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Demographic studies of cosmic populations must contend with measurement errors and selection effects. We survey some of the key ideas astronomers have developed to deal with these complications, in the context of galaxy surveys and the literature on corrections for Malmquist and Eddington bias. From the perspective of modern statistics, such corrections arise naturally in the context of multilevel models, particularly in Bayesian treatments of such models: hierarchical Bayesian models. We survey some key lessons from hierarchical Bayesian modeling, including shrinkage estimation, which is closely related to traditional corrections devised by astronomers. We describe a framework for hierarchical Bayesian modeling of cosmic populations, tailored to features of astronomical surveys that are not typical of surveys in other disciplines. This thinned latent marked point process framework accounts for the tie between selection (detection) and measurement in astronomical surveys, treating selection and measurement error effects in a self-consistent manner., 33 pages, 5 figures

Wave dark matter (WaveDM) has recently gained attention as a viable candidate to account for the dark matter content of the universe. In this paper we explore the extent to which, and under what conditions, dark matter halos in this model are able to reproduce strong-lensing systems. First, we explore analytically the lensing properties of the model, finding that a pure WaveDM density profile, the soliton profile, produces a weaker lensing effect than similar cored profiles. Then, we analyze models with a soliton embedded within a Navarro, Frenk, and White (NFW) profile, as has been found in numerical simulations of structure formation. We use a benchmark model with a boson mass of ma = 10−22 eV, for which we see that there is a bimodality in the contribution of the external NFW part of the profile, and some of the free parameters associated with it are not well constrained. We find that for configurations with boson masses 10−23 to 10−22 eV, a range of masses preferred by dwarf galaxy kinematics, the soliton profile alone can fit the data, but its size is incompatible with the luminous extent of the lens galaxies. Likewise, boson masses of the order of 10−21 eV, which would be consistent with Lyα constraints and consist of more compact soliton configurations, necessarily require the NFW part in order to reproduce the observed Einstein radii. We then conclude that lens systems impose a conservative lower bound ma > 10−24 eV and that the NFW envelope around the soliton must be present to satisfy the observational requirements.

Wave Dark Matter (WaveDM) has recently gained attention as a viable candidate to account for the dark matter content of the Universe. In this paper we explore the extent to which dark matter halos in this model, and under what conditions, are able to reproduce strong lensing systems. First, we analytically explore the lensing properties of the model -- finding that a pure WaveDM density profile, a soliton profile, produces a weaker lensing effect than other similar cored profiles. Then we analyze models with a soliton embedded in an NFW profile, as has been found in numerical simulations of structure formation. We use a benchmark model with a boson mass of $m_a=10^{-22}{\rm eV}$, for which we see that there is a bi-modality in the contribution of the external NFW part of the profile, and actually some of the free parameters associated with it are not well constrained. We find that for configurations with boson masses $10^{-23}$ -- $10^{-22}{\rm eV}$, a range of masses preferred by dwarf galaxy kinematics, the soliton profile alone can fit the data but its size is incompatible with the luminous extent of the lens galaxies. Likewise, boson masses of the order of $10^{-21}{\rm eV}$, which would be consistent with Lyman-$\alpha$ constraints and consist of more compact soliton configurations, necessarily require the NFW part in order to reproduce the observed Einstein radii. We then conclude that lens systems impose a conservative lower bound $m_a > 10^{-24}$ and that the NFW envelope around the soliton must be present to satisfy the observational requirements., Comment: 26 pages, 7 figures, Published

This paper continues our development of non-parametric tests for analysing the completeness in apparent magnitude of magnitude-redshift surveys. The purpose of this third and final paper in our completeness series is two-fold: firstly we explore how certain forms of incompleteness for a given flux-limited galaxy redshift survey would manifest themselves in the ROBUST Tc and Tv completeness estimators introduced in our earlier papers; secondly we provide a comprehensive error propagation for these estimators. By using both real surveys and Monte Carlo mock survey data, we have found distinct, characteristic behaviour of the Tc and Tv estimators which identify incompleteness in the form of e.g. missing objects within a particular magnitude range. Conversely we have identified signatures of `over' completeness, in cases where a survey contains a small region in apparent magnitude that may have too many objects relative to the rest of the data set. We also demonstrate how incompleteness resulting from luminosity evolution can be identified and provide a framework for using our estimators as a robust tool for constraining models of luminosity evolution. Finally we explore the error propagation for Tc andTv. This builds on Completeness II by allowing the definition of these estimators, and their errors, via an adaptive procedure that accounts for the effects of sampling error on the observed distribution of apparent magnitude and redshift in a survey., 18 pages, 12 figures, 1 table, Accepted version for publication in MNRAS

