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E-grāmata: Forensic Metrology: Scientific Measurement and Inference for Lawyers, Judges, and Criminalists

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"Foreword Facts are inherently nonexplanatory. A report of "70 degrees" means nothing without some context: Is it January or July? Juneau or Jakarta? Celsius or Fahrenheit? Shewhart's dictum ("Data has no meaning apart from its context") is central to all sciences, including--perhaps particularly--forensic science. A few assumptions underly this concept. First is that the context trumps the data in that, as Deming said, "Experience without theory teaches nothing. In fact, experience can not even be recorded unless there is some theory, however crude. . . " (Deming, 1986, p. 317). If you must be "this tall" to ride this roller coaster, then in the context (the roller coaster's safety design), height (the measurement) is important because it is ultimately based on theory (human biological height is predictably proportional to age and weight): Children of a certain age are large enough to be protected by the coaster's safety mechanisms, which were designed with bodies of a minimal size in mind. Simply saying a child is 40 inches tall means very little. The second assumption is that there are data, that is, plural. Science is based on reproducibility and with that comes the collection of multiple data points, either by ourselves to ensure accuracy or by others to check validity. In each measurement is a minor bit of error (in the statistical sense) and multiple measurements help us capture, understand, and control that error. Twenty one different Six Flags Amusement Parks exist and each one has different roller coasters, ranging from children's coasters to Mega Coasters, all with different height requirements (Table 0.1). Multiple measurements are taken, recorded, and communicated to each of Six Flags' parks to ensure that the requirements are consistent between parks"--

"With contributions from professionals in forensic science, law, and engineering, this book serves as an introduction to the field of metrology, its application to the forensic sciences, and its use in the courtroom. Written for professionals and students, the text begins at a general level, demonstrating that the principles of metrology are familiar to all. It then builds a more sophisticated level of coverage, combining the scientific machinery of metrology and forensics with the practice of law so practitioners will be able to apply the principles discussed. Examples, case studies, and diagrams are included for ease of understanding and application"--

Forensic metrology provides a standard language for a variety of different measurements associated with crime investigations including blood alcohol and drug concentrations and the weights of seized drugs that allow forensic scientists, lawyers and judges to better be able to do their jobs. This book is aimed at providing scientists and nonscientists alike with the skills needed to take the measurements and understand what they represent and the inferences that can be made from them. The book moves from basic to advanced techniques with legal advice, real world examples and graphics throughout to make the information approachable. The included CD has additional practice materials with court decisions, legal motions and expert reports. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

Forensic metrology is the application of scientific measurement to the investigation and prosecution of crime. Forensic measurements are relied upon to determine breath and blood alcohol and drug concentrations, weigh seized drugs, perform accident reconstruction, and for many other applications. Forensic metrology provides a basic framework for the performance and critical evaluation of all forensic measurements. It enables forensic scientists to better develop, perform and communicate forensic measurements; lawyers to better understand, present and cross-examine the results of forensic measurements; and judges to better subject testimony and evidence based on forensic measurements to the appropriate gatekeeping analysis.

Forensic Metrology Scientific Measurement and Inference for Lawyers, Judges, and Criminalists sets forth the metrological framework required to reach sound conclusions based on measured results and the inferences those results support. Armed with this knowledge, scientists and nonscientists alike can:

  • Engage in critical analysis of forensic measurements across a broad spectrum

  • Better understand what measured results represent

  • Successfully prepare and present testimony and/or cases that involve such evidence

  • Recognize poor measurement practices and prevent bad science from undermining the search for truth in the courtroom

The book begins by introducing and developing metrological principles and concepts. Next, it presents advanced and mathematically rigorous principles and methods of inference in metrology. Throughout the book, scientific and legal aspects of measurements are addressed and accompanied by examples. The accompanying CD includes an in-depth Primer on Forensic Metrology and provides practice materials for legal and forensic professionals that include court decisions, legal motions, and expert reports.

A basic understanding of forensic metrology will improve the practices of both legal and forensic professionals, helping to ensure the integrity of the legal system, its fact-finding functions, and the practice of justice in the courtroom.

