Data from recent galaxy surveys reveal that, even at fixed stellar mass, quiescent galaxies are preferentially found around other red galaxies, an observation referred to as galactic conformity. This detection may offer important clues toward a fuller understanding of galaxy formation and evolution. While dark matter halo mass is thought to be the dominant reason that star-forming galaxies are eventually quenched, galaxy conformity suggests that additional physics or environmental factors could be required. This has important implications for modeling large-scale surveys and understanding cosmology from small-scale clustering. We present an analysis of galactic conformity in the Illustris Suite of cosmological hydro simulations. We find that a strong galactic conformity signal is present out to r = 3 Mpc and that a smaller signal is present to r = 10 Mpc for the lowest mass galaxies in our sample. The red fraction is higher around red galaxies than around blue galaxies in bins of either stellar mass or halo mass. We show that this galactic conformity is matched by a dark matter halo conformity in which older halos are preferentially located nearby other older halos. We connect the two types of conformity with a semi-empirical model that connect stellar mass and color with dark matter halos, and we study how using different galaxy properties in our model affects the resultant galactic conformity signal. We discuss the implications of these results for interpreting similar signals in observations. We show the results of a small-scale clustering investigation from the PRIMUS redshift survey. We use spectroscopic-photometric cross-correlations to calculate local galaxy overdensities as function of galaxy properties from 0.2 < z < 1. We present the luminosity and color dependencies of galaxy clustering as a function of physical scale. We show that there exists a luminosity-dependence for both red and blue galaxies, but that they differ in shape, with red galaxies showing non-monotonic behavior as a function of luminosity while blue galaxies are reasonably fit with a power-law. We discuss these results in light of physics of galaxy evolution. We then extend our PRIMUS small-scale clustering study to incorporate an exploration of galactic conformity. We now select photometric galaxies by their inferred stellar mass and color, and we use the quotient of the relative overdensities calculated from the clustering amplitude to define a quiescent fraction around each PRIMUS galaxy. We present study this quiescent fraction as a function of primary mass, secondary mass, and redshift. We show that, at 0.2 < z < 0.6, there exists a galactic conformity signal out to r ≈ 1 Mpc, at least for lower mass primary galaxies. We also show that there exists a strong mass dependence in our lowest redshift bin. In our highest redshift bin, we show that the signal is weaker than at lower redshift. We explain our results in the context of both the current observational and theoretical literature. / Astronomy

In this thesis, we present three topics broadly connected to the concept and use of statistical information, and specifically regarding the problems of hypothesis testing and model selection, astronomical image analysis, and Monte Carlo integration. The first chapter is inspired by the work of DeGroot (1962) and Nicolae et al. (2008) and is the most directly focused on the theme of statistical information. DeGroot (1962) developed a general framework for constructing Bayesian measures of the expected information that an experiment will provide for estimation. We propose an analogous framework for measures of information for hypothesis testing, and illustrate how these measures can be applied in experimental design. In contrast to estimation information measures that are typically used in experimental design for surface estimation, test information measures are more useful in experimental design for hypothesis testing and model selection. Indeed, one test information measure suggested by our framework is probability based, and in design contexts where decision problem are of interest, it has more appealing properties than variance based measures. The underlying intuition of our design proposals is straightforward: to distinguish between two or more models we should collect data from regions of the covariate space for which the models differ most. Nicolae et al. (2008) give an asymptotic equivalence between their test information measures and Fisher information. We extend this result to all test information measures under our framework, and hence further our understanding of the links between test and estimation information measures. In the second chapter, we present a powerful new algorithm that combines both spatial and spectral (energy) information to separate photons from overlapping sources (e.g., stars) in an astronomical image. We use Bayesian statistical methods to simultaneously infer the number of overlapping sources, to probabilistically separate the photons among the sources, and to fit the parameters describing the individual sources. Using the Bayesian joint posterior distribution, we are able to coherently quantify the uncertainties associated with all these parameters. The advantages of combining spatial and spectral information are demonstrated through a simulation study. The utility of the approach is then illustrated by analysis of observations of the sources FK Aqr and FL Aqr with the XMM-Newton Observatory and the central region of the Orion Nebula Cluster with the Chandra X-ray Observatory. In this chapter we make additional effort to explain relevant standard statistical ideas and methods in order to make the exposition more accessible to astronomers unfamiliar with statistics. The last chapter extends the maximum likelihood theory developed by Kong et al. (2003) for deriving Monte Carlo estimators of normalizing constants. Kong et al. (2003) had the fundamental idea of treating the baseline measure as an unknown quantity to be estimated, and found that this suggested a maximum likelihood method for estimating integrals of interest. Their work shows that sub-models of the baseline measure can be used to incorporate some of our knowledge of the true measure, thus allowing greater statistical precision to be gained at the expense of more function evaluations, but without the need for more Monte Carlo samples. Our contribution is to introduce a simple extension of this framework which greatly increases its flexibility for trading off statistical and computational efficiency. As a result, we gain an appealing maximum likelihood interpretation of the very effective warp transformations proposed by Meng and Schilling (2002). We additionally investigate the open problem of optimally choosing parameters for sub-models of the baseline measure. / Statistics

