Investigation of Simple Linear Measurement Error Models (SLMEMS) with Correlated Data

The primary goal of this research is to develop statistical methods to determine if observed real responses are adequately modeled by (possibly stochastic) simulation models that incorporate first-order autoregressive measurement errors. We assume the measurement errors are normally distributed to allow development of likelihood-based methods of inference. Simulated true responses are modeled as a simple linear regression on the true response values. That is, we wish to detect if either additive or multiplicative biases exist in the simulation model. Efficient score and likelihood ratio tests using observed real process data are developed to test the joint null hypothesis that no significant additive or multiplicative biases exist in the stochastic simulation model. Tests for adequacy of both stochastic and deterministic simulation models are developed using, respectively, structural and functional simple linear measurement error models that allow the measurement errors to satisfy normal first-order autoregressive processes. A byproduct of this research is developments of analogous tests of the null hypothesis that errors of measurement are independent. Such tests would be of use if the real process is not a times series and there was uncertainty whether the simulation model should allow for correlated measurement errors. Analytic and simulation results show that all maximum likelihood estimators (MLEs) of model parameters MLEs are consistent under the structural model, but some MLEs of parameters are inconsistent under functional model. Test statistics developed under the structural model are shown to be asymptotically distributed as chi-squared random variables with two degrees of freedom when testing for additive and multiplicative biases in the simulation model having correlated measurement errors. Test statistics developed under the structural model are shown to be asymptotically distributed as chi-squared random variables with one degree of freedom when testing for independence of the measurement errors. However, for functional models, the corresponding test statistics are asymptotically distributed as random variables that are two times the chi-squared distributions. Empirical power curves are plotted under different parameter configurations. Behaviors of test statistics and power curves are found to be affected by the sample size, signal to noise ratio and strength of correlations among measurement errors

Practical Statistics for Particle Physics

This is the write-up of a set of lectures given at the Asia Europe Pacific School of High Energy Physics in Quy Nhon, Vietnam in September 2018, to an audience of PhD students in all branches of particle physics They cover the different meanings of 'probability', particularly frequentist and Bayesian, the binomial, Poisson and Gaussian distributions, hypothesis testing, estimation, errors (including asymmetric and systematic errors) and goodness of fit. Several different methods used in setting upper limits are explained, followed by a discussion on why 5 sigma are conventionally required for a 'discovery'

A semiparametric regression model for paired longitudinal outcomes with application in childhood blood pressure development

This research examines the simultaneous influences of height and weight on longitudinally measured systolic and diastolic blood pressure in children. Previous studies have shown that both height and weight are positively associated with blood pressure. In children, however, the concurrent increases of height and weight have made it all but impossible to discern the effect of height from that of weight. To better understand these influences, we propose to examine the joint effect of height and weight on blood pressure. Bivariate thin plate spline surfaces are used to accommodate the potentially nonlinear effects as well as the interaction between height and weight. Moreover, we consider a joint model for paired blood pressure measures, that is, systolic and diastolic blood pressure, to account for the underlying correlation between the two measures within the same individual. The bivariate spline surfaces are allowed to vary across different groups of interest. We have developed related model fitting and inference procedures. The proposed method is used to analyze data from a real clinical investigation.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS567 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Probability and Statistics for Particle Physicists

Lectures presented at the 1st CERN Asia-Europe-Pacific School of High-Energy Physics, Fukuoka, Japan, 14-27 October 2012. A pedagogical selection of topics in probability and statistics is presented. Choice and emphasis are driven by the author's personal experience, predominantly in the context of physics analyses using experimental data from high-energy physics detectors.Comment: Updated version of lectures given at the First Asia-Europe-Pacific School of High-Energy Physics, Fukuoka, Japan, 14-27 October 2012. Published as a CERN Yellow Report (CERN-2014-001) and KEK report (KEK-Proceedings-2013-8), K. Kawagoe and M. Mulders (eds.), 2014, p. 219. Total 28 pages, 36 figure

Detecting Baryon Acoustic Oscillations

Baryon Acoustic Oscillations are a feature imprinted in the galaxy distribution by acoustic waves traveling in the plasma of the early universe. Their detection at the expected scale in large-scale structures strongly supports current cosmological models with a nearly linear evolution from redshift approximately 1000, and the existence of dark energy. Besides, BAOs provide a standard ruler for studying cosmic expansion. In this paper we focus on methods for BAO detection using the correlation function measurement. For each method, we want to understand the tested hypothesis (the hypothesis H0 to be rejected) and the underlying assumptions. We first present wavelet methods which are mildly model-dependent and mostly sensitive to the BAO feature. Then we turn to fully model-dependent methods. We present the most often used method based on the chi^2 statistic, but we find it has limitations. In general the assumptions of the chi^2 method are not verified, and it only gives a rough estimate of the significance. The estimate can become very wrong when considering more realistic hypotheses, where the covariance matrix of the measurement depends on cosmological parameters. Instead we propose to use a new method based on two modifications: we modify the procedure for computing the significance and make it rigorous, and we modify the statistic to obtain better results in the case of varying covariance matrix. We verify with simulations that correct significances are different from the ones obtained using the classical chi^2 procedure. We also test a simple example of varying covariance matrix. In this case we find that our modified statistic outperforms the classical chi^2 statistic when both significances are correctly computed. Finally we find that taking into account variations of the covariance matrix can change both BAO detection levels and cosmological parameter constraints