Probabilistic Techniques in Exposure Assessment

by Cullen, Alison C.; Frey, H. Christopher

• ISBN13: 9780306459566
• ISBN10: 0306459566
• Format: Hardcover
• Copyright: 1998-11-01
• Publisher: Plenum Pub Corp

Summary

At this time when regulatory agencies are accepting and actively encouraging probabilistic approaches and the attribution of overall uncertainty among inputs to support Value of Information analyses, a comprehensive sourcebook on methods for addressing variability and uncertainty in exposure analysis is sorely needed. This need is adroitly met in Probabilistic Techniques in Exposure Assessment. A host of expert contributors provide a straightforward introduction to the practical tools for addressing variability and uncertainty in support of environmental and human health decision making. 151 graphs, plots, charts, and figures supplement a broad range of detailed and practical examples.

Table of Contents

Introduction	1	(14)
Background	2	(2)
Historical Context for Probabilistic Exposure Assessment	4	(3)
When Is Probabilistic Analysis Useful and/or Justified?	7	(1)
Assessing the Existing Information Base	8	(2)
Structure of the Text	10	(2)
Composition of Exposure Assessment Teams	12	(1)
Conventions Used in This Text	12	(1)
Terminology	12	(1)
Use of Examples	13	(1)
Scope	13	(1)
Summary of Goals and Philosophy	13	(2)
A Basic Framework for Probabilistic Analysis	15	(22)
Philosophy of Probabilistic Analysis	15	(6)
The Frequentist View of Probability	15	(3)
Subjective or Bayesian Views of Probability	18	(2)
Discussion	20	(1)
Taxonomy of Variability and Uncertainty	21	(12)
Model Uncertainty	21	(9)
Variability	30	(1)
Input Uncertainty	31	(2)
Comparison of Variability and Uncertainty	33	(4)
Approaches to Model Uncertainty	37	(22)
Purpose of Using Models	38	(2)
Model Complexity	40	(7)
Uncertainty Propagation Characteristics of Models	41	(3)
When Is a Complex Model Needed?	44	(1)
Simplifying a Complex Model	45	(2)
Setting Up the Right Problem	47	(1)
Model Verification	48	(2)
Model Validation	50	(3)
Validating with Data: The Elusive Ideal	50	(2)
Partial Validation: When You Have Some Data	52	(1)
What If There Are No Data?	52	(1)
Can You Validate by Comparing Models?	53	(1)
Extrapolation and Uncertainty	53	(1)
Can Input Uncertainties Reflect Model Uncertainty?	54	(1)
What Do You Do When Models Disagree?	55	(1)
Examples of Model Uncertainty Issues	56	(3)
Characterizing Variability and Uncertainty in Model Inputs	59	(22)
Data Availability and Characteristics	59	(3)
Temporal Variability	60	(1)
Spatial Variability	61	(1)
Interindividual Variability	61	(1)
Uncertainty	62	(1)
Deciding How Far to Go	62	(2)
Families and Models for Probability Distributions	64	(17)
Theoretical Basis for Probability Distribution Models	64	(14)
Characterizing Uncertainty in Distribution Parameters	78	(3)
Data and Distributions	81	(80)
Summary Statistics	82	(7)
Central Tendency	82	(3)
Spread	85	(2)
Shape	87	(2)
Empirical Basis for Selecting a Parametric Probability Distribution Model	89	(3)
Empirical Cumulative Distribution Functions	92	(4)
Plotting Position	93	(1)
Examples of Empirical Cumulative Distributions	94	(2)
Other Ways to Visualize Data	96	(3)
Uncertainty in Summary Statistics	99	(23)
Uncertainty in the Mean	99	(8)
Uncertainty in the Variance and Standard Deviation	107	(5)
Uncertainty in Skewness	112	(1)
Uncertainty in Kurtosis	112	(1)
Multivariate Distributions for Uncertainty in Statistics	113	(3)
Small Data Sets	116	(2)
Summary of Uncertainty in Statistics for the PCB Concentration Data Sets	118	(4)
Probability Distribution Models	122	(3)
Method of Matching Moments Estimates of Distribution Parameters	122	(1)
Maximum Likelihood Estimates of Distribution Parameters	122	(1)
Examples of the Use of Statistical Estimators	123	(2)
Probability Plots	125	(18)