List of Figures xxi
List of Tables xxv
List of Materials on Accompanying Disk xxvii
Series Preface-International Forensic Science Series xxxi
Foreword xxxiii
Acknowledgments xxxvii
Authors xxxix
Prologue xli
Section I An Introduction to Forensic Metrology for Lawyers, Judges, and Forensic Scientists
Chapter 1 Science, Metrology, and the Law
3(30)
1.1 Science!
3(2)
1.1.1 Science and the Law
3(1)
1.1.2 A Foundation for Science in the Courtroom
4(1)
1.2 What is Science?
5(17)
1.2.1 Knowledge of the Physical Universe
5(3)
1.2.1.1 Descriptive versus Explanatory
5(1)
1.2.1.2 Example: Quantum Considerations
6(1)
1.2.1.3 Knowledge as Description and Model
6(1)
1.2.1.4 Example: The Ptolemaic Model of the Universe
7(1)
1.2.2 Empiricism
8(2)
1.2.2.1 Information versus Fact
9(1)
1.2.2.2 Example: Blood Alcohol Measurements
9(1)
1.2.2.3 Incomplete Information
9(1)
1.2.3 Recap
10(1)
1.2.4 Hallmarks of Science
10(5)
1.2.4.1 Falsifiability and Testability
10(1)
1.2.4.2 Puzzle Solving
11(1)
1.2.4.3 Example: Puzzle Solving in Forensic Toxicology
11(1)
1.2.4.4 Predicting Novel Phenomena
12(1)
1.2.4.5 Example: Prediction of a New Planet
12(1)
1.2.4.6 The Scientific Method
13(1)
1.2.4.7 Defining Terms, Concepts, and Phenomena
14(1)
1.2.4.8 Example: What Is an Analogue?
15(1)
1.2.5 Specific Principles of Reasoning: The Inferential Process
15(3)
1.2.5.1 Rules of Inference
16(1)
1.2.5.2 Example: Chemistry and Rules of Inference
17(1)
1.2.5.3 Hierarchy of Inferential Rules
17(1)
1.2.5.4 Creation and Destruction of Inferential Rules
18(1)
1.2.6 Epistemological Robustness of Scientific Conclusions
18(2)
1.2.6.1 Example: Error Analysis and the Discovery of Planetary Laws
19(1)
1.2.7 A Working Definition of Science
20(2)
1.3 Forensic Science and the Law
22(2)
1.3.1 Science in the Courtroom
22(1)
1.3.2 Forensic Science as Science
23(1)
1.4 Metrology: The Science of Measurement
24(6)
1.4.1 Measurement
24(1)
1.4.2 Components of Measurement
25(3)
1.4.2.1 The Quantity Intended to Be Measured
25(1)
1.4.2.2 An Exercise in Comparison
25(1)
1.4.2.3 Universally Accepted Scales
26(1)
1.4.2.4 How to Measure
26(1)
1.4.2.5 Performing the Measurement
27(1)
1.4.2.6 Conclusions Supported
27(1)
1.4.2.7 Information and Inference
28(1)
1.4.3 Metrology
28(5)
1.4.3.1 Who Is a "Metrologist"?
29(1)
1.4.3.2 Forensic Metrology
29(1)
1.5 Why Forensic Metrology for Judges, Lawyers, and Scientists?
30(1)
Endnotes
30(3)
Chapter 2 Introduction to Measurement: The Measurand
33(24)