Current observational evidence does not yet exclude the possibility that dark energy could be in the form of phantom energy. A universe consisting of a phantom constituent will be driven toward a drastic end known as the `Big Rip' singularity where all the matter in the universe will be destroyed. Motivated by this possibility, other evolutionary scenarios have been explored by Barrow, including the phenomena which he called Sudden Future Singularities (SFS). In such a model it is possible to have a blow up of the pressure occurring at sometime in the future evolution of the universe while the energy density would remain unaffected. The particular evolution of the scale factor of the universe in this model that results in a singular behaviour of the pressure also admits acceleration in the current era. In this paper we will present the results of our confrontation of one example class of SFS models with the available cosmological data from high redshift supernovae, baryon acoustic oscillations (BAO) and the cosmic microwave background (CMB). We then discuss the viability of the model in question as an alternative to dark energy., Comment: 9 pages, 7 figures. Accepted for publication in MNRAS

This is the second paper in our completeness series which addresses some of the issues raised in the previous article by Johnston, Teodoro & Hendry (2007) in which we developed statistical tests for assessing the completeness in apparent magnitude of magnitude-redshift surveys defined by two flux limits. The statistics, Tc and Tv, associated with these tests are non-parametric and defined in terms of the observed cumulative distribution function of sources; they represent powerful tools for identifying the true flux limit and/or characterising systematic errors in magnitude-redshift data. In this paper we present a new approach to constructing these estimators that resembles an "adaptive smoothing" procedure - i.e. by seeking to maintain the same amount the information, as measured by the signal-to-noise ratio, allocated to each galaxy. For consistency with our previous work, we apply our improved estimators to the Millennium Galaxy Catalogue (MGC) and the Two Degree Field Galaxy Redshift Survey (2dFGRS) data, and demonstrate that one needs to use a signal-to-noise appropriately tailored for each individual catalogue to optimise the performance of the completeness estimators. Furthermore, unless such an adaptive procedure is employed, the assessment of completeness may result in a spurious outcome if one uses other estimators present in the literature which have not been designed taking into account "shot noise" due to sampling., 9 pages, 6 figures, MNRAS accepted

Supermassive black hole binary systems (SMBHB) are standard sirens -- the gravitational wave analogue of standard candles -- and if discovered by gravitational wave detectors, they could be used as precise distance indicators. Unfortunately, gravitational lensing will randomly magnify SMBHB signals, seriously degrading any distance measurements. Using a weak lensing map of the SMBHB line of sight, we can estimate its magnification and thereby remove some uncertainty in its distance, a procedure we call "delensing." We find that delensing is significantly improved when galaxy shears are combined with flexion measurements, which reduce small-scale noise in reconstructed magnification maps. Under a Gaussian approximation, we estimate that delensing with a 2D mosaic image from an Extremely Large Telescope (ELT) could reduce distance errors by about 30-40% for a SMBHB at z=2. Including an additional wide shear map from a space survey telescope could reduce distance errors by 50%. Such improvement would make SMBHBs considerably more valuable as cosmological distance probes or as a fully independent check on existing probes., Comment: 9 pages, 4 figures, submitted to MNRAS

We investigate methods to best estimate the normalisation of the mass density fluctuation power spectrum (sigma_8) using peculiar velocity data from a survey like the Six degree Field Galaxy Velocity Survey (6dFGSv). We focus on two potential problems (i) biases from nonlinear growth of structure and (ii) the large number of velocities in the survey. Simulations of LambdaCDM-like models are used to test the methods. We calculate the likelihood from a full covariance matrix of velocities averaged in grid cells. This simultaneously reduces the number of data points and smooths out nonlinearities which tend to dominate on small scales. We show how the averaging can be taken into account in the predictions in a practical way, and show the effect of the choice of cell size. We find that a cell size can be chosen that significantly reduces the nonlinearities without significantly increasing the error bars on cosmological parameters. We compare our results with those from a principal components analysis following Watkins et al (2002) and Feldman et al (2003) to select a set of optimal moments constructed from linear combinations of the peculiar velocities that are least sensitive to the nonlinear scales. We conclude that averaging in grid cells performs equally well. We find that for a survey such as 6dFGSv we can estimate sigma_8 with less than 3% bias from nonlinearities. The expected error on sigma_8 after marginalising over Omega_m is approximately 16 percent., Accepted for publication in MNRAS, 12 pages, 5 figures. V2 Discussion clarified, 1 figure added, improvements to the text and figures; V3 Figure 5 Plotting error corrected, SN1a contours smaller

We present a new method for fitting peculiar velocity models to complete flux limited magnitude-redshifts catalogues, using the luminosity function of the sources as a distance indicator. The method is characterized by its robustness. In particular, no assumptions are made concerning the spatial distribution of sources and their luminosity function. Moreover the inclusion of additional observables, such for example the one carrying the Tully-Fisher information, is straightforward. As an illustration of the method, the predicted IRAS peculiar velocity model is herein tested using the fluxes of the IRAS 1.2 Jy sample as the distance indicator. The results suggest that this model, while successful in reproducing locally the cosmic flow, fails to describe the kinematics on larger scales., Comment: 4 pages, 2 figures, Cosmic Flows Workshop, Victoria B.C. Canada, July 1999, ed. S. Courteau, M. Strauss & J. Willick, ASP conf. series