MERLOT Search - category=2513&createdSince=2012-12-29&sort.property=dateCreated
http://www.merlot.org:80/merlot/
A search of MERLOT materialsCopyright 1997-2015 MERLOT. All rights reserved.Thu, 5 Mar 2015 08:02:20 PSTThu, 5 Mar 2015 08:02:20 PSTMERLOT Search - category=2513&createdSince=2012-12-29&sort.property=dateCreatedhttp://www.merlot.org:80/merlot/images/merlot.gif
http://www.merlot.org:80/merlot/
4434Introduction to Probability - Probability Examples c-1
http://www.merlot.org/merlot/viewMaterial.htm?id=992042
'In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.Topics as Elementary probability calculus, density functions and stochastic processes are illustrated.This book requires knowledge of Calculus 1 and Calculus 2.'Quantitative Analysis - Algebra with a Business Perspective
http://www.merlot.org/merlot/viewMaterial.htm?id=989756
This is a free textbook from Bookboon.'This tutorial textbook has been organized into 4 chapters (units) with several individual tutorial lessons within each chapter. As presented in the table of contents, each of the tutorials has been listed separately with its objective and its starting page. For coding purposes: “Tutorial N.M” means that the tutorial is the Mth lesson in chapter N.I attempted to present each of the tutorials as if a person (teacher, tutor) was sitting next to the reader talking each of the concepts through. My goal was to make sure that each of the lessons was fully explained but still fully understandable. Hopefully this goal was met.- description of whom I believe might be interested in using these tutorials…The purpose of this tutorial textbook is to present mathematical skills (algebraic concepts) and their various applications that may be important to students of management (business) science. The applications included should allow readers to view math in a practical setting relevant to their intended careers.'Topics include:Equations, Inequalities & Linear ProgrammingMatrices & Array OperationsQuadratic & Other Special FunctionsMathematics of FinanceAbout the AuthorRegressIt -- free Excel add-in for regression and data analysis
http://www.merlot.org/merlot/viewMaterial.htm?id=988548
Free Excel add-in for linear regression and multivariate data analysis which offers presentation-quality graphics and support for good analytical practices, especially data and model visualization, tests of model assumptions, appropriate use of transformed variables in linear models, intelligent formatting of tables and charts, keeping a detailed and well-organized audit trail, and uniquely identifying the user who performed the analysis. It provides a good complement, if not a substitute, for commercial statistical software as far as linear regression modeling and descriptive analysis are concerned. It was developed in a university teaching environment but is also intended for professional use.Calculus - Early Transcendentals
http://www.merlot.org/merlot/viewMaterial.htm?id=988248
'From the MAA review of this book: "The discussions and explanations are succinct and to the point, in a way that pleases mathematicians who don't like calculus books to go on and on." There are eleven chapters beginning with analytic geometry and ending with sequences and series. The book covers the standard material in a one variable calculus course for science and engineering. The size of the book is such that an instructor does not have to skip sections in order to fit the material into the typical course schedule. There are sufficiently many exercises at the end of each sections, but not as many as the much bigger commercial texts. Some students and instructors may want to use something like a Schaum's outline for additional problems.'Dynamical Systems with Applications using MATLAB
http://www.merlot.org/merlot/viewMaterial.htm?id=987445
'״Dynamical Systems with Applications using MATLAB 2nd Edition" covers standard material for an introduction to dynamical systems theory. The text deals with both discrete and continuous systems. There are applications in computing, mechanical systems, chemical kinetics, electric circuits, interacting species, economics, nonlinear optics, biology, neural networks and materials science, for example. These MATLAB programs have been written to supplement the textbook, and give the reader a real hands-on experience. The text is aimed at senior undergraduates, graduate students, and working scientists in industry.'Nonlinear Dynamics and Chaos
http://www.merlot.org/merlot/viewMaterial.htm?id=987443
'This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. Strogatz's book, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.״ The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the course is its emphasis on applications. These include airplane wing vibrations, biological rhythms, insect outbreaks, chemical oscillators, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory. The theoretical work is enlivened by frequent use of computer graphics, simulations, and videotaped demonstrations of nonlinear phenomena.The essential prerequisite is single-variable calculus, including curve sketching, Taylor series, and separable differential equations. In a few places, multivariable calculus (partial derivatives, Jacobian matrix, divergence theorem) and linear algebra (eigenvalues and eigenvectors) are used. Fourier analysis is not assumed, and is developed where needed. Introductory physics is used throughout. Other scientific prerequisites would depend on the applications considered, but in all cases, a first course should be adequate preparation.'Nonlinear Dynamics and Chaos
http://www.merlot.org/merlot/viewMaterial.htm?id=987463
'This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory.Richly illustrated, and with many exercises and worked examples, this book is ideal for an introductory course at the junior/senior or first-year graduate level. It is also ideal for the scientist who has not had formal instruction in nonlinear dynamics, but who now desires to begin informal study. The prerequisites are multivariable calculus and introductory physics.'An Introduction to Instrumental Variables
http://www.merlot.org/merlot/viewMaterial.htm?id=966496