2.1 What is Measurement?
33(2)
2.1.1 Definition
33(2)
2.1.1.1 Comparison as Experiment
33(1)
2.1.1.2 Quantity
33(1)
2.1.1.3 Quantity Value
34(1)
2.1.1.4 Measurement Unit
34(1)
2.1.1.5 Quantitative Information
34(1)
2.1.1.6 Measurement Summary
35(1)
2.2 The Measurand
35(3)
2.2.1 Specification of the Measurand
35(1)
2.2.1.1 Example: Ambiguity in Specification
36(1)
2.2.2 The Well-Defined Measurand
36(2)
2.2.2.1 Example: Weighing Drugs
37(1)
2.3 Intended to be Measured versus Subject to Measurement
38(3)
2.3.1 The "Measurand Problem"
38(1)
2.3.2 Direct and Indirect Measurements
39(1)
2.3.3 Measurement Model
40(1)
2.3.4 Measurement Function
40(1)
2.3.5 Example: Measurement Function in Blood Alcohol Testing
41(1)
2.4 Case Study: The Measurand in Forensic Breath Alcohol Testing
41(14)
2.4.1 Blood Alcohol Concentration
42(1)
2.4.2 Breath Tests to Measure BAC
42(1)
2.4.3 Failure of a Model
43(1)
2.4.4 Refining the Model
44(1)
2.4.4.1 Breath Alcohol as Measurement Indication
44(1)
2.4.4.2 A "New" Measurement Function
44(1)
2.4.5 Breath Alcohol as Measurand
45(2)
2.4.5.1 What Is Breath?
45(1)
2.4.5.2 What Is Breath Alcohol Concentration?
46(1)
2.4.6 Simplifying the Model: End-Expiratory Breath
47(1)
2.4.7 End-Expiratory Breath: An Underdefined Measurand
47(4)
2.4.7.1 A Set of Quantities Satisfying the Defined Measurand
47(1)
2.4.7.2 Multivalued
48(1)
2.4.7.3 How Badly Underdefined?
49(2)
2.4.7.4 Constitutional Infirmities?
51(1)
2.4.8 The Measurand Problem in Breath Alcohol Testing
51(3)
2.4.8.1 Three Types of Breath Test Jurisdictions
52(2)
2.4.8.2 Summary of the Measurand Problem
54(1)
2.4.9 Most Rational Measurand for a Breath Test: BAC?
54(1)
Endnotes
55(2)
Chapter 3 Weights and Measures
57(34)
3.1 Weights and Measures Generally
57(3)
3.1.1 Ambiguity in Measurement
57(1)
3.1.2 Overcoming Ambiguity
58(1)
3.1.3 Recognized Importance
59(1)
3.1.4 The International System of Weights and Measures
59(1)
3.2 International System of Quantities (ISQ)
60(3)
3.2.1 Derived Quantities and Quantity Relationships
61(1)
3.2.2 Quantity Dimensions
62(1)
3.2.3 Quantities of the Same Kind
63(1)
3.3 The International System of Units
63(17)
3.3.1 Measurement Units
63(1)
3.3.2 Quantity Value Is Dependent Upon Units
63(1)
3.3.3 The International System of Units
64(2)
3.3.4 Acceptable Non-SI Units
66(1)
3.3.5 Large and Small Values Expressed in Units
67(1)
3.3.6 Units of Measure in Forensic Practice
68(3)
3.3.6.1 Nonuniform Conventions
69(1)
3.3.6.2 Origin of g/210 L Unit Convention in Forensic Breath Alcohol Testing
70(1)
3.3.7 Definitions and History of SI Units
71(8)
3.3.7.1 The Meter: Base Unit of Length
72(1)
3.3.7.2 The Kilogram: Base Unit of Mass
73(1)
3.3.7.3 The Second: Base Unit of Time
73(1)
3.3.7.4 The Ampere: Base Unit of Electric Current
74(1)
3.3.7.5 The Kelvin: Base Unit of Thermodynamic Temperature
75(1)
3.3.7.6 The Mole: Base Unit of the Amount of Substance
76(2)
3.3.7.7 The Candela: Base Unit of Luminous Intensity
78(1)
3.3.8 Ensuring That Reported Units Correspond to Their Definition
79(1)
3.4 Metrological Traceability
80(5)
3.4.1 Property of a Measurement Result
80(1)
3.4.2 Related to a Reference
80(1)
3.4.3 Unbroken Chain of Comparisons
81(1)
3.4.4 Uncertainty
82(1)
3.4.5 Documentation
82(1)
3.4.6 A Fundamental Element of Good Measurement Results
82(1)
3.4.7 The Role of National Metrological Authorities
83(1)
3.4.8 Traceability in Forensics
83(2)
3.5 The National Institute of Standards and Technology
85(2)
3.5.1 State Weights and Measures
86(1)
