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It has become increasingly useful to answer questions in gravitational-wave astronomy using transdimensional models where the number of free parameters can be varied depending on the complexity required to fit the data. Given the growing interest in transdimensional inference, we introduce a new package for the Bayesian inference Library (Bilby) called tBilby. The tBilby package allows users to set up transdimensional inference calculations using the existing Bilby architecture with off-the-shelf nested samplers and/or Markov Chain Monte Carlo algorithms. Transdimensional models are particularly helpful when we seek to test theoretically uncertain predictions described by phenomenological models. For example, bursts of gravitational waves can be modelled using a superposition of N wavelets where N is itself a free parameter. Short pulses are modelled with small values of N whereas longer, more complicated signals are represented with a large number of wavelets stitched together. Other transdimensional models have found use describing instrumental noise and the population properties of gravitational-wave sources. We provide a few demonstrations of tBilby, including fitting the gravitational-wave signal GW150914 with a superposition of N sine-Gaussian wavelets. We outline our plans to further develop the tbilby code suite for a broader range of transdimensional problems., Comment: 12 pages, 7 figures

A number of pulsar timing arrays have recently reported preliminary evidence for the existence of a nanohertz frequency gravitational-wave background. These analyses rely on detailed noise analyses, which are inherently complex due to the many astrophysical and instrumental factors that contribute to the pulsar noise budget. We investigate whether realistic systematic errors, stemming from misspecified noise models that fail to capture salient features of the pulsar timing noise, could bias the evidence for gravitational waves. We consider two plausible forms of misspecification: small unmodeled jumps and unmodeled chromatic noise. Using simulated data, we calculate the distribution of the commonly used optimal statistic with no signal present and using plausibly misspecified noise models. By comparing the optimal statistic distribution with the distribution created using ``quasi-resampling'' techniques (such as sky scrambles and phase shifts), we endeavor to determine the extent to which plausible misspecification might lead to a false positive. The results are reassuring: we find that quasi-resampling techniques tend to underestimate the significance of pure-noise datasets. We conclude that recent reported evidence for a nanohertz gravitational-wave background is likely robust to the most obvious sources of systematic errors; if anything, the significance of the signal is potentially underestimated., Comment: 8 pages, 10 figures

The noise in millisecond pulsar (MSP) timing data can include contributions from observing instruments, the interstellar medium, the solar wind, solar system ephemeris errors, and the pulsars themselves. The noise environment must be accurately characterized in order to form the null hypothesis from which signal models can be compared, including the signature induced by nanohertz-frequency gravitational waves (GWs). Here we describe the noise models developed for each of the MSPs in the Parkes Pulsar Timing Array (PPTA) third data release, which have been used as the basis of a search for the isotropic stochastic GW background. We model pulsar spin noise, dispersion measure variations, scattering variations, events in the pulsar magnetospheres, solar wind variability, and instrumental effects. We also search for new timing model parameters and detected Shapiro delays in PSR~J0614$-$3329 and PSR~J1902$-$5105. The noise and timing models are validated by testing the normalized and whitened timing residuals for Gaussianity and residual correlations with time. We demonstrate that the choice of noise models significantly affects the inferred properties of a common-spectrum process. Using our detailed models, the recovered common-spectrum noise in the PPTA is consistent with a power law with a spectral index of $\gamma=13/3$, the value predicted for a stochastic GW background from a population of supermassive black hole binaries driven solely by GW emission., Comment: 18 pages, 10 figures. Accepted for publication in ApJL

We present the third data release from the Parkes Pulsar Timing Array (PPTA) project. The release contains observations of 32 pulsars obtained using the 64-m Parkes "Murriyang" radio telescope. The data span is up to 18 years with a typical cadence of 3 weeks. This data release is formed by combining an updated version of our second data release with $\sim 3$ years of more recent data primarily obtained using an ultra-wide-bandwidth receiver system that operates between 704 and 4032 MHz. We provide calibrated pulse profiles, flux-density dynamic spectra, pulse times of arrival, and initial pulsar timing models. We describe methods for processing such wide-bandwidth observations, and compare this data release with our previous release., Comment: 15 pages, 6 figures. Accepted for publication in PASA