Empirical Basis for Selecting Probability Models	126	(1)
Methods for Probability Plotting	127	(2)
Identifying Distribution Types Based upon Probability Plotting	129	(6)
Normal and Lognormal Probability Plots	135	(1)
Estimating Distribution Parameters Using Probability Plots	135	(2)
Probability Plots for the Weibull Distribution	137	(1)
Probability Plots and Censored Data Sets	138	(1)
Percentile-Percentile Plots	139	(3)
Frequency Comparisons	142	(1)
Goodness-of-Fit Tests	143	(18)
Chi-Squared Test	144	(5)
Kolmogorov--Smirnov Test	149	(6)
Anderson--Darling Test	155	(6)
Special Topics Related to Distribution Development	161	(20)
Initial Distributions	161	(2)
Suggested Information to Accompany Initial Distributions	162	(1)
Maximum Entropy Inference Approach	163	(2)
The Basis of Maximum Entropy Inference	163	(1)
Example	164	(1)
Combining Information	165	(7)
What to Combine?	167	(1)
Why Combine Information?	168	(1)
When to Consider Preserving Separate Sources of Information?	169	(1)
An Example	169	(3)
Surprise	172	(3)
Defining Surprise	173	(1)
Accounting for Surprise	174	(1)
Dependence among Inputs	175	(2)
Expert Elicitation	177	(4)
Sources of Bias in Judgments about Uncertainty	178	(1)
Elicitation Protocols	178	(3)
Probabilistic Modeling Techniques	181	(62)
Implications of the Central Limit Theorem for Propagation of Distributions	181	(2)
Properties of the Mean and Variance	183	(1)
Analytical Methods: transformation of Variables	184	(2)
Approximation Methods Based upon Taylor Series Expansions	186	(8)
Numerical Simulation Methods	194	(23)
Monte Carlo Simulation	196	(11)
Latin Hypercube Sampling	207	(6)
Other Sampling Techniques	213	(1)
Selecting a Sample Size for Numerical Simulations	213	(2)
Verification of Monte Carlo Results	215	(1)
Available Software Tools	216	(1)
Two-Dimensional Simulations	217	(20)
Background on Two-Dimensional Methods	217	(2)
Distinctions between Variability and Uncertainty in Simulations	219	(1)
Characterization of Uncertainty as an Aid to Model Validation	219	(2)
Taxonomy of Variability and Uncertainty in Model Inputs	221	(2)
General Approach for Simulation of Variability and Uncertainty	223	(1)
Developing Input Assumptions for Two-Dimensional Analyses	224	(12)
Simulating Correlations among Frequency Distributions for Variability in Two-Dimensional Analyses	236	(1)
Discussion of Analytical, Approximation, and Numerical Methods	237	(3)
Assessing Model Uncertainties	240	(1)
Uncertainty Reduction Techniques	241	(2)
Identifying Key Constributors to Variability and Uncertainty in Model Outputs	243	(28)
Introduction to the Examples	244	(3)
Case A	245	(1)
Case B	245	(2)
Methods to Use Prior to Simulation	247	(2)
Apportioning Variance by the Gaussian Approximation	247	(1)
Coefficient of Variation	248	(1)
Methods to Use after Simulation	249	(19)
Scatter Plot	249	(4)
Correlation Coefficient	253	(10)
Correlation Ratio	263	(1)
Multivariate Linear Regression	264	(2)
Nominal Range Sensitivity	266	(1)
Probabilistic Sensitivity Analysis	267	(1)
Contribution to Variance	268	(1)
Screening and Iteration	268	(1)
Summary	269	(2)
An Example of Probabilistic Exposure Assessment in the Community Surrounding New Bedford Harbor	271	(38)
Defining the Exposure Scenario	271	(6)
Temporal Scope	272	(2)
Spatial/Population Scope	274	(1)
Model Structure	274	(3)
Distribution Development for Exposure Model Inputs	277	(26)
Correlation	277	(1)
Concentration of PCBs in Environmental Media	278	(14)
Human Physical Characteristics	292	(4)
Inputs Related to Intake and Consumption Rates	296	(5)
Setup of Analysis	301	(2)
Results	303	(6)
One-Dimensional Analysis of Variability	303	(1)
Two-Dimensional Analysis of Variability and Uncertainty	304	(2)
Identification of Key Contributors to Variability in Output	306	(3)
Glossary	309	(8)
References	317	(10)
Index	327