3.5.2 Case Note: A Question of Supremacy in Forensic Science?
87(1)
Endnotes
87(4)
Chapter 4 Validation and Good Measurement Practices
91(32)
4.1 Finding an Appropriate Method
91(6)
4.1.1 Method Validation
91(2)
4.1.2 Characteristics Subject to Validation
93(1)
4.1.3 Method Verification
94(1)
4.1.4 Example: Consequences of Failing to Validate/Verify a Method
94(2)
4.1.5 Fitness for Purpose
96(1)
4.2 Good Measurement Practices
97(12)
4.2.1 Performing a Measurement
97(1)
4.2.2 Standard Operating Procedures
97(2)
4.2.2.1 Example: SOPs in Forensic Toxicology
98(1)
4.2.3 Calibration
99(10)
4.2.3.1 Common Calibration Technique
99(1)
4.2.3.2 Calibration, Bias, and the Best Estimate of a Measurand's Value
100(1)
4.2.3.3 Calibration and Bias in Forensic Measurements
101(2)
4.2.3.4 Example: Calibration Requirements in the Courtroom
103(3)
4.2.3.5 Required for Valid Measurement
106(1)
4.2.3.6 Range of Calibration
106(1)
4.2.3.7 Example: Range of Calibration in Breath Alcohol Measurements
107(1)
4.2.3.8 Example: Measurements by Law Enforcement Officers in the Field
107(2)
4.3 Consensus Standards
109(6)
4.3.1 ISO 17025: The Gold Standard
111(1)
4.3.2 Metrological Terminology: The VIM and the TAM
111(1)
4.3.3 Consensus Standards for Chemical Measurements
112(1)
4.3.4 Consensus Standards in Forensic Practice
112(1)
4.3.5 Example: Consensus Standards in the Courtroom
113(2)
4.4 Accreditation
115(3)
4.4.1 Accrediting the Accreditors: ILAC
116(1)
4.4.2 NIST's Role in Accreditation
116(1)
4.4.2.1 Case Note: Accreditation as a Party Admission
117(1)
4.4.3 Accreditation in Forensic Science
117(1)
Endnotes
118(5)
Chapter 5 Result Interpretation-I: Metrological Prerequisites to Knowledge
123(6)
5.1 Result Interpretation
123(1)
5.2 Metrological Prerequisites to Knowledge
123(2)
5.2.1 Specification of the Measurand
124(1)
5.2.2 The International System of Weights and Measures
124(1)
5.2.3 Method Validation
125(1)
5.2.4 Good Measurement Practices
125(1)
5.3 Circumscribing and Ranking Available Inferences
125(1)
5.4 Limitations of Knowledge
126(1)
5.5 Accounting for Limitations
126(1)
Endnotes
127(2)
Chapter 6 Result Interpretation-II: Measurement Error
129(22)
6.1 Result Interpretation
129(1)
6.2 Illusions of Certainty
129(1)
6.3 Accuracy and Reliability
130(2)
6.3.1 Relative and Qualitative
130(1)
6.3.2 Example: Misleading in the Courtroom
131(1)
6.3.3 Usefulness
132(1)
6.4 Measurement Error
132(18)
6.4.1 Error Analysis
133(1)
6.4.2 Systematic Error and Bias
133(2)
6.4.3 Random Error and Standard Deviation
135(3)
6.4.3.1 Example: Random Error in Forensic Measurements
136(2)
6.4.4 Mean Measured Values
138(6)
6.4.4.1 Types of Means
139(2)
6.4.4.2 Standard Deviation of the Mean
141(1)
6.4.4.3 Outliers
141(1)
6.4.4.4 Example: Forensics and Problems with Outliers
142(2)
6.4.5 Error Analysis and Estimates of a Quantity's Value
144(1)
6.4.6 The Confidence Interval
145(2)
