Cross-Comparison of Sampling Algorithms for Pulse Profile Modeling of PSR J0740+6620

Abstract

In the last few years, NICER data has enabled mass and radius inferences for various pulsars, and thus shed light on the equation of state for dense nuclear matter. This is achieved through a technique called pulse profile modeling. The importance of the results necessitates careful validation and testing of the robustness of the inference procedure. In this paper, we investigate the effect of sampler choice for X-PSI (X-ray Pulse Simulation and Inference), an open-source package for pulse profile modeling and Bayesian statistical inference that has been used extensively for analysis of NICER data. We focus on the specific case of the high-mass pulsar PSR J0740+6620. Using synthetic data that mimics the most recently analyzed NICER and XMM-Newton data sets of PSR J0740+6620, we evaluate the parameter recovery performance, convergence, and computational cost for MultiNest's multimodal nested sampling algorithm and UltraNest's slice nested sampling algorithm. We find that both samplers perform reliably, producing accurate and unbiased parameter estimation results when analyzing simulated data. We also investigate the consequences for inference using the real data for PSR J0740+6620, finding that both samplers produce consistent credible intervals.

Figures (4)

• Figure 1: Illustration of two different methods for identifying a new live point (white circles) within an arbitrary parameter space. Left panel: multi-ellipsoidal nested sampling, as implemented in MultiNest, approximates the unknown likelihood surface (colored contours) by constructing multi-ellipsoidal regions (blue dashed lines) around the current set of live points (white circles). Rejection sampling based on these contours can become inefficient if the contours are too large, and problematic for nested sampling integration if a region is missed (e.g., the top-right yellow tail). For clarity, the enlargement of the ellipsoids is intentionally chosen to be too small here. Right panel: slice sampling, as implemented in UltraNest, performs a Metropolis-like random walk (black arrows) starting from an existing live point (white circle) along "slice" axes. Steps that fall outside the likelihood contour are rejected. After a sufficient number of steps and with well-tuned proposals, a new live point (red circle) is identified that is independent of the initial point.
• Figure 2: P-P plot with ten synthetic datasets (as described in Section \ref{['subsec:synthetic_data']}). Upper panel: showing the parameter recovery performance of MultiNest using $4\times10^3$ live points and a sampling efficiency of 0.1. The gray regions cover the cumulative 1-, 2-, and 3-$\sigma$ credible intervals in order of decreasing opacity. Each colored line tracks the cumulative fraction of events within this credible interval for a different parameter, including the individual parameter p-values displayed in parentheses in the plot legend, with M for MultiNest and U for UltraNest. The combined p-value for MultiNest is 0.976. Lower panel: same as the upper panel, but results are shown for UltraNest using a minimum of 400 live points and 240 steps. The combined p-value for UltraNest is 0.607.
• Figure 3: Radius, compactness, and mass posterior distributions using the PSR J0740+6620 joint NICER and XMM-Newton data set conditional on the ST-U model. Two posterior distributions are shown: the results from Salmi2024-J0740 using MultiNest using $4\times10^4$ live points and a sampling efficiency of 0.01, and the results obtained with the UltraNest's slice sampling algorithm using a minimum of 1000 live points and 600 steps. The marginal prior PDFs for each parameter are displayed as dashed-dotted lines. The shaded regions in the diagonal panels contain the 68.3% credible interval for each parameter symmetric around the median. The contours in the off-diagonal panels contain the 68.3%, 95.4%, and 99.7% credible regions.
• Figure 4: Posterior distributions for the hot region parameters using the PSR J0740+6620 joint NICER and XMM-Newton data set conditional on the ST-U model. See Figure \ref{['fig:corner_small']} for more details about the figure elements. Notably, the contours appear more "wobbly" for UltraNest compared to MultiNest, which can be attributed to the smaller number of samples.