The chapter "Identification of Outliers" by D. M. Hawkins, originally published in 1980, provides a comprehensive overview of the theory and methods for identifying outliers in statistical data. The book is divided into several sections, each focusing on different aspects of outlier detection: 1. **Introduction**: Discusses the definition of outliers, their origin, and the treatment of outliers, including slippage tests and the significance levels. 2. **General Theoretical Principles**: Explains measures of performance, optimal tests, and the use of 'departure from model' statistics. It also addresses the inadequacies of current optimality theory and the relationship with tolerance regions. 3. **A Single Outlier in Normal Samples**: Introduces notation, optimal and non-optimal statistics, and the performance of outlier tests, including the use of normal approximations. 4. **The Gamma Distribution**: Covers the problem of unequal degrees of freedom, the performance of tests, and comparisons with the Bartlett test. 5. **Multiple Outliers**: Discusses stepwise procedures and their performance. 6. **Non-parametric Tests**: Examines the Mosteller and Doornbos statistics, slippage in scale, and large-sample outlier detection. 7. **Outliers from the Linear Model**: Focuses on recursive residuals, regression formulations, and the identification of multiple outliers. 8. **Multivariate Outlier Detection**: Reviews general testing principles, alternative approaches, and distribution theory. 9. **Bayesian Approach to Outliers**: Introduces a Bayesian 'test' for outliers. 10. **Miscellaneous Topics**: Covers discrete distributions and outliers in time series. The preface highlights the historical context of outlier detection, the current state of research, and the limitations of existing theories. It also acknowledges the contributions of various institutions and individuals who supported the preparation of the monograph.The chapter "Identification of Outliers" by D. M. Hawkins, originally published in 1980, provides a comprehensive overview of the theory and methods for identifying outliers in statistical data. The book is divided into several sections, each focusing on different aspects of outlier detection: 1. **Introduction**: Discusses the definition of outliers, their origin, and the treatment of outliers, including slippage tests and the significance levels. 2. **General Theoretical Principles**: Explains measures of performance, optimal tests, and the use of 'departure from model' statistics. It also addresses the inadequacies of current optimality theory and the relationship with tolerance regions. 3. **A Single Outlier in Normal Samples**: Introduces notation, optimal and non-optimal statistics, and the performance of outlier tests, including the use of normal approximations. 4. **The Gamma Distribution**: Covers the problem of unequal degrees of freedom, the performance of tests, and comparisons with the Bartlett test. 5. **Multiple Outliers**: Discusses stepwise procedures and their performance. 6. **Non-parametric Tests**: Examines the Mosteller and Doornbos statistics, slippage in scale, and large-sample outlier detection. 7. **Outliers from the Linear Model**: Focuses on recursive residuals, regression formulations, and the identification of multiple outliers. 8. **Multivariate Outlier Detection**: Reviews general testing principles, alternative approaches, and distribution theory. 9. **Bayesian Approach to Outliers**: Introduces a Bayesian 'test' for outliers. 10. **Miscellaneous Topics**: Covers discrete distributions and outliers in time series. The preface highlights the historical context of outlier detection, the current state of research, and the limitations of existing theories. It also acknowledges the contributions of various institutions and individuals who supported the preparation of the monograph.