Search

Since the first gravitational wave (GW) event from binary black hole (BBH) was detected by LIGO-Virgo, GWs have become a useful probe on astrophysics and cosmology. If compact dark matter (DM) objects e.g. primordial black holes, contribute a significant fraction of DM at wide mass range, they will cause microlensing in the GW signals with long wavelengths that are distinct from the lensing effects of electromagnetic signals from astrophysical objects. In this paper, we apply the lensing effect of GW from BBH to derive constraints on the abundance of compact DM for the Cosmic Explorer, a third-generation ground-based GW detector. We first consider two channels of formation of BBH that contribute to low- and high-redshift GW sources, including the astrophysical origin BBH scenario, and the primordial origin BBH scenario. Secondly, comparing with the method of optical depth, we use the Bayesian analysis to derive constraints on the abundance of compact DM with different mass function of lens taken into consideration. For a null search with 1000 detected GW events of BBH, we find that the abundance of compact DM could be constrained to |$\lesssim 0.1\,\mathrm{ per}\,\mathrm{ cent}$| in the mass range |$\ge 500\, {\rm M}_{\odot }$| at 68 per cent confidence level. In addition, if a GW event lensed by a compact DM object with |$M_{\rm l}\in [100\, {\rm M}_{\odot },300\, {\rm M}_{\odot }]$| is detected in 100 detected GW events of BBH, we can derive that the estimation of the abundance of compact DM is from |$2.3$| to |$25.2$| per cent in this mass range with the Bayesian analysis. [ABSTRACT FROM AUTHOR]

As the initial effort in a multi-step uncertainty analysis of a biologically based cancer model for formaldehyde, a Markov chain Monte Carlo (MCMC) analysis was performed for a compartmental model that predicts DNA-protein cross-links (DPX) produced by formaldehyde exposure. The Bayesian approach represented by the MCMC analysis integrates existing knowledge of the model parameters with observed, formaldehyde-DPX-specific data, providing a statistically sound basis for estimating model output uncertainty. Uncertainty and variability were evaluated through a hierarchical structure, where interindividual variability was considered for all model parameters and that variability was assumed to be uncertain on population levels. The uncertainty of the population mean and that of the population variance were significantly reduced through the MCMC analysis. Our investigation highlights several issues that must be dealt with in many real-world analyses (e.g., issues of parameters' nonidentifiability due to limited data) while demonstrating the feasibility of conducting a comprehensive quantitative uncertainty evaluation. The current analysis can be viewed as a case study, for a relatively simple model, illustrating some of the constraints that analysts will face when applying Bayesian approaches to biologically or physiologically based models of increasing complexity. [ABSTRACT FROM AUTHOR]