyper-efficient model-independent Bayesian method for the analysis of pulsar timing data
• New advances in the Gaussian-process approach to pulsar-timing data analysis
• From Spin Noise to Systematics: Stochastic Processes in the First International Pulsar Timing Array Data Release
• The second data release from the European Pulsar Timing Array: IV. Implications for massive black holes, dark matter and the early Universe
• The MeerKAT Pulsar Timing Array: First Data Release
• Identifying and mitigating noise sources in precision pulsar timing data sets
• Time-domain Implementation of the Optimal Cross-Correlation Statistic for Stochastic Gravitational-Wave Background Searches in Pulsar Timing Data
• From Bright Binaries To Bumpy Backgrounds: Mapping Realistic Gravitational Wave Skies With Pulsar-Timing Arrays
• The Need For Speed: Rapid Refitting Techniques for Bayesian Spectral Characterization of the Gravitational Wave Background Using PTAs
• The noise properties of 42 millisecond pulsars from the European Pulsar Timing Array and their impact on gravitational wave searches
• Noise-marginalized optimal statistic: A robust hybrid frequentist-Bayesian statistic for the stochastic gravitational-wave background in pulsar timing arrays
• Hellings and Downs correlation of an arbitrary set of pulsars
• An Efficient Approximation to the Likelihood for Gravitational Wave Stochastic Background Detection Using Pulsar Timing Data
• A Trans-dimensional Bayesian Approach to Pulsar Timing Noise Analysis
• Accelerating pulsar timing data analysis
• Pulsar Timing Arrays require hierarchical models
• Exploring the Capabilities of Gibbs Sampling in Pulsar Timing Arrays

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• The NANOGrav 15 yr Data Set: Customized Chromatic Noise Models
• On the calculation of p-values for quadratic statistics in Pulsar Timing Arrays