Normal And Student S T Distributions And Their Applications

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Normal And Student S T Distributions And Their Applications

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Author : Mohammad Ahsanullah
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-02-07

Normal And Student S T Distributions And Their Applications written by Mohammad Ahsanullah and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-07 with Mathematics categories.

The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.

Theorems On The Prevalence Threshold And The Geometry Of Screening Curves

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Author : Jacques Balayla
language : en
Publisher: Springer Nature
Release Date : 2024-11-09

Theorems On The Prevalence Threshold And The Geometry Of Screening Curves written by Jacques Balayla and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-09 with Medical categories.

In Theorems on the Prevalence Threshold and the Geometry of Screening Curves, the author explores the mathematical underpinnings of screening and diagnostic testing, offering a unique and novel perspective which employs classical differential geometry and Bayesian theory to elucidate critical aspects of clinical decision-making. Taking the reader on a mathematical journey which bridges these seemingly unrelated worlds, the author presents a quantifiable framework on clinical judgement by introducing the “prevalence threshold” – a novel statistical parameter derived from Bayesian principles by means of the study of the geometry of screening curves. As the prevalence threshold demarcates the pretest probability level beyond which additional information ceases to significantly enhance the yield and reliability of a clinical assessment, it may serve as a benchmark for confidence in clinical decision-making. Given the theorems herein described, readers will find comprehensive analyses and insightful explorations of how these geometric concepts apply to real-world diagnostic scenarios, allowing the clinician to navigate clinical care more effectively at both the individual and public health levels.

Multivariate T Distributions And Their Applications

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Author : Samuel Kotz
language : en
Publisher: Cambridge University Press
Release Date : 2004-02-16

Multivariate T Distributions And Their Applications written by Samuel Kotz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-16 with Mathematics categories.

Almost all the results available in the literature on multivariate t-distributions published in the last 50 years are now collected together in this comprehensive reference. Because these distributions are becoming more prominent in many applications, this book is a must for any serious researcher or consultant working in multivariate analysis and statistical distributions. Much of this material has never before appeared in book form. The first part of the book emphasizes theoretical results of a probabilistic nature. In the second part of the book, these are supplemented by a variety of statistical aspects. Various generalizations and applications are dealt with in the final chapters. The material on estimation and regression models is of special value for practitioners in statistics and economics. A comprehensive bibliography of over 350 references is included.

Introduction To Biostatistical Applications In Health Research With Microsoft Office Excel

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Author : Robert P. Hirsch
language : en
Publisher: John Wiley & Sons
Release Date : 2016-02-05

Introduction To Biostatistical Applications In Health Research With Microsoft Office Excel written by Robert P. Hirsch and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-05 with Medical categories.

A practical and methodological approach to the statistical logic of biostatistics in the field of health research Focusing on a basic understanding of the methods and analyses in health research, Introduction to Biostatistical Applications in Health Research with Microsoft® Office Excel® provides statistical concepts for interpreting results using Excel. The book emphasizes the application of methods and presents the most common methodological procedures in health research, which includes multiple regression, ANOVA, ANCOVA, logistic regression, Cox regression, stratified analysis, life table analysis, and nonparametric parallels. The book is constructed around a flowchart that outlines the appropriate circumstances for selecting a method to analyze a specific set of data. Beginning with an introduction to the foundational methods of statistical logic before moving on to more complex methods, Introduction to Biostatistical Applications in Health Research with Microsoft® Office Excel® also includes: Detailed discussions of how knowledge and skills in health research have been integrated with biostatistical methods Numerous examples with clear explanations that use mostly real-world health research data in order to provide a better understanding of the practical applications Implements Excel graphic representations throughout to help readers evaluate and analyze individual results An appendix with basic information on how to use Excel A companion website with additional Excel files, data sets, and homework problems as well as an Instructor’s Solutions Manual Introduction to Biostatistical Applications in Health Research with Microsoft® Office Excel® is an excellent textbook for upper-undergraduate and graduate-level courses in biostatistics and public health. In addition, the book is an appropriate reference for both health researchers and professionals.