Pulsar timing arrays aim to detect nanohertz-frequency gravitational waves (GWs). A background of GWs modulates pulsar arrival times and manifests as a stochastic process, common to all pulsars, with a signature spatial correlation. Here we describe a search for an isotropic stochastic gravitational-wave background (GWB) using observations of 30 millisecond pulsars from the third data release of the Parkes Pulsar Timing Array (PPTA), which spans 18 years. Using current Bayesian inference techniques we recover and characterize a common-spectrum noise process. Represented as a strain spectrum $h_c = A(f/1 {\rm yr}^{-1})^{\alpha}$, we measure $A=3.1^{+1.3}_{-0.9} \times 10^{-15}$ and $\alpha=-0.45 \pm 0.20$ respectively (median and 68% credible interval). For a spectral index of $\alpha=-2/3$, corresponding to an isotropic background of GWs radiated by inspiraling supermassive black hole binaries, we recover an amplitude of $A=2.04^{+0.25}_{-0.22} \times 10^{-15}$. However, we demonstrate that the apparent signal strength is time-dependent, as the first half of our data set can be used to place an upper limit on $A$ that is in tension with the inferred common-spectrum amplitude using the complete data set. We search for spatial correlations in the observations by hierarchically analyzing individual pulsar pairs, which also allows for significance validation through randomizing pulsar positions on the sky. For a process with $\alpha=-2/3$, we measure spatial correlations consistent with a GWB, with an estimated false-alarm probability of $p \lesssim 0.02$ (approx. $2\sigma$). The long timing baselines of the PPTA and the access to southern pulsars will continue to play an important role in the International Pulsar Timing Array., Comment: 19 pages, 10 figures, Accepted for publication in ApJL

The recent observation of a common red-noise process in pulsar timing arrays (PTAs) suggests that the detection of nanohertz gravitational waves might be around the corner. However, in order to confidently attribute this red process to gravitational waves, one must observe the Hellings-Downs curve -- the telltale angular correlation function associated with a gravitational-wave background. This effort is complicated by the complex modelling of pulsar noise. Without proper care, mis-specified noise models can lead to false-positive detections. Background estimation using bootstrap methods such as sky scrambles and phase shifts, which use the data to characterize the noise, are therefore important tools for assessing significance. We investigate the ability of current PTA experiments to estimate their background with "quasi-independent" scrambles -- characterized by a statistical "match" below the fiducial value: $|M|<0.1$. We show that sky scrambling is affected by "saturation" after $O(10)$ quasi-independent realizations; subsequent scrambles are no longer quasi-independent. We show phase scrambling saturates after $O(100)$ quasi-independent realizations. With so few independent scrambles, it is difficult to make reliable statements about the $\gtrsim 5 \sigma$ tail of the null distribution of the detection statistic. We discuss various methods by which one may increase the number of independent scrambles. We also consider an alternative approach wherein one re-frames the background estimation problem so that the significance is calculated using statistically dependent scrambles. The resulting $p$-value is in principle well-defined but may be susceptible to failure if assumptions about the data are incorrect., Comment: Paper accepted for publication on ApJ on the 7th of August 2023

We consider an evolving system for which a sequence of observations is being made, with each observation revealing additional information about current and past states of the system. We suppose each observation is made without error, but does not fully determine the state of the system at the time it is made. Our motivating example is drawn from invasive species biology, where it is common to know the precise location of invasive organisms that have been detected by a surveillance program, but at any time during the program there are invaders that have not been detected. We propose a sequential importance sampling strategy to infer the state of the invasion under a Bayesian model of such a system. The strategy involves simulating multiple alternative states consistent with current knowledge of the system, as revealed by the observations. However, a difficult problem that arises is that observations made at a later time are invariably incompatible with previously simulated states. To solve this problem, we propose a two-step iterative process in which states of the system are alternately simulated in accordance with past observations, then corrected in light of new observations. We identify criteria under which such corrections can be made while maintaining appropriate importance weights., Comment: 19 pages, 6 figures, uses arxiv.sty