6.4.6.1 What Does the Confidence Interval Tell Us?
146(1)
6.4.7 Total Error and Evaluating Estimates
147(2)
6.4.7.1 Frequentist Statistical Theory
148(1)
6.4.7.2 Systematic and Random Errors in Frequentist Statistics
148(1)
6.4.7.3 The Best Error Analysis Can Offer
149(1)
6.4.8 Beyond the Constraints of Measurement Error
149(1)
Endnotes
150(1)
Chapter 7 Result Interpretation-III: Measurement Uncertainty
151(56)
7.1 Result Interpretation
151(1)
7.2 Response to Limitations of Measurement Error Approach
151(2)
7.2.1 Replacing Error
152(1)
7.2.2 The GUM
152(1)
7.2.3 Bayesian Probability
153(1)
7.3 Measurement Uncertainty: Ideas and Concepts
153(12)
7.3.1 The Lingering Effects of Error
154(2)
7.3.1.1 Systematic and Random Effects
154(1)
7.3.1.2 Best Estimate of a Measurand's Value
155(1)
7.3.2 Measurement as Packet of Values
156(1)
7.3.3 Belief
157(1)
7.3.4 Measurement as Probability Distribution
157(3)
7.3.4.1 Example: State of Knowledge as a Probability Distribution
157(3)
7.3.5 Mapping Measurement to "Reality"
160(1)
7.3.6 Reasonably Attributable Values
160(2)
7.3.7 Expanded Uncertainty and Coverage Intervals
162(2)
7.3.8 Reporting Results
164(1)
7.3.9 Measure of the Epistemological Robustness of Conclusions
164(1)
7.4 Case Notes: Measurement Uncertainty in the Courtroom
165(12)
7.4.1 Legal Background
165(3)
7.4.2 The National Academy of Sciences
168(1)
7.4.3 Example: The Importance of Uncertainty in the Courtroom
169(2)
7.4.4 Recognizing the Necessity of Uncertainty in Achieving Justice
171(2)
7.4.5 Rejecting Science
173(1)
7.4.6 Example: The Fatal Flaw—Identical Results... Different Meanings
174(2)
7.4.7 Overcoming Bad Law
176(1)
7.5 Overview of Mechanics Provided by the GUM
177(20)
7.5.1 Two Types of Uncertainty: Type A and Type B
177(2)
7.5.1.1 Equivalency of Uncertainties
178(1)
7.5.1.2 Objective versus Subjective
178(1)
7.5.2 Standard Uncertainty
179(1)
7.5.2.1 Example: Type B Determination of Standard Uncertainty
179(1)
7.5.3 Step 1: Identifying Systematic Effects and Their Associated Uncertainty
180(4)
7.5.3.1 Example: Type A Analysis
180(2)
7.5.3.2 Example: Type B Analysis
182(2)
7.5.4 Step 2: Identifying Sources and Magnitudes of Uncertainty
184(2)
7.5.4.1 No Accounting for Poor Performance
185(1)
7.5.5 Step 3: Quantifying Uncertainties
186(1)
7.5.5.1 Example: Type A Evaluation
186(1)
7.5.5.2 Example: Type B Evaluation
186(1)
7.5.6 Step 4: Documenting Sources and Magnitudes
187(1)
7.5.7 Step 5: Combined Uncertainty
187(5)
7.5.7.1 Overcoming the Limitations of the Error Approach
188(1)
7.5.7.2 Relating Uncertainties
188(1)
7.5.7.3 Uncertainties Directly Affecting Result
188(1)
7.5.7.4 Addition through Modeling: The Law of Propagation of Uncertainty
189(1)
7.5.7.5 Applications of Propagation of Uncertainty
190(1)
7.5.7.6 Example: Applications of Propagation of Uncertainty in Forensic Science
191(1)
7.5.8 Expanded Uncertainty and Coverage Intervals
192(3)
7.5.9 Reporting Results
195(1)
7.5.9.1 Reporting Forensic Results
195(1)
7.5.10 Tricks of the Trade: Reverse Engineering Probabilities
196(1)
7.6 The Top-Down Approach
197(1)
7.7 Propagation of Distributions Method
198(1)
7.8 Choices, Choices
199(1)
7.8.1 Uncertain Choices and the Law
199(1)
7.9 Case Study: Definitional Uncertainty in Breath Alcohol Testing
200(3)
7.9.1 Definitional Uncertainty
200(1)
7.9.2 Determining Definitional Uncertainty
201(1)
7.9.3 Combining Definitional Uncertainty
202(1)
7.9.4 Expanded Uncertainty
203(1)
7.10 Result Interpretation in the Uncertainty Paradigm
203(1)
Endnotes
204(3)
Chapter 8 Epistemological Structure of Metrology
207(10)
8.1 The Acquisition of Knowledge through Measurement
207(1)
8.2 A Brief Outline of the Epistemological Structure of Metrology
207(3)
8.2.1 Specification of the Measurand
208(1)
8.2.2 The International System of Weights and Measures
208(1)
8.2.3 Method Validation
209(1)
8.2.4 Good Measurement Practices
209(1)
8.2.5 Measurement Uncertainty
209(1)
Endnote
210(7)
Section II Mathematical Background
Chapter 9 Models and Uncertainty
217(8)