Nbs Special Publication

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Author :
language : en
Publisher:
Release Date : 1970

Nbs Special Publication written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Weights and measures categories.

The Theory Of Perfect Learning

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Author : Nonvikan Karl-Augustt Alahassa
language : en
Publisher: Nonvikan Karl-Augustt Alahassa
Release Date : 2021-08-17

The Theory Of Perfect Learning written by Nonvikan Karl-Augustt Alahassa and has been published by Nonvikan Karl-Augustt Alahassa this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-17 with Science categories.

The perfect learning exists. We mean a learning model that can be generalized, and moreover, that can always fit perfectly the test data, as well as the training data. We have performed in this thesis many experiments that validate this concept in many ways. The tools are given through the chapters that contain our developments. The classical Multilayer Feedforward model has been re-considered and a novel $N_k$-architecture is proposed to fit any multivariate regression task. This model can easily be augmented to thousands of possible layers without loss of predictive power, and has the potential to overcome our difficulties simultaneously in building a model that has a good fit on the test data, and don't overfit. His hyper-parameters, the learning rate, the batch size, the number of training times (epochs), the size of each layer, the number of hidden layers, all can be chosen experimentally with cross-validation methods. There is a great advantage to build a more powerful model using mixture models properties. They can self-classify many high dimensional data in a few numbers of mixture components. This is also the case of the Shallow Gibbs Network model that we built as a Random Gibbs Network Forest to reach the performance of the Multilayer feedforward Neural Network in a few numbers of parameters, and fewer backpropagation iterations. To make it happens, we propose a novel optimization framework for our Bayesian Shallow Network, called the {Double Backpropagation Scheme} (DBS) that can also fit perfectly the data with appropriate learning rate, and which is convergent and universally applicable to any Bayesian neural network problem. The contribution of this model is broad. First, it integrates all the advantages of the Potts Model, which is a very rich random partitions model, that we have also modified to propose its Complete Shrinkage version using agglomerative clustering techniques. The model takes also an advantage of Gibbs Fields for its weights precision matrix structure, mainly through Markov Random Fields, and even has five (5) variants structures at the end: the Full-Gibbs, the Sparse-Gibbs, the Between layer Sparse Gibbs which is the B-Sparse Gibbs in a short, the Compound Symmetry Gibbs (CS-Gibbs in short), and the Sparse Compound Symmetry Gibbs (Sparse-CS-Gibbs) model. The Full-Gibbs is mainly to remind fully-connected models, and the other structures are useful to show how the model can be reduced in terms of complexity with sparsity and parsimony. All those models have been experimented, and the results arouse interest in those structures, in a sense that different structures help to reach different results in terms of Mean Squared Error (MSE) and Relative Root Mean Squared Error (RRMSE). For the Shallow Gibbs Network model, we have found the perfect learning framework : it is the $(l_1, \boldsymbol{\zeta}, \epsilon_{dbs})-\textbf{DBS}$ configuration, which is a combination of the \emph{Universal Approximation Theorem}, and the DBS optimization, coupled with the (\emph{dist})-Nearest Neighbor-(h)-Taylor Series-Perfect Multivariate Interpolation (\emph{dist}-NN-(h)-TS-PMI) model [which in turn is a combination of the research of the Nearest Neighborhood for a good Train-Test association, the Taylor Approximation Theorem, and finally the Multivariate Interpolation Method]. It indicates that, with an appropriate number $l_1$ of neurons on the hidden layer, an optimal number $\zeta$ of DBS updates, an optimal DBS learnnig rate $\epsilon_{dbs}$, an optimal distance \emph{dist}$_{opt}$ in the research of the nearest neighbor in the training dataset for each test data $x_i^{\mbox{test}}$, an optimal order $h_{opt}$ of the Taylor approximation for the Perfect Multivariate Interpolation (\emph{dist}-NN-(h)-TS-PMI) model once the {\bfseries DBS} has overfitted the training dataset, the train and the test error converge to zero (0). As the Potts Models and many random Partitions are based on a similarity measure, we open the door to find \emph{sufficient} invariants descriptors in any recognition problem for complex objects such as image; using \emph{metric} learning and invariance descriptor tools, to always reach 100\% accuracy. This is also possible with invariant networks that are also universal approximators. Our work closes the gap between the theory and the practice in artificial intelligence, in a sense that it confirms that it is possible to learn with very small error allowed.

