Reconstructing Probability Distributions with Gaussian Processes

Modern cosmological analyses constrain physical parameters using Markov Chain Monte Carlo (MCMC) or similar sampling techniques. Oftentimes, these techniques are computationally expensive to run and require up to thousands of CPU hours to complete. Here we present a method for reconstructing the log-probability distributions of completed experiments from an existing MCMC chain (or any set of posterior samples). The reconstruction is performed using Gaussian process regression for interpolating the log-probability. This allows for easy resampling, importance sampling, marginalization, testing different samplers, investigating chain convergence, and other operations. As an example use-case, we reconstruct the posterior distribution of the most recent Planck 2018 analysis. We then resample the posterior, and generate a new MCMC chain with forty times as many points in only thirty minutes. Our likelihood reconstruction tool can be found online at https://github.com/tmcclintock/AReconstructionTool.Comment: 7 pages, 4 figures, repository at https://github.com/tmcclintock/AReconstructionToo

Annealing a Follow-up Program: Improvement of the Dark Energy Figure of Merit for Optical Galaxy Cluster Surveys

The precision of cosmological parameters derived from galaxy cluster surveys is limited by uncertainty in relating observable signals to cluster mass. We demonstrate that a small mass-calibration follow-up program can significantly reduce this uncertainty and improve parameter constraints, particularly when the follow-up targets are judiciously chosen. To this end, we apply a simulated annealing algorithm to maximize the dark energy information at fixed observational cost, and find that optimal follow-up strategies can reduce the observational cost required to achieve a specified precision by up to an order of magnitude. Considering clusters selected from optical imaging in the Dark Energy Survey, we find that approximately 200 low-redshift X-ray clusters or massive Sunyaev-Zel'dovich clusters can improve the dark energy figure of merit by 50%, provided that the follow-up mass measurements involve no systematic error. In practice, the actual improvement depends on (1) the uncertainty in the systematic error in follow-up mass measurements, which needs to be controlled at the 5% level to avoid severe degradation of the results; and (2) the scatter in the optical richness-mass distribution, which needs to be made as tight as possible to improve the efficacy of follow-up observations.Comment: 12 pages, 7 figures, replaced to match published versio

Beyond Bubbles: The role of asset prices in early-warning indicators

Asset prices have recently become a common topic in economic debate. Nevertheless, much time has been spent in determining if they effectively exhibit a bubble component, and not in examining whether asset prices affectively contain relevant information concerning future market developments. This paper is a first effort in Colombia in this direction, aimed towards the construction of early - warning indicators using financial and real variables. Results show evidence to support that there is relevant information embedded in these series, as all indicators (except the new housing price indicator) show a significant deviation for the year(s) prior to the 98-99 crisis. Additionally, the exercises here conducted show that the performance of asset price indicators is enhanced by including credit and investment. When the early-warning indicators are on, the role of the policy maker should be more active in the market; not necessarily in terms of altering interest rates, but in communicating with market agents, promoting portfolio and perspective (i.e. short and long-term) diversification and urging financial agents to make the best use of the tools that are available to them.Asset Price Bubbles, Early-Warning Indicators, Present Value Model, Financial Crisis, Prudential Regulation. Classification JEL: E58; E44; G12; G18.

Multimarket spatial competition in the Colombian deposit market

This paper presents a multimarket spatial competition oligopoly model for the Colombian deposit market, in line with the New Empirical Industrial Organization (NEIO) approach. In this framework, banks use price and non-price strategies to compete in the market, which allows us to analyze the country and the regional competitiveness level. The theoretical model is applied to quarterly Colombian data that covers the period between 1996 and 2005. Our results suggest that, although the country deposit market appears to be more competitive than the Nash equilibrium, there are some local areas within the country that present evidence of market power.Banking; Location; Competition; Colombia. Classification JEL: D4; G21; L13; R12.

Weak Lensing Peak Finding: Estimators, Filters, and Biases

Large catalogs of shear-selected peaks have recently become a reality. In order to properly interpret the abundance and properties of these peaks, it is necessary to take into account the effects of the clustering of source galaxies, among themselves and with the lens. In addition, the preferred selection of lensed galaxies in a flux- and size-limited sample leads to fluctuations in the apparent source density which correlate with the lensing field (lensing bias). In this paper, we investigate these issues for two different choices of shear estimators which are commonly in use today: globally-normalized and locally-normalized estimators. While in principle equivalent, in practice these estimators respond differently to systematic effects such as lensing bias and cluster member dilution. Furthermore, we find that which estimator is statistically superior depends on the specific shape of the filter employed for peak finding; suboptimal choices of the estimator+filter combination can result in a suppression of the number of high peaks by orders of magnitude. Lensing bias generally acts to increase the signal-to-noise \nu of shear peaks; for high peaks the boost can be as large as \Delta \nu ~ 1-2. Due to the steepness of the peak abundance function, these boosts can result in a significant increase in the abundance of shear peaks. A companion paper (Rozo et al., 2010) investigates these same issues within the context of stacked weak lensing mass estimates.Comment: 11 pages, 8 figures; comments welcom

The Ysz--Yx Scaling Relation as Determined from Planck and Chandra

SZ clusters surveys like Planck, the South Pole Telescope, and the Atacama Cosmology Telescope, will soon be publishing several hundred SZ-selected systems. The key ingredient required to transport the mass calibration from current X-ray selected cluster samples to these SZ systems is the Ysz--Yx scaling relation. We constrain the amplitude, slope, and scatter of the Ysz--Yx scaling relation using SZ data from Planck, and X-ray data from Chandra. We find a best fit amplitude of \ln (D_A^2\Ysz/CY_X) = -0.202 \pm 0.024 at the pivot point CY_X=8\times 10^{-5} Mpc^2. This corresponds to a Ysz/Yx-ratio of 0.82\pm 0.024, in good agreement with X-ray expectations after including the effects of gas clumping. The slope of the relation is \alpha=0.916\pm 0.032, consistent with unity at \approx 2.3\sigma. We are unable to detect intrinsic scatter, and find no evidence that the scaling relation depends on cluster dynamical state

Constraining the Scatter in the Mass-Richness Relation of maxBCG Clusters With Weak Lensing and X-ray Data

We measure the logarithmic scatter in mass at fixed richness for clusters in the maxBCG cluster catalog, an optically selected cluster sample drawn from SDSS imaging data. Our measurement is achieved by demanding consistency between available weak lensing and X-ray measurements of the maxBCG clusters, and the X-ray luminosity--mass relation inferred from the 400d X-ray cluster survey, a flux limited X-ray cluster survey. We find \sigma_{\ln M|N_{200}}=0.45^{+0.20}_{-0.18} (95% CL) at N_{200} ~ 40, where N_{200} is the number of red sequence galaxies in a cluster. As a byproduct of our analysis, we also obtain a constraint on the correlation coefficient between \ln Lx and \ln M at fixed richness, which is best expressed as a lower limit, r_{L,M|N} >= 0.85 (95% CL). This is the first observational constraint placed on a correlation coefficient involving two different cluster mass tracers. We use our results to produce a state of the art estimate of the halo mass function at z=0.23 -- the median redshift of the maxBCG cluster sample -- and find that it is consistent with the WMAP5 cosmology. Both the mass function data and its covariance matrix are presented.Comment: 14 pages, 6 figures, submitted to Ap