Probabilistic forecasts and optimal decisions / Roman Krzysztofowicz

Format:

Book

Author/Creator:

Krzysztofowicz, R. (Roman), 1947- author.

Language:

English

Subjects (All):

Bayesian statistical decision theory.

Probabilities.

Physical Description:

1 online resource (xxiii, 542 pages) : illustrations

Edition:

1st ed.

Place of Publication:

Newark : John Wiley & Sons, Incorporated, 2025.

Summary:

"Since its origin in the 18th century, decision theory has developed as a coherent mathematical-logical framework, and there are effective analytical tools for dealing with all major sources of the decisional difficulty. And yet making decisions can still be difficult. What makes deciding difficult?"-- Provided by publisher.

Contents:

Chapter 1 Forecast-Decision Theory

1.1 Decision Problem

1.1.1 Decision

1.1.2 Uncertainty

1.2 Forecast-Decision System

1.2.1 Structure

1.2.2 Design: Requirements

1.2.3 Design: Models

1.2.4 Operation

1.2.5 Evaluation

1.2.6 Coupling

1.3 Rational Deciding

1.3.1 The Procedure

1.3.2 The Mind‐Set

1.4 Mathematical Modeling

1.4.1 The Model

1.4.2 The Guideposts

1.5 Notes on Using the Book

Bibliographical Notes

Part I Elements of Probability

Chapter 2 Basic Elements

2.1 Sets and Functions

2.1.1 Sets

2.1.2 Functions

2.2 Variates and Sample Spaces

2.2.1 Variates

2.2.2 Sample Spaces

2.2.3 Samples

2.3 Distributions

2.3.1 Discrete Distribution

2.3.2 Continuous Distribution

2.3.3 Quantile Function

2.4 Moments

2.4.1 Mean

2.4.2 Variance

2.4.3 Invariance and Coherence

2.5 The Uniform Distribution

2.6 The Gaussian Distributions

2.6.1 The Standard Normal Distribution

2.6.2 The Normal Distribution

2.6.3 The Standard Transform

2.6.4 The Log‐Normal Distribution

2.6.5 The Log‐Ratio Normal Distribution

2.6.6 The Reflected Log‐Normal Distribution

2.7 The Gamma Function

2.7.1 Definition and Properties

2.7.2 Polynomial Approximation

2.8 The Incomplete Gamma Function

2.8.1 Definition and Properties

2.8.2 Asymptotic Approximation

Exercises

Chapter 3 Distribution Modeling

3.1 Distribution Modeling Methodology

3.2 Constructing Empirical Distribution

3.3 Specifying the Sample Space

3.3.1 Types of Sample Space

3.3.2 Assessing the Bounds

3.4 Hypothesizing Parametric Models

3.4.1 All Models

3.4.2 Narrowing the Hypotheses

3.5 Estimating Parameters

3.5.1 Types of Parameters

3.5.2 Estimation Problem.

3.6 Evaluating Goodness of Fit

3.6.1 Graphical Comparison

3.6.2 Uniform Distance

3.6.3 The Kolmogorov‐Smirnov Test

3.6.4 Insights into the Kolmogorov‐Smirnov Test

3.7 Illustration of Modeling Methodology

3.8 Derived Distribution Theory

3.8.1 Transformation of Variate

3.8.2 Derived Bounds

3.8.3 Derived Distribution Function

3.8.4 Derived Density Function

3.8.5 Examples of Power Transformation

3.8.6 Example of Log‐Ratio Transformation

3.8.7 Example of Reflection Transformation

Mini‐Projects

Part II Discrete Models

Chapter 4 Judgmental Forecasting

4.1 A Perspective on Probability

4.1.1 Interpretation of Probability

4.1.2 Determination of Probability

4.1.3 Probability as Logic

4.1.4 Judgmental Task

4.2 Judgmental Probability

4.2.1 Definition of Judgmental Probability

4.2.2 Assessment of Judgmental Probability

4.2.3 Allowable Forecast Probabilities

4.2.4 Cromwell's Rule

4.3 Forecasting Fraction of Events

4.4 Revising Probability Sequentially

4.4.1 Revision Paradigms

4.4.2 Bayesian Revision Theory

4.4.3 Conditional Stochastic Independence

4.4.4 Bayesian Revision Model

4.4.5 Probabilistic Reasoning

4.4.6 Adjustment Factors for Judgmental Revision

4.4.7 Judgmental Revision Procedure

4.4.8 Likelihood Ratios for Judgmental Revision

4.5 Analysis of Judgmental Task

4.5.1 Analysis of Events

4.5.2 Analysis of Responses

Historical Notes

Chapter 5 Statistical Forecasting

5.1 Bayesian Forecaster

5.1.1 Variates

5.1.2 Input Elements

5.1.3 Output Elements

5.1.4 Theoretic Structure

5.1.5 Structural Properties

5.2 Samples and Examples

5.2.1 Samples

5.2.2 Examples

5.3 Modeling and Estimation

5.3.1 Prior Probability.

5.3.2 Conditional Distribution Functions

5.3.3 Conditional Density Functions

5.3.4 Monotone Likelihood Ratio Function

5.3.5 Conditional Sample Spaces

5.4 An Application

5.4.1 Predictand and Predictor

5.4.2 Samples

5.4.3 Conditional Distribution Functions

5.4.4 Conditional Density Functions

5.4.5 Posterior Probability

5.4.6 Real‐Time Forecasting

5.4.7 Nonstationary Prior Probability

5.5 Informativeness of Predictor

5.5.1 The Concept

5.5.2 Limiting Predictors

5.5.3 Receiver Operating Characteristic

5.5.4 ROC Construction and Usage

Chapter 6 Verification of Forecasts

