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Statistical Evidence : A Likelihood Paradigm
Interpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data in this way.Statistics has long neglected this principle, resulting in a seriously defective methodology.This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects.After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm which provides, in the law of likelihood, the explicit concept of evidence missing from the other paradigms.At the same time, this new paradigm retains the elements of objective measurement and control of the frequency of misleading results, features which made the old paradigms so important to science.The likelihood paradigm leads to statistical methods that have a compelling rationale and an elegant simplicity, no longer forcing the reader to choose between frequentist and Bayesian statistics.
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Statistical Inference Based on the likelihood
The Likelihood plays a key role in both introducing general notions of statistical theory, and in developing specific methods.This book introduces likelihood-based statistical theory and related methods from a classical viewpoint, and demonstrates how the main body of currently used statistical techniques can be generated from a few key concepts, in particular the likelihood. Focusing on those methods, which have both a solid theoretical background and practical relevance, the author gives formal justification of the methods used and provides numerical examples with real data.
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Maximum Likelihood Estimation with Stata, Fifth Edition
Maximum Likelihood Estimation with Stata, Fifth Edition is the essential reference and guide for researchers in all disciplines who wish to write maximum likelihood (ML) estimators in Stata.Beyond providing comprehensive coverage of Stata’s commands for writing ML estimators, the book presents an overview of the underpinnings of maximum likelihood and how to think about ML estimation. The fifth edition includes a new second chapter that demonstrates the easy-to-use mlexp command.This command allows you to directly specify a likelihood function and perform estimation without any programming. The core of the book focuses on Stata's ml command.It shows you how to take full advantage of ml’s noteworthy features:Linear constraintsFour optimization algorithms (Newton–Raphson, DFP, BFGS, and BHHH)Observed information matrix (OIM) variance estimatorOuter product of gradients (OPG) variance estimatorHuber/White/sandwich robust variance estimatorCluster–robust variance estimatorComplete and automatic support for survey data analysisDirect support of evaluator functions written in MataWhen appropriate options are used, many of these features are provided automatically by ml and require no special programming or intervention by the researcher writing the estimator. In later chapters, you will learn how to take advantage of Mata, Stata's matrix programming language.For ease of programming and potential speed improvements, you can write your likelihood-evaluator program in Mata and continue to use ml to control the maximization process.A new chapter in the fifth edition shows how you can use the moptimize() suite of Mata functions if you want to implement your maximum likelihood estimator entirely within Mata. In the final chapter, the authors illustrate the major steps required to get from log-likelihood function to fully operational estimation command.This is done using several different models: logit and probit, linear regression, Weibull regression, the Cox proportional hazards model, random-effects regression, and seemingly unrelated regression.This edition adds a new example of a bivariate Poisson model, a model that is not available otherwise in Stata. The authors provide extensive advice for developing your own estimation commands.With a little care and the help of this book, users will be able to write their own estimation commands---commands that look and behave just like the official estimation commands in Stata. Whether you want to fit a special ML estimator for your own research or wish to write a general-purpose ML estimator for others to use, you need this book.
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Forensic DNA Profiling : A Practical Guide to Assigning Likelihood Ratios
DNA testing and its forensic analysis are recognized as the “gold standard” in forensic identification science methods.However, there is a great need for a hands-on step-by-step guide to teach the forensic DNA community how to interpret DNA mixtures, how to assign a likelihood ratio, and how to use the subsequent likelihood ratio when reporting interpretation conclusions. Forensic DNA Profiling: A Practical Guide to Assigning Likelihood Ratios will provide a roadmap for labs all over the world and the next generation of analysts who need this foundational understanding.The techniques used in forensic DNA analysis are based upon the accepted principles of molecular biology.The interpretation of a good-quality DNA profile generated from a crime scene stain from a single-source donor provides an unambiguous result when using the most modern forensic DNA methods.Unfortunately, many crime scene profiles are not single source.They are described as mixed since they contain DNA from two or more individuals. Interpretation of DNA mixtures represents one of the greatest challenges to the forensic DNA analyst.As such, the book introduces terms used to describe DNA profiles and profile interpretation.Chapters explain DNA extraction methods, the polymerase chain reaction (PCR), capillary electrophoresis (CE), likelihood ratios (LRs) and their interpretation, and population genetic models—including Mendelian inheritance and Hardy-Weinberg equilibrium.It is important that analysts understand how LRs are generated in a probabilistic framework, ideally with an appreciation of both semicontinuous and fully continuous probabilistic approaches.KEY FEATURES:• The first book to focus entirely on DNA mixtures and the complexities involved with interpreting the results • Takes a hands-on approach offering theory with worked examples and exercises to be easily understood and implementable by laboratory personnel • New methods, heretofore unpublished previously, provide a means to innovate deconvoluting a mixed DNA profile, assign an LR, and appropriately report the weight of evidence • Includes a chapter on assigning LRs for close relatives (i.e., “It’s not me, it was my brother”), and discusses strategies for the validation of probabilistic genotyping softwareForensic DNA Profiling fills the void for labs unfamiliar with LRs, and moving to probabilistic solutions, and for labs already familiar with LRs, but wishing to understand how they are calculated in more detail.The book will be a welcome read for lab professionals and technicians, students, and legal professionals seeking to understand and apply the techniques covered.