This video was recorded at Workshop on Inverse Problems: Econometry, Numerical Analysis and Optimization, Statistics, Touluse 2005. What statisticians, numericians, engineers or econometricians mean by "inverse problem" often differs. For a statistician, an inverse problem is an estimation problem of a function which is not directly observed. The data are finite in number and contain errors, whose variance decreases with the number of observations, as they do in classical inference problems, while the unknown typically is infinite dimensional, as it is in nonparametric regression. For numericians, the noise is more an error induced by the fact that the real data are not directly observed. But the asymptotics differ, as the regularity conditions imposed for the solution. Finally, in econometrics the structural approach combines data observation and economic model. The parameter of interest is defined as a solution of a functional equation depending on the data distribution. Hence the operator in the underlying inverse problem is in general unknown. Many questions arise naturally in all the different fields, which are of great both applied and theoretical interest: identifiability, consistency and optimality in various forms, iterative methods. There have been great advances in the study of inverse problems within these three communities and we think that it is time for a workshop where the different point of views could be confronted, leading to exchanges of methodologies and several improvements. For instance non linear inverse problems have been studied in numerical analysis while statistical literature on this topics is scarce. Unknown inverse operators are common in econometrics but the problem is not well studied in statistics. On the other hand, adaptive estimation and optimal rates of convergence are common in statistics but not in the other fields.Regularization: Quadratic Versus Sparsity-enforcing and Deterministic Versus Stochastic Methods
http://www.merlot.org/merlot/viewMaterial.htm?id=966508
This video was recorded at Workshop on Inverse Problems: Econometry, Numerical Analysis and Optimization, Statistics, Touluse 2005. What statisticians, numericians, engineers or econometricians mean by "inverse problem" often differs. For a statistician, an inverse problem is an estimation problem of a function which is not directly observed. The data are finite in number and contain errors, whose variance decreases with the number of observations, as they do in classical inference problems, while the unknown typically is infinite dimensional, as it is in nonparametric regression. For numericians, the noise is more an error induced by the fact that the real data are not directly observed. But the asymptotics differ, as the regularity conditions imposed for the solution. Finally, in econometrics the structural approach combines data observation and economic model. The parameter of interest is defined as a solution of a functional equation depending on the data distribution. Hence the operator in the underlying inverse problem is in general unknown. Many questions arise naturally in all the different fields, which are of great both applied and theoretical interest: identifiability, consistency and optimality in various forms, iterative methods. There have been great advances in the study of inverse problems within these three communities and we think that it is time for a workshop where the different point of views could be confronted, leading to exchanges of methodologies and several improvements. For instance non linear inverse problems have been studied in numerical analysis while statistical literature on this topics is scarce. Unknown inverse operators are common in econometrics but the problem is not well studied in statistics. On the other hand, adaptive estimation and optimal rates of convergence are common in statistics but not in the other fields.Slowly but surely, Bayesian ideas revolutionize medical research
http://www.merlot.org/merlot/viewMaterial.htm?id=966851
This video was recorded at International Society for Bayesian Analysis (ISBA) Lectures on Bayesian Foundations, Kyoto 2012. Bayesian theory is elegant and intuitive. But elegance may have little value in practical settings. The "Bayesian Revolution" of the last half of the 20th century was irrelevant for biostatisticians. They were busy changing the world in another way, and they neither needed nor wanted more methodology than they already had. The randomized controlled trial (RCT) came into existence in the 1940s and it changed medical research from an art into a science, with biostatisticians guiding the process. To make matters worse for the reputation of Bayesians, we seemed to be anti-randomization, and medical researchers feared we wanted to return them to the dark ages. The standard approach to clinical experimentation is frequentist, which has advantages and disadvantages. One disadvantage is that unit of statistical inference is the entire experiment. As a consequence, the RCT has remained largely unchanged. It is still the gold standard of medical research, but it can make research ponderously slow. And it is not ideally suited for the "personalized medicine" approach of today, identifying which types of patients benefit from which therapies. In this presentation I'll chronicle the increased use of the Bayesian perspective in medical research over this period. An important niche regards adaptive design. I'll describe a variety of approaches, most of which employ randomization, and all employ Bayesian updating. Accumulating trial results are analyzed frequently with the possibility of modifying the trial's future course based on the overall theme of the trial. It is possible to have many treatment arms. Including combination therapies enables learning howtreatments interact with each other aswell as the way they interact with biomarkers of disease that are specific to individual patients. I will give an example (called I-SPY 2) of a Bayesian adaptive biomarker-driven trial in neoadjuvant breast cancer. The goal is to efficiently identify biomarker signatures for a variety of agents and combinations being considered simultaneously. Longitudinal modeling plays a vital role. Although the Bayesian approach supplies important tools for designing informative and efficient clinical trials, I've learned to not try to change things too abruptly. In particular, we can stay rooted in the well established frequentist tradition by evaluating false-positive rates and statistical power using simulation. The most exciting aspect of this story is the potential for utilizing Bayesian ideas in the future to build ever more efficient study designs and associated processes for developing therapies, based on the existing solid foundation.