6.1 Data and Inputs

6.1.1 Variates and Samples

6.1.2 Necessary Sample Properties

6.1.3 Discretization Algorithm

6.1.4 Contingency Table

6.1.5 Prior Probability

6.1.6 Conditional Probability Functions

6.2 Calibration

6.2.1 The Concept

6.2.2 Bayesian Processor of Forecast

6.2.3 The Role of Prior Probability

6.2.4 Probability Calibration Function

6.2.5 Generic Calibration Functions

6.2.6 Common Biases

6.3 Informativeness

6.3.1 The Concept

6.3.2 Performance Probabilities

6.3.3 The ROC Algorithm

6.3.4 Receiver Operating Characteristic

6.3.5 Limiting Cases

6.3.6 Special Cases

6.4 Verification Scores

6.4.1 Bernoulli Distribution

6.4.2 Calibration Score

6.4.3 Variance Score

6.4.4 Uncertainty Score

6.4.5 Quadratic Score

6.5 Forecast Attributes and Mental Processes

6.5.1 Cognition and Metacognition

6.5.2 Skill Measures

6.6 Concepts and Proofs

6.6.1 Calibration of Bayesian Forecaster

6.6.2 Calibration Measures

6.6.3 Informativeness Measures

6.6.4 Decomposition of Quadratic Score

Chapter 7 Detection‐Decision Theory.

7.1 Prototypical Decision Problems

7.2 Basic Decision Model

7.2.1 Elements

7.2.2 Decision Tree

7.2.3 Optimal Decision Procedure

7.2.4 Optimality Condition

7.2.5 Sensitivity Analysis

7.2.6 Economic Estimation of Disutilities

7.2.7 Subjective Assessment of Disutilities

7.3 Decision with Perfect Forecast

7.3.1 Decision Tree with Perfect Forecast

7.3.2 Decision Procedure with Perfect Forecast

7.3.3 Value of Perfect Forecaster

7.3.4 Properties of Value of Perfect Forecaster

7.4 Decision Model with Forecasts

7.4.1 Repetitive Decisions with Forecasts

7.4.2 Input Elements

7.4.3 Optimal Decision Procedure

7.4.4 Evaluation of Decision Procedure

7.4.5 Value of Forecaster

7.4.6 Efficiency of Forecaster

7.5 Informativeness of Forecaster

7.5.1 The Comparison Problem

7.5.2 Mathematical Definition

7.5.3 Informativeness Relation

7.6 Concepts and Proofs

7.6.1 Order of Disutilities

7.6.2 Integrated Minimum Disutility

7.6.3 Comparison of Forecasters

7.6.4 Comparison of Predictors

7.6.5 Total Probability of Decision Error

Chapter 8 Various Discrete Models

8.1 Search Planning Model

8.1.1 Search and Rescue Situation

8.1.2 Events, Outcomes, Information

8.1.3 Judgmental Probabilities

8.1.4 Assumptions

8.1.5 Bayesian Revision Model

8.1.6 Sequential Revision Equations

8.1.7 Decision Model

8.1.8 Allocation of Resources

8.2 Flash‐Flood Warning Model

8.2.1 Flash‐Flood Situation

8.2.2 Warning System Structure

8.2.3 Model of the Monitor

8.2.4 Model of the Forecaster

8.2.5 Model of the Decider

8.2.6 Performance of Forecaster

8.2.7 Performance of Monitor-Forecaster

8.2.8 System Evaluation

Bibliographical Note

Part III Continuous Models.

Chapter 9 Judgmental Forecasting

9.1 A Perspective on Forecasting

9.1.1 Prototypical Forecasting Problems

9.1.2 Characteristics of Forecasting Problems

9.1.3 Elements of Methodology

9.2 Judgmental Distribution Function

9.2.1 Definition of Judgmental Distribution Function

9.2.2 Assessment Procedure

9.2.3 Predictive Information

9.2.4 Assessment of Quantiles

9.2.5 Validation of Coherence

9.2.6 Judgmental Task

9.3 Parametric Distribution Function

9.3.1 Modeling Procedure

9.3.2 Gaussian Models

9.4 Group Forecasting

9.4.1 Reconciling Assessments

9.4.2 Combining Assessments

9.5 Adjusting Distribution Function

9.6 Applications

9.6.1 Auditing Financial Statements

9.6.2 Forecasting Net Income

9.6.3 Forecasting Precipitation Amount

9.7 Judgment, Data, Analytics

9.8 Concepts and Proofs

9.8.1 Group Decision Making

9.8.2 Majority Rule

9.8.3 Median Rule

Mini-Projects

Chapter 10 Statistical Forecasting

10.1 Bayesian Forecaster

10.1.1 Variates

10.1.2 Input Elements

10.1.3 Output Elements

10.1.4 Theoretic Structure

10.2 Bayesian Gaussian Forecaster

10.2.1 Prior Density Function

10.2.2 Family of Conditional Density Functions

10.2.3 Expected Density Function

10.2.4 Posterior Density Function

10.2.5 Distribution Functions

10.2.6 Quantile Functions

10.2.7 Central Credible Intervals

10.3 Estimation and Validation

10.3.1 Estimation of Prior Parameters

10.3.2 Estimation of Likelihood Parameters

10.3.3 Validation of Assumptions

10.3.4 Fusion of Information

10.4 Informativeness of Predictor

10.4.1 The Concept

10.4.2 Posterior Variance

10.4.3 Sufficiency Characteristic

10.4.4 Informativeness Score

10.4.5 Comparison Theorem

10.5 Communication of Probabilistic Forecast.

10.5.1 Sophisticated Deciders.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

ISBN:

9781394319060

1394319061

9781394221875

1394221878

9781394221882

1394221886

OCLC:

1458761340