Improving PSF modelling for weak gravitational lensing using new methods in model selection

A simple theoretical framework for the description and interpretation of spatially correlated modelling residuals is presented, and the resulting tools are found to provide a useful aid to model selection in the context of weak gravitational lensing. The description is focused upon the specific problem of modelling the spatial variation of a telescope point spread function (PSF) across the instrument field of view, a crucial stage in lensing data analysis, but the technique may be used to rank competing models wherever data are described empirically. As such it may, with further development, provide useful extra information when used in combination with existing model selection techniques such as the Akaike and Bayesian Information Criteria, or the Bayesian evidence. Two independent diagnostic correlation functions are described and the interpretation of these functions demonstrated using a simulated PSF anisotropy field. The efficacy of these diagnostic functions as an aid to the correct choice of empirical model is then demonstrated by analyzing results for a suite of Monte Carlo simulations of random PSF fields with varying degrees of spatial structure, and it is shown how the diagnostic functions can be related to requirements for precision cosmic shear measurement. The limitations of the technique, and opportunities for improvements and applications to fields other than weak gravitational lensing, are discussed.Comment: 18 pages, 12 figures. Modified to match version accepted for publication in MNRA

A renewal cluster model for the inter-arrival times of rainfall events

A statistical model, based on a renewal cluster point process, is proposed and used to infer the distributional properties of dry periods in a continuous-time record. The model incorporates a mixed probability distribution in which inter-arrival times are classified into two distinct types, representing cyclonic and anticyclonic weather. This results in rainfall events being clustered in time, and enables objective probabilistic statements to be made about storm properties, e.g. the expected number of events in a storm cluster. The model is fitted to data taken from a gauge near Wellington, New Zealand, by maximising the likelihood function with respect to the parameters. The Akaike Information Criteria is used to select the best fitting distributions from a range of candidates. The log-Normal distribution is found to provide the best fit to the times between successive storm clusters, whilst the Weibull distribution is found to provide the best fit to the times between successive events in the same storm cluster. Harmonic curves are used to provide a parsimonious parameterisation, allowing for the seasonal variation in precipitation. Under the fitted model, the interval series is transformed into a residual series, which is assessed to determine overall goodness-of-fit

Quantifying correlations between galaxy emission lines and stellar continua

We analyse the correlations between continuum properties and emission line equivalent widths of star-forming and active galaxies from the Sloan Digital Sky Survey. Since upcoming large sky surveys will make broad-band observations only, including strong emission lines into theoretical modelling of spectra will be essential to estimate physical properties of photometric galaxies. We show that emission line equivalent widths can be fairly well reconstructed from the stellar continuum using local multiple linear regression in the continuum principal component analysis (PCA) space. Line reconstruction is good for star-forming galaxies and reasonable for galaxies with active nuclei. We propose a practical method to combine stellar population synthesis models with empirical modelling of emission lines. The technique will help generate more accurate model spectra and mock catalogues of galaxies to fit observations of the new surveys. More accurate modelling of emission lines is also expected to improve template-based photometric redshift estimation methods. We also show that, by combining PCA coefficients from the pure continuum and the emission lines, automatic distinction between hosts of weak active galactic nuclei (AGNs) and quiescent star-forming galaxies can be made. The classification method is based on a training set consisting of high-confidence starburst galaxies and AGNs, and allows for the similar separation of active and star-forming galaxies as the empirical curve found by Kauffmann et al. We demonstrate the use of three important machine learning algorithms in the paper: k-nearest neighbour finding, k-means clustering and support vector machines.Comment: 14 pages, 14 figures. Accepted by MNRAS on 2015 December 22. The paper's website with data and code is at http://www.vo.elte.hu/papers/2015/emissionlines

Approximate Bayesian Computation by Modelling Summary Statistics in a Quasi-likelihood Framework

Approximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy between prior and posterior. Therefore, more elaborate methods, such as ABC with the Markov chain Monte Carlo algorithm (ABC-MCMC), should be used. However, the elaboration of a proposal density for MCMC is a sensitive issue and very difficult in the ABC setting, where the likelihood is intractable. We discuss an automatic proposal distribution useful for ABC-MCMC algorithms. This proposal is inspired by the theory of quasi-likelihood (QL) functions and is obtained by modelling the distribution of the summary statistics as a function of the parameters. Essentially, given a real-valued vector of summary statistics, we reparametrize the model by means of a regression function of the statistics on parameters, obtained by sampling from the original model in a pilot-run simulation study. The QL theory is well established for a scalar parameter, and it is shown that when the conditional variance of the summary statistic is assumed constant, the QL has a closed-form normal density. This idea of constructing proposal distributions is extended to non constant variance and to real-valued parameter vectors. The method is illustrated by several examples and by an application to a real problem in population genetics.Comment: Published at http://dx.doi.org/10.1214/14-BA921 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

A general class of zero-or-one inflated beta regression models

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented.Comment: 21 pages, 3 figures, 5 tables. Computational Statistics and Data Analysis, 17 October 2011, ISSN 0167-9473 (http://www.sciencedirect.com/science/article/pii/S0167947311003628

Automated model selection in finance: General-to-specic modelling of the mean and volatility specications

General-to-Specific (GETS) modelling has witnessed major advances over the last decade thanks to the automation of multi-path GETS specification search. However, several scholars have argued that the estimation complexity associated with financial models constitutes an obstacle to multi-path GETS modelling in finance. Making use of a recent result on log-GARCH Models, we provide and study simple but general and flexible methods that automate financial multi-path GETS modelling. Starting from a general model where the mean specification can contain autoregressive (AR) terms and explanatory variables, and where the exponential volatility specification can include log-ARCH terms, asymmetry terms, volatility proxies and other explanatory variables, the algorithm we propose returns parsimonious mean and volatility specifications. The finite sample properties of the methods are studied by means of extensive Monte Carlo simulations, and two empirical applications suggest the methods are very useful in practice.general-to-specific; specification search; model selection; finance; volatility

General to specific modelling of exchange rate volatility : a forecast evaluation

The general-to-specific (GETS) methodology is widely employed in the modelling of economic series, but less so in financial volatility modelling due to computational complexity when many explanatory variables are involved. This study proposes a simple way of avoiding this problem when the conditional mean can appropriately be restricted to zero, and undertakes an out-of-sample forecast evaluation of the methodology applied to the modelling of weekly exchange rate volatility. Our findings suggest that GETS specifications perform comparatively well in both ex post and ex ante forecasting as long as sufficient care is taken with respect to functional form and with respect to how the conditioning information is used. Also, our forecast comparison provides an example of a discrete time explanatory model being more accurate than realised volatility ex post in 1 step forecasting