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Signal Detection for Medical Scientists : Likelihood Ratio Test-based Methodology
Signal Detection for Medical Scientists: Likelihood Ratio Based Test-Based Methodology presents the data mining techniques with focus on likelihood ratio test (LRT) based methods for signal detection.It emphasizes computational aspect of LRT methodology and is pertinent for first-time researchers and graduate students venturing into this interesting field. The book is written as a reference book for professionals in pharmaceutical industry, manufactures of medical devices, and regulatory agencies.The book deals with the signal detection in drug/device evaluation, which is important in the post-market evaluation of medical products, and in the pre-market signal detection during clinical trials for monitoring procedures. It should also appeal to academic researchers, and faculty members in mathematics, statistics, biostatistics, data science, pharmacology, engineering, epidemiology, and public health.Therefore, this book is well suited for both research and teaching. Key Features:Includes a balanced discussion of art of data structure, issues in signal detection, statistical methods and analytics, and implementation of the methodsProvides a comprehensive summary of the LRT methods for signal detection including the basic theory and extensions for varying datasets that may be large post-market data or pre-market clinical trial dataContains details of scientific background, statistical methods, and associated algorithms that a reader can quickly master the materials and apply methods in the book on one’s own problems
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Trademark Dilution : The Protection of Reputed Trademarks Beyond Likelihood of Confusion
The Protection of Reputed Trademarks Beyond Likelihood of Confusion.The world has changed materially since the foundation of traditional trademark laws, according to which the purpose of a trademark was to serve as a differentiating source indicator, preventing source confusion in the marketplace.Traditionally, trademarks protected the public from likelihood of confusion, assisted in consumer decisions and reduced search costs.The need to award a special scope of protection to famous trademarks from use on non-competing goods was first discussed in Kodak in 1898, holding that the use of the word Kodak for a bicycle company
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Forensic DNA Trace Evidence Interpretation : Activity Level Propositions and Likelihood Ratios
Forensic DNA Trace Evidence Interpretation: Activity Level Propositions and Likelihood Ratios provides all foundational information required for a reader to understand the practice of evaluating forensic biology evidence given activity level propositions and to implement the practice into active casework within a forensic institution.The book begins by explaining basic concepts and foundational theory, pulling together research and studies that have accumulated in forensic journal literature over the last 20 years.The book explains the laws of probability - showing how they can be used to derive, from first principles, the likelihood ratio - used throughout the book to express the strength of evidence for any evaluation.Concepts such as the hierarchy of propositions, the difference between experts working in an investigative or evaluative mode and the practice of case assessment and interpretation are explained to provide the reader with a broad grounding in the topics that are important to understanding evaluation of evidence.Activity level evaluations are discussed in relation to biological material transferred from one object to another, the ability for biological material to persist on an item for a period of time or through an event, the ability to recover the biological material from the object when sampled for forensic testing and the expectations of the prevalence of biological material on objects in our environment.These concepts of transfer, persistence, prevalence and recovery are discussed in detail in addition to the factors that affect each of them. The authors go on to explain the evaluation process: how to structure case information and formulate propositions.This includes how a likelihood ratio formula can be derived to evaluate the forensic findings, introducing Bayesian networks and explaining what they represent and how they can be used in evaluations and showing how evaluation can be tested for robustness.Using these tools, the authors also demonstrate the ways that the methods used in activity level evaluations are applied to questions about body fluids.There are also chapters dedicated to reporting of results and implementation of activity level evaluation in a working forensic laboratory.Throughout the book, four cases are used as examples to demonstrate how to relate the theory to practice and detail how laboratories can integrate and implement activity level evaluation into their active casework.
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