9.1 Where Do the Uncertainties Come From?
217(1)
9.2 Uncertainty: A Random Quantity
217(1)
9.3 Definition of a Mathematical Model
218(1)
9.4 Deterministic and Stochastic Behavior
219(1)
9.5 Equivalence of Models
220(1)
9.6 Distinction between Conditional Information I and Environmental Information E
221(1)
9.7 Uncertainty, Decisions, Risk
221(4)
Chapter 10 Logic, Plausibility, and Probability
225(10)
10.1 Logical Arguments and Reasoning
225(1)
10.2 Inductive Reasoning: Plausibility and Probability
225(1)
10.3 Logical Reasoning
225(3)
10.3.1 Deductive Reasoning
226(1)
10.3.1.1 Deductive Logic: Validity and Soundness
226(1)
10.3.2 Inductive Reasoning
226(1)
10.3.2.1 Statistical Syllogism
227(1)
10.3.2.2 Simple Induction
227(1)
10.3.2.3 Inductive Logic
227(1)
10.3.3 Abductive Reasoning
227(1)
10.4 Truth, Plausibility, Credibility, Probability
228(2)
10.4.1 Numerical Values
230(1)
10.5 Plausibility and Probability
230(2)
10.5.1 Shorthand Notation
231(1)
10.5.2 Venn Diagram
231(1)
10.6 Examples of Plausibility
232(3)
10.6.1 Deductive Reasoning: A Special Subset of Plausibility
232(1)
10.6.2 Kleptoparasitism
233(2)
Chapter 11 Bayes' Relation
235(10)
11.1 Notation Used for Bayesian Inference
236(1)
11.2 Examples of the Use of Bayes' Relation
236(7)
11.2.1 Medical Tests Using Frequencies
237(2)
11.2.2 Relative Likelihood: Effect of Data
239(1)
11.2.3 The Monte Hall Problem: A Study in Conditional Probabilities
239(2)
11.2.4 Actors
241(1)
11.2.5 Anticipated Measurement Results
242(1)
11.3 Inference and Domination of the Measurements
243(2)
Chapter 12 Statistics and the Characterizing of Uncertainties
245(18)
12.1 Why Statistics
245(1)
12.2 Data and Populations
245(3)
12.3 Relative Frequency
248(2)
12.3.1 Central Tendencies: Expected Values and Averages
248(1)
12.3.2 Dispersion (Deviation) of Samples
248(1)
12.3.3 Equivalent Values for the Population
249(1)
12.3.4 Sample versus Global Frequencies
249(1)
12.3.5 Deviations from Expected Values
250(1)
12.4 Statistical Distributions
250(8)
12.4.1 The Bernoulli (Binomial) Distribution: The Urn Problem
251(3)
12.4.1.1 Expected Value and Standard Deviation of W
252(1)
12.4.1.2 Plot of Monte Carlo Simulation
252(1)
12.4.1.3 Inverse Probability of the Bernoulli Distribution
252(2)
12.4.2 The Normal Distribution: The Bell Curve
254(3)
12.4.2.1 Central Limit Theorem
255(1)
12.4.2.2 Range of Variable for a Normal Distribution
256(1)
12.4.3 Student's t-Distribution
257(1)
12.5 How Many Samples Are Needed: The Law of Large Numbers
258(2)
12.6 Frequency versus Probability
260(2)
12.7 Conclusions
262(1)
Chapter 13 Hypothesis Testing, Evidence, Likelihood, Data
263(12)
13.1 Scientific Method
263(1)
13.2 Hypothesis Testing
263(1)
13.3 Types of Hypothesis Problems
264(6)
13.3.1 Single Hypothesis
264(1)
13.3.2 Binary Hypotheses
265(1)
13.3.3 Urn Problem Treated as an Hypothesis
266(2)