Introduction To Biostatistical Applications In Health Research With Microsoft Office Excel And R

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Author : Robert P. Hirsch
language : en
Publisher: John Wiley & Sons
Release Date : 2021-02-17

Introduction To Biostatistical Applications In Health Research With Microsoft Office Excel And R written by Robert P. Hirsch and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-17 with Medical categories.

The second edition of Introduction to Biostatistical Applications in Health Research delivers a thorough examination of the basic techniques and most commonly used statistical methods in health research. Retaining much of what was popular with the well-received first edition, the thoroughly revised second edition includes a new chapter on testing assumptions and how to evaluate whether those assumptions are satisfied and what to do if they are not. The newest edition contains brand-new code examples for using the popular computer language R to perform the statistical analyses described in the chapters within. You'll learn how to use Excel to generate datasets for R, which can then be used to conduct statistical calculations on your data. The book also includes a companion website with a new version of BAHR add-in programs for Excel. This new version contains new programs for nonparametric analyses, Student-Newman-Keuls tests, and stratified analyses. Readers will also benefit from coverage of topics like: Extensive discussions of basic and foundational concepts in statistical methods, including Bayes' Theorem, populations, and samples A treatment of univariable analysis, covering topics like continuous dependent variables and ordinal dependent variables An examination of bivariable analysis, including regression analysis and correlation analysis An analysis of multivariate calculations in statistics and how testing assumptions, like assuming Gaussian distributions or equal variances, affect statistical outcomes Perfect for health researchers of all kinds, Introduction to Biostatistical Applications in Health Research also belongs on the bookshelves of anyone who wishes to better understand health research literature. Even those without a great deal of mathematical background will benefit greatly from this text.

Statistics For Big Data For Dummies

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Author : Alan Anderson
language : en
Publisher: John Wiley & Sons
Release Date : 2015-08-11

Statistics For Big Data For Dummies written by Alan Anderson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-11 with Computers categories.

The fast and easy way to make sense of statistics for big data Does the subject of data analysis make you dizzy? You've come to the right place! Statistics For Big Data For Dummies breaks this often-overwhelming subject down into easily digestible parts, offering new and aspiring data analysts the foundation they need to be successful in the field. Inside, you'll find an easy-to-follow introduction to exploratory data analysis, the lowdown on collecting, cleaning, and organizing data, everything you need to know about interpreting data using common software and programming languages, plain-English explanations of how to make sense of data in the real world, and much more. Data has never been easier to come by, and the tools students and professionals need to enter the world of big data are based on applied statistics. While the word "statistics" alone can evoke feelings of anxiety in even the most confident student or professional, it doesn't have to. Written in the familiar and friendly tone that has defined the For Dummies brand for more than twenty years, Statistics For Big Data For Dummies takes the intimidation out of the subject, offering clear explanations and tons of step-by-step instruction to help you make sense of data mining—without losing your cool. Helps you to identify valid, useful, and understandable patterns in data Provides guidance on extracting previously unknown information from large databases Shows you how to discover patterns available in big data Gives you access to the latest tools and techniques for working in big data If you're a student enrolled in a related Applied Statistics course or a professional looking to expand your skillset, Statistics For Big Data For Dummies gives you access to everything you need to succeed.

Bootstrap Methods And Their Application

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Author : A. C. Davison
language : en
Publisher: Cambridge University Press
Release Date : 1997-10-28

Bootstrap Methods And Their Application written by A. C. Davison and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-28 with Computers categories.

Disk contains the library functions and documentation for use with Splus for Windows.

Catalogue Of The University Of Michigan

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Author : University of Michigan
language : en
Publisher:
Release Date : 1964

Catalogue Of The University Of Michigan written by University of Michigan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with categories.

Announcements for the following year included in some vols.