@article{lin_ishak_2021, title={A Bayesian interpretation of inconsistency measures in cosmology}, ISSN={["1475-7516"]}, DOI={10.1088/1475-7516/2021/05/009}, abstractNote={Abstract
               Measures of inconsistency and tension between datasets have become an essential part of cosmological analyses. It is important to accurately evaluate the significance of such tensions when present. We propose here a Bayesian interpretation of inconsistency measures that can extract information about physical inconsistencies in the presence of data scatter. This new framework is based on the conditional probability distribution of the level of physical inconsistency given the obtained value of the measure. We use the index of inconsistency as a case study to illustrate the new interpretation framework, but this can be generalized to other metrics. Importantly, there are two aspects in the quantification of inconsistency that behave differently as the number of model parameters increases. The first is the probability for the level of physical inconsistency to reach a threshold which drops with the increase of the number of parameters under consideration. The second is the actual level of physical inconsistency which remains rather insensitive to such an increase in parameters. The difference between these two aspects is often overlooked, which leads to a long-standing ambiguity: when a given  inconsistency is found between two constraints, its “significance” seems to be lower when considered in a higher-dimensional parameter space. This ambiguity is resolved by the Bayesian interpretation we introduce in this work because the conditional probability distribution includes all the statistical information of the level of physical inconsistency. Finally, we apply the Bayesian interpretation to examine the (in)consistency between Planck versus the Cepheid-based local measurement, the Dark Energy Survey (DES), the Atacama Cosmology Telescope (ACT) and WMAP. We confirm and revisit the degrees of previous physical inconsistencies and show the stability of the new interpretation with respect to the number of cosmological parameters compared to the commonly used n-σ interpretation when applied to cosmological tensions in multi-parameter spaces.}, number={5}, journal={JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS}, author={Lin, Weikang and Ishak, Mustapha}, year={2021}, month={May} }
 @article{lin_chen_mack_2021, title={Early Universe Physics Insensitive and Uncalibrated Cosmic Standards: Constraints on omega(m) and Implications for the Hubble Tension}, volume={920}, ISSN={["1538-4357"]}, url={https://doi.org/10.3847/1538-4357/ac12cf}, DOI={10.3847/1538-4357/ac12cf}, abstractNote={Abstract
               To further gain insight into whether pre-recombination models can resolve the Hubble tension, we explore constraints on the evolution of the cosmic background that are insensitive to early universe physics. The analysis of the CMB anisotropy has been thought to highly rely on early universe physics. However, we show that the fact that the sound horizon at recombination being close to that at the end of the drag epoch is insensitive to early universe physics. This allows us to link the absolute sizes of the two horizons and treat them as free parameters. Jointly, the CMB peak angular size, baryon acoustic oscillations, and Type Ia supernovae can be used as early universe physics insensitive and uncalibrated cosmic standards, which measure the cosmic history from recombination to today. They can set strong and robust constraints on the post-recombination cosmic background, especially the matter density parameter with Ωm = 0.302 ± 0.008 (68% C.L.), assuming a flat Λ cold dark matter universe after recombination. When we combine these with other nonlocal observations, we obtain several constraints on H
                  0 with significantly reduced sensitivity to early universe physics. These are all more consistent with the Planck 2018 result than the local measurement results such as those based on Cepheids. This suggests a tension between the post-recombination, but nonlocal, observations, and the local measurements that cannot be resolved by modifying pre-recombination early universe physics.}, number={2}, journal={ASTROPHYSICAL JOURNAL}, author={Lin, Weikang and Chen, Xingang and Mack, Katherine J.}, year={2021}, month={Oct} }
 @article{lin_mack_hou_2020, title={Investigating the Hubble Constant Tension: Two Numbers in the Standard Cosmological Model}, volume={904}, ISSN={["2041-8213"]}, url={https://doi.org/10.3847/2041-8213/abc894}, DOI={10.3847/2041-8213/abc894}, abstractNote={Abstract
               The current Hubble constant tension is usually presented by comparing constraints on H
                  0 only. However, the postrecombination background cosmic evolution is determined by two parameters in the standard ΛCDM model, the Hubble constant (H
                  0) and today’s matter energy fraction (Ωm). If we therefore compare all constraints individually in the H
                  0–Ωm plane, (1) various constraints can be treated as independently as possible, (2) single-sided constraints are easier to consider, (3) compatibility among different constraints can be viewed in a more robust way, (4) the model dependence of each constraint is clear, and (5) whether or not a nonstandard model is able to reconcile all constraints in tension can be seen more effectively. We perform a systematic comparison of different constraints in the H
                  0–Ωm space based on a flat ΛCDM model, treating them as separately as possible. Constraints along different degeneracy directions consistently overlap in one region of the space, with the local measurement from Cepheid variable–calibrated supernovae being the most outlying, followed by the time-delay strong-lensing result. Considering the possibility that some nonstandard physics may reconcile the constraints, we provide a general discussion of nonstandard models with modifications at high, mid, or low redshifts and the effect of local environmental factors. Due to the different responses of individual constraints to a modified model, it is not easy for nonstandard models to reconcile all constraints if none of them have unaccounted-for systematic effects.}, number={2}, journal={ASTROPHYSICAL JOURNAL LETTERS}, author={Lin, Weikang and Mack, Katherine J. and Hou, Liqiang}, year={2020}, month={Dec} }
 @article{garcia-quintero_ishak_fox_lin_2019, title={Cosmological discordances. III. More on measure properties, large-scale-structure constraints, the Hubble constant and Planck data}, volume={100}, ISSN={["2470-0029"]}, DOI={10.1103/PhysRevD.100.123538}, abstractNote={Consistency between cosmological data sets is essential for ongoing and future cosmological analyses. We first investigate the questions of stability and applicability of some moment-based inconsistency measures to multiple data sets. We show that the recently introduced index of inconsistency (IOI) is numerically stable while it can be applied to multiple data sets. We use an illustrative construction of constraints as well as an example with real data sets (i.e. WMAP versus Planck) to show some limitations of the application of the Karhunen-Loeve decomposition to discordance measures. Second, we perform various consistency analyzes using IOI between multiple current data sets while \textit{working with the entire common parameter spaces}. We find current Large-Scale-Structure (LSS) data sets (Planck CMB lensing, DES lensing-clustering and SDSS RSD) all to be consistent with one another. This is found to be not the case for Planck temperature (TT) versus polarization (TE,EE) data, where moderate inconsistencies are present. Noteworthy, we find a strong inconsistency between joint LSS probes and Planck with IOI=5.27, and a moderate tension between DES and Planck with IOI=3.14. Next, using the IOI metric, we compare the Hubble constant from five independent probes. We confirm previous strong tensions between local measurement (SH0ES) and Planck as well as between H0LiCOW and Planck, but also find new strong tensions between SH0ES measurement and the joint LSS probes with IOI=6.73 (i.e. 3.7-$\sigma$ in 1D) as well as between joint LSS and combined probes SH0ES+H0LiCOW with IOI=8.59 (i.e. 4.1-$\sigma$ in 1D). Whether due to systematic effects in the data sets or problems with the underlying model, sources of these old and new tensions need to be identified and dealt with.}, number={12}, journal={PHYSICAL REVIEW D}, author={Garcia-Quintero, Cristhian and Ishak, Mustapha and Fox, Logan and Lin, Weikang}, year={2019}, month={Dec} }