John Verzani

Bio: John Verzani is an academic researcher from College of Staten Island. The author has contributed to research in topics: Brownian motion & Martingale (probability theory). The author has an hindex of 7, co-authored 13 publications receiving 321 citations. Previous affiliations of John Verzani include University of York.

Using R for Introductory Statistics

Abstract: DATA What Is Data? Some R Essentials Accessing Data by Using Indices Reading in Other Sources of Data UNIVARIATE DATA Categorical Data Numeric Data Shape of a Distribution BIVARIATE DATA Pairs of Categorical Variables Comparing Independent Samples Relationships in Numeric Data Simple Linear Regression MULTIVARIATE DATA Viewing Multivariate Data R Basics: Data Frames and Lists Using Model Formula with Multivariate Data Lattice Graphics Types of Data in R DESCRIBING POPULATIONS Populations Families of Distributions The Central Limit Theorem SIMULATION The Normal Approximation for the Binomial for loops Simulations Related to the Central Limit Theorem Defining a Function Investigating Distributions Bootstrap Samples Alternates to for loops CONFIDENCE INTERVALS Confidence Interval Ideas Confidence Intervals for a Population Proportion, p Confidence Intervals for the Population Mean, u Other Confidence Intervals Confidence Intervals for Differences Confidence Intervals for the Median SIGNIFICANCE TESTS Significance Test for a Population Proportion Significance Test for the Mean (t-Tests) Significance Tests and Confidence Intervals Significance Tests for the Median Two-Sample Tests of Proportion Two-Sample Tests of Center GOODNESS OF FIT The Chi-Squared Goodness-of-Fit Test The Chi-Squared Test of Independence Goodness-of-Fit Tests for Continuous Distributions LINEAR REGRESSION The Simple Linear Regression Model Statistical Inference for Simple Linear Regression Multiple Linear Regression ANALYSIS OF VARIANCE One-Way ANOVA Using lm() for ANOVA ANCOVA Two-Way ANOVA TWO EXTENSIONS OF THE LINEAR MODEL Logistic Regression Nonlinear Models APPENDIX A: GETTING, INSTALLING, AND RUNNING R Installing and Starting R Extending R Using Additional Packages APPENDIX B: GRAPHICAL USER INTERFACES AND R The Windows GUI The Mac OS X GUI Rcdmr APPENDIX C: TEACHING WITH R APPENDIX D: MORE ON GRAPHICS WITH R Low- and High-Level Graphic Functions Creating New Graphics in R APPENDIX E: PROGRAMMING IN R Editing Functions Using Functions Using Files and a Better Editor Object-Oriented Programming with R INDEX

On the conditioned exit measures of super Brownian motion

Abstract: In this paper we present a martingale related to the exit measures of super Brownian motion. By changing measure with this martingale in the canonical way we have a new process associated with the conditioned exit measure. This measure is shown to be identical to a measure generated by a non-homogeneous branching particle system with immigration of mass. An application is given to the problem of conditioning the exit measure to hit a number of specified points on the boundary of a domain. The results are similar in flavor to the “immortal particle” picture of conditioned super Brownian motion but more general, as the change of measure is given by a martingale which need not arise from a single harmonic function.

On the conditioned exit measures of super-Brownian motion

Abstract: In this paper we present a martingale related to the exit measures of super-Brownian motion. By changing measure with this martingale in the canonical way we have a new process associated with the conditioned exit measure. This measure is shown to be identical to a measure generated by a non-homogeneous branching particle system with immigration of mass. An application is given to the problem of conditioning the exit measure to hit a number of specified points on the boundary of a domain. The results are similar in flavor to the "immortal particle" picture of conditioned super-Brownian motion but more general, as the change of measure is given by a martingale which need not arise from a single harmonic function.

Getting Started with RStudio

Abstract: This e-book will introduce users to the RStudio framework for using and programming R, the widely used open source statistical computing environment. The RStudio framework, is an open source project that brings together many powerful coding tools into an intuitive interface. It runs under all major platforms (Windows, Mac, Linux) and through a web browser (using the server installation). This text should appeal to newer R users and students who want to explore the interface to get the most out of R and to older R users who want to use a more modern looking development environment. The book will serve as both a resource to look up specific features provided by RStudio and as an introduction to the following processes with R: data analysis, programming and report generation.

Extending the Linear Model with R

Abstract: Extending the linear model with R , Extending the linear model with R , کتابخانه دیجیتال جندی شاپور اهواز

GA: A Package for Genetic Algorithms in R

Abstract: Genetic algorithms (GAs) are stochastic search algorithms inspired by the basic principles of biological evolution and natural selection. GAs simulate the evolution of living organisms, where the fittest individuals dominate over the weaker ones, by mimicking the biological mechanisms of evolution, such as selection, crossover and mutation. GAs have been successfully applied to solve optimization problems, both for continuous (whether differentiable or not) and discrete functions. This paper describes the R package GA, a collection of general purpose functions that provide a flexible set of tools for applying a wide range of genetic algorithm methods. Several examples are discussed, ranging from mathematical functions in one and two dimensions known to be hard to optimize with standard derivative-based methods, to some selected statistical problems which require the optimization of user defined objective functions. (This paper contains animations that can be viewed using the Adobe Acrobat PDF viewer.)

FEAR: A software package for frontier efficiency analysis with R

Abstract: This paper describes a software package for computing non-parametric efficiency estimates, making inference, and testing hypotheses in frontier models. Commands are provided for bootstrapping as well as computation of some new, robust estimators of efficiency, etc.

An introduction to R

Abstract: This tutorial manual provides a comprehensive introduction to R, a software package for statistical computing and graphics. R supports a wide range of statistical techniques, and is easily extensible via user-defined functions written in its own language or using C, C++ or Fortran. One of R's strengths is the ease with which well-designed publication-quality plots can be produced. This is a printed copy of the tutorial manual from the R distribution, with additional examples, notes and corrections. It is based on R version 2.9.0, released April 2009. R is free software, distributed under the terms of the GNU General Public License (GPL). It can be used with GNU/Linux, Unix and Microsoft Windows. All the money raised from the sale of this book supports the development of free software and documentation.

Random Trees, Levy Processes and Spatial Branching Processes

Abstract: We investigate the genealogical structure of general critical or subcritical continuous-state branching processes. Analogously to the coding of a discrete tree by its contour function, this genealogical structure is coded by a real-valued stochastic process called the height process, which is itself constructed as a local time functional of a Levy process with no negative jumps. We present a detailed study of the height process and of an associated measure-valued process called the exploration process, which plays a key role in most applications. Under suitable assumptions, we prove that whenever a sequence of rescaled Galton-Watson processes converges in distribution, their genealogies also converge to the continuous branching structure coded by the appropriate height process. We apply this invariance principle to various asymptotics for Galton-Watson trees. We then use the duality properties of the exploration process to compute explicitly the distribution of the reduced tree associated with Poissonnian marks in the height process, and the finite-dimensional marginals of the so-called stable continuous tree. This last calculation generalizes to the stable case a result of Aldous for the Brownian continuum random tree. Finally, we combine the genealogical structure with an independent spatial motion to develop a new approach to superprocesses with a general branching mechanism. In this setting, we derive certain explicit distributions, such as the law of the spatial reduced tree in a domain, consisting of the collection of all historical paths that hit the boundary.