scholarly journals Bayesian cross validation for gravitational-wave searches in pulsar-timing array data

2019 ◽  
Vol 487 (3) ◽  
pp. 3644-3649 ◽  
Author(s):  
Haochen Wang ◽  
Stephen R Taylor ◽  
Michele Vallisneri

ABSTRACT Gravitational-wave data analysis demands sophisticated statistical noise models in a bid to extract highly obscured signals from data. In Bayesian model comparison, we choose among a landscape of models by comparing their marginal likelihoods. However, this computation is numerically fraught and can be sensitive to arbitrary choices in the specification of parameter priors. In Bayesian cross validation, we characterize the fit and predictive power of a model by computing the Bayesian posterior of its parameters in a training data set, and then use that posterior to compute the averaged likelihood of a different testing data set. The resulting cross-validation scores are straightforward to compute; they are insensitive to prior tuning; and they penalize unnecessarily complex models that overfit the training data at the expense of predictive performance. In this article, we discuss cross validation in the context of pulsar-timing-array data analysis, and we exemplify its application to simulated pulsar data (where it successfully selects the correct spectral index of a stochastic gravitational-wave background), and to a pulsar data set from the NANOGrav 11-yr release (where it convincingly favours a model that represents a transient feature in the interstellar medium). We argue that cross validation offers a promising alternative to Bayesian model comparison, and we discuss its use for gravitational-wave detection, by selecting or refuting models that include a gravitational-wave component.

2012 ◽  
Vol 8 (S291) ◽  
pp. 543-545
Author(s):  
Jingbo Wang ◽  
G. Hobbs ◽  
Na Wang

AbstractGravitational wave bursts produced by supermassive binary black hole mergers will leave a persistent imprint on the space-time metric. Such gravitational wave memory signals are detectable by pulsar timing arrays as a glitch event that would seem to occur simultaneously for all pulsars. In this paper, we describe an initial algorithm which can be used to search for gravitational wave memory signals. We apply this algorithm to the Parkes Pulsar Timing Array data set. No significant gravitational wave memory signal is founded in the data set.


2014 ◽  
Vol 10 (S306) ◽  
pp. 5-8 ◽  
Author(s):  
Daniel J. Mortlock

AbstractThe standard Bayesian model formalism comparison cannot be applied to most cosmological models as they lack well-motivated parameter priors. However, if the data-set being used is separable, then it is possible to use some of the data to obtain the necessary parameter distributions, the rest of the data being retained for model comparison. While such methods are not fully prescriptive, they provide a route to applying Bayesian model comparison in cosmological situations where it could not otherwise be used.


PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0243390
Author(s):  
Eduardo G. Altmann

Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling explicitly the effect of interactions between individuals at different locations. Parameters that describe the scaling law and the spatial interactions are inferred from data simultaneously, allowing for rigorous (Bayesian) model comparison and overcoming the problem of defining the boundaries of urban regions. Results in five different datasets show that including spatial interactions typically leads to better models and a change in the exponent of the scaling law.


2014 ◽  
pp. 101-117
Author(s):  
Michael D. Lee ◽  
Eric-Jan Wagenmakers

2020 ◽  
Vol 501 (2) ◽  
pp. 1663-1676
Author(s):  
R Barnett ◽  
S J Warren ◽  
N J G Cross ◽  
D J Mortlock ◽  
X Fan ◽  
...  

ABSTRACT We present the results of a new, deeper, and complete search for high-redshift 6.5 < z < 9.3 quasars over 977 deg2 of the VISTA Kilo-Degree Infrared Galaxy (VIKING) survey. This exploits a new list-driven data set providing photometry in all bands Z, Y, J, H, Ks, for all sources detected by VIKING in J. We use the Bayesian model comparison (BMC) selection method of Mortlock et al., producing a ranked list of just 21 candidates. The sources ranked 1, 2, 3, and 5 are the four known z > 6.5 quasars in this field. Additional observations of the other 17 candidates, primarily DESI Legacy Survey photometry and ESO FORS2 spectroscopy, confirm that none is a quasar. This is the first complete sample from the VIKING survey, and we provide the computed selection function. We include a detailed comparison of the BMC method against two other selection methods: colour cuts and minimum-χ2 SED fitting. We find that: (i) BMC produces eight times fewer false positives than colour cuts, while also reaching 0.3 mag deeper, (ii) the minimum-χ2 SED-fitting method is extremely efficient but reaches 0.7 mag less deep than the BMC method, and selects only one of the four known quasars. We show that BMC candidates, rejected because their photometric SEDs have high χ2 values, include bright examples of galaxies with very strong [O iii] λλ4959,5007 emission in the Y band, identified in fainter surveys by Matsuoka et al. This is a potential contaminant population in Euclid searches for faint z > 7 quasars, not previously accounted for, and that requires better characterization.


2020 ◽  
Vol 501 (1) ◽  
pp. 701-712
Author(s):  
N Yonemaru ◽  
S Kuroyanagi ◽  
G Hobbs ◽  
K Takahashi ◽  
X-J Zhu ◽  
...  

ABSTRACT Cosmic strings are potential gravitational-wave (GW) sources that can be probed by pulsar timing arrays (PTAs). In this work we develop a detection algorithm for a GW burst from a cusp on a cosmic string, and apply it to Parkes PTA data. We find four events with a false alarm probability less than 1 per cent. However further investigation shows that all of these are likely to be spurious. As there are no convincing detections we place upper limits on the GW amplitude for different event durations. From these bounds we place limits on the cosmic string tension of Gμ ∼ 10−5, and highlight that this bound is independent from those obtained using other techniques. We discuss the physical implications of our results and the prospect of probing cosmic strings in the era of Square Kilometre Array.


2018 ◽  
Vol 265 ◽  
pp. 271-278 ◽  
Author(s):  
Tyler B. Grove ◽  
Beier Yao ◽  
Savanna A. Mueller ◽  
Merranda McLaughlin ◽  
Vicki L. Ellingrod ◽  
...  

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