The first chapter addresses a Beta-Binomial-Logit model that is a Beta-Binomial conjugate hierarchical model with covariate information incorporated via a logistic regression. Various researchers in the literature have unknowingly used improper posterior distributions or have given incorrect statements about posterior propriety because checking posterior propriety can be challenging due to the complicated functional form of a Beta-Binomial-Logit model. We derive data-dependent necessary and sufficient conditions for posterior propriety within a class of hyper-prior distributions that encompass those used in previous studies. Frequency coverage properties of several hyper-prior distributions are also investigated to see when and whether Bayesian interval estimates of random effects meet their nominal confidence levels. The second chapter deals with a time delay estimation problem in astrophysics. When the gravitational field of an intervening galaxy between a quasar and the Earth is strong enough to split light into two or more images, the time delay is defined as the difference between their travel times. The time delay can be used to constrain cosmological parameters and can be inferred from the time series of brightness data of each image. To estimate the time delay, we construct a Gaussian hierarchical model based on a state-space representation for irregularly observed time series generated by a latent continuous-time Ornstein-Uhlenbeck process. Our Bayesian approach jointly infers model parameters via a Gibbs sampler. We also introduce a profile likelihood of the time delay as an approximation of its marginal posterior distribution. The last chapter specifies a repelling-attracting Metropolis algorithm, a new Markov chain Monte Carlo method to explore multi-modal distributions in a simple and fast manner. This algorithm is essentially a Metropolis-Hastings algorithm with a proposal that consists of a downhill move in density that aims to make local modes repelling, followed by an uphill move in density that aims to make local modes attracting. The downhill move is achieved via a reciprocal Metropolis ratio so that the algorithm prefers downward movement. The uphill move does the opposite using the standard Metropolis ratio which prefers upward movement. This down-up movement in density increases the probability of a proposed move to a different mode. / Statistics

Though dark energy constitutes 72% of the Universe’s present-day energy density, its nature remains unknown. Precise measurements of the Universe’s expansion over cosmic time constrain dark energy’s ratio of pressure to energy density and allow model discrimination. One of the leading techniques for measuring the expansion rate is the Baryon Acoustic Oscillation (BAO) method, which uses the imprint on galaxy clustering today of relativistic waves in the ionized early Universe as a standard ruler. Thus far, the BAO method has used correlations of pairs of galaxies (the 2-point correlation function or 2PCF) to make 1% precision cosmic distance measurements. We present a derivation of the BAO’s late-time signature from first principles and then explore one of the few known possible sources of systematic error in the BAO method: a relative velocity between baryons and dark matter sourced by their different behaviors prior to redshift roughly 1000. We show how this systematic can shift the BAO scale measured from the 2PCF, and that it has a unique signature in correlations of galaxy triplets (the 3-point correlation function or 3PCF). We then present a reformulation of the 3PCF with several transformative advantages: speed comparable to the 2PCF calculation, a tractable covariance matrix, and the ability to exploit all triangles. Using an algorithm this reformulation enables, we report the first high-significance (4.5σ) detection of the BAO in the 3PCF, allowing us to measure the distance to redshift 0.57 with 1.7% precision from the 3PCF alone. This distance scale measurement is highly independent of that from the 2PCF. Using it in conjunction with the 2PCF is equivalent to extending the observing time of the Baryon Oscillation Spectroscopic Survey (BOSS) by roughly 30%. We also make highly precise measurements of the linear biasing of galaxy formation and a moderate-significance (2.5σ) detection of tidal tensor biasing of galaxy formation. Finally, we place a 1% precision constraint on the baryon-dark matter relative velocity bias. This constraint means that the possible shift in the BAO scale measured from the BOSS 2PCF is less than a quarter percent and thus greatly sub-dominant to the statistical errors. / Astronomy

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