13.3.4 The Best Hypothesis: Repetitive Experiments
268(2)
13.4 Considering All Other Hypotheses Related to the Evidence
270(2)
13.4.1 Jurisprudence
272(1)
13.5 Causal versus Logical Independence
272(3)
13.5.1 Confirmation
273(2)
Chapter 14 Confidence and Credible Intervals, Statistical Inference
275(10)
14.1 The Confidence Interval
275(1)
14.2 CI and Coverage Rates
276(3)
14.2.1 Binomial Distribution
277(1)
14.2.2 Normal Distribution
278(1)
14.3 Bayesian Credible Intervals CrI
279(6)
14.3.1 Are Confidence and Credible Intervals Always Different
280(1)
14.3.1.1 Frequentist-Confidence Interval
280(1)
14.3.1.2 Bayesian-Credible Interval
281(1)
14.3.1.3 Robot and Plausibility
281(1)
14.3.2 Second Example
281(5)
14.3.2.1 Comparison
283(2)
Chapter 15 Least Squares, Parameter Estimation, and Correlation
285(38)
15.1 The Car Problem: A Toy Problem
285(1)
15.2 Interval Estimation
286(3)
15.2.1 Interval Estimation of V0 and d for the Car Problem
287(1)
15.2.2 Interval Method of Parameter Estimation versus Least Squares
287(2)
15.3 Least Squares (LS)
289(1)
15.4 Hierarchical Bayesian and Likelihood
290(22)
15.4.1 Maximum Likelihood versus Bayesian Inference
291(2)
15.4.1.1 Noninformative Prior, Maximum Likelihood
292(1)
15.4.2 Marginalization
293(3)
15.4.2.1 Estimation of the Standard Deviation of Measured Data
295(1)
15.4.3 Priors
296(2)
15.4.3.1 Influence of the Prior
298(1)
15.4.4 Improper Priors: Marginalization Paradox
298(4)
15.4.4.1 Marginalization Paradoxes
299(2)
15.4.4.2 Objective Bayesian Inference
301(1)
15.4.5 Solving Equation 15.10
302(8)
15.4.5.1 Numerical Integration
302(1)
15.4.5.2 Monte Carlo Integration
303(1)
15.4.5.3 Fundamentals of Monte Carlo Integration
303(2)
15.4.5.4 Errors in x and MCMC
305(2)
15.4.5.5 MCMC—Metropolis—Hastings
307(3)
15.4.6 Gibbs Sampling
310(1)
15.4.7 M versus Likelihood Model
311(1)
15.5 MCMC versus Gaussian Quadrature
312(1)
15.6 Correlations
312(9)
15.6.1 Sensitivity and Information
315(1)
15.6.1.1 Fisher's Information and Matrix
315(1)
15.6.2 Spurious Correlations and Conditional Correlations
316(2)
15.6.3 Simpson's Paradox and Confounding Variables
318(1)
15.6.4 Use of Residuals for Estimating Properties of e
318(7)
15.6.4.1 Non-Time Series
321(1)
15.6.4.2 Treatment of Correlations in the GUM
321(1)
15.7 Conclusions about Statistical Analysis
321(2)
Chapter 16 Measurements: Errors versus Uncertainty
323(20)
16.1 The Model and Uncertainty
323(1)
16.2 Measurements
323(2)
16.3 Representing the Measurement
325(3)
16.3.1 Estimators
325(1)
16.3.2 Representing the Base Value, A = y
325(2)
16.3.2.1 Maximum A Posterior Probability
326(1)
16.3.2.2 Maximum Likelihood
326(1)
16.3.2.3 Loss Functions and Risk, Bayes' Estimators
326(1)
16.3.3 Arithmetic and Weighted Means, LS, and Maximum Likelihood
327(1)
16.3.3.1 Gaussian Distribution of Errors
328(1)
16.3.4 Representing the Uncertainty, ±U
328(1)
16.3.4.1 Where Do Errors and Uncertainty Come From?
328(1)
16.4 Traditional Error Analysis: Propagation of Errors
328(5)
16.4.1 Shortcomings of Error Propagation
330(1)
16.4.2 Theory of Uncertainty
331(2)
16.5 Drawbacks of Theory of Uncertainty
333(1)
16.6 Examples of Uncertainty: z = f(x,y)
333(10)
16.6.1 Example 1: Effects of Nonindependent Model Variables
333(2)
16.6.2 Example 2: z = x/y
335(1)
16.6.3 Marginalization by Transformed Variables: z =
336(1)
16.6.4 Sensor Calibration, z = x/c
337(3)
16.6.5 Combined Uncertainty
340(1)
16.6.6 Systematic versus Random Errors
341(2)
Chapter 17 Plausibility and the Law
343(6)
17.1 Arguments for Bayesian Inference
344(1)
17.2 Arguments against Bayesian Inference
345(1)
17.3 Arguments Both for and against Bayesian Inference
346(1)
17.4 Additional References about the Law
346(3)
Chapter 18 Reading List
349(4)
18.1 Basic Reading
349(4)
Section III For the Mathematically Adventurous
Chapter 19 Example: Effect of a Calibration Constant
353(12)
19.1 Common Value of the Calibration Constant
353(4)
19.1.1 Exact Solution for p(z)
353(1)
19.1.2 Treatment by Theory of Propagation of Errors
354(1)
19.1.3 z — xc
355(2)
19.2 Example 2: Independent Values of c, Method 2A
357(4)
19.2.1 Method 2B
358(1)
19.2.2 Method 3
358(2)
19.2.3 Method 4
360(1)
19.2.4 Method 5
361(1)
19.2.5 Correction of Method 1
361(1)
19.3 Effect of Correlation of c
361(1)
19.4 Summary
361(1)
19.4.1 Effect of the Number of Measurements and &simga;(c)
362(1)
19.5 Confidence in &simga;(x) and &simga;(c)
362(3)
References 365(8)
Appendix A: Statistical Equations 373(8)
Appendix B: Symbols 381(4)
Appendix C: Glossary 385(8)
Appendix D: Metrology Organizations and Standards 393(6)
Appendix E: Legal Authorities 399(6)
Index 405
Ted Vosk is a criminal defense attorney and legal/forensic consultant. Over the past decade, he has been a driving force behind the reform of forensic practices in Washington State and the laws governing the use of the evidence they produce. His work in and out of the courtroom continues to help shape law in jurisdictions around the country. He has been awarded the Presidents Award from the Washington Association of Criminal Defense Lawyers and the Certificate of Distinction from the Washington Foundation for Criminal Justice. A Fellow of the American Academy of Forensic Sciences and member of Mensa, he has written, broadcast, presented, and taught around the country on topics ranging from the origins of the universe to the doctrine of constitutional separation of powers. He has been published in legal and scientific media, including the Journal of Forensic Sciences, and his work has been cited in others, including Law Reviews and treatises.

Ashley F. Emery is a professor of mechanical engineering at the University of Washington and an adjunct professor of architecture and of industrial and systems energy. He has been an associate dean of the College of Engineering, chair of the Department of Mechanical Engineering, and director for the Thermal Transport Program of the National Science Foundation. His areas of research interest are heat transfer, fluid dynamics, architectural and building energy, thermal stresses, fracture, design and interpretation of experiments, and Bayesian inference. He has published more than 200 technical papers in refereed journals. He is a fellow of the American Society of Mechanical Engineers and the American Society of Heating, Refrigerating and Air-Conditioning Engineers. He is a recipient of the American Society of Mechanical Engineers Heat Transfer Memorial Award and the 75th Anniversary Heat Transfer Award.
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