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"A pocket guide to risk mathematics: key concepts every auditor should know": Contents list
The book is 208 pages, with roughly 42,000 words. The contents list may seem a bit intimidating but remember that each item is a short explanation of the terminology, written as clearly as humanly possible. Once you've read this book all the following numbered phrases will have a meaning for you:
The order of the concepts is carefully chosen so that explanations use only concepts covered earlier in the book, usually just before so they are still fresh in your mind.
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This book
How this book works
The myth of mathematical clarity
The myths of quantification
The auditor’s mission
Auditing simple risk assessments
1 Probabilities
2 Probabilistic forecaster
3 Calibration (also known as reliability)
4 Resolution
5 Proper score function
6 Audit point: Judging probabilities
7 Probability interpretations
8 Degree of belief
9 Situation (also known as an experiment)
10 Long run relative frequency
11 Degree of belief about long run relative frequency
12 Degree of belief about an outcome
13 Audit point: Mismatched interpretations of probability
14 Audit point: Ignoring uncertainty about probabilities
15 Audit point: Not using data to illuminate probabilities
16 Outcome space (also known as sample space, or possibility space)
17 Audit point: Unspecified situations
18 Outcomes represented without numbers
19 Outcomes represented with numbers
20 Random variable
21 Event
22 Audit point: Events with unspecified boundaries
23 Audit point: Missing ranges
24 Audit point: Top 10 risk reporting
25 Probability of an outcome
26 Probability of an event
27 Probability measure (also known as probability distribution, probability function, or even probability distribution function)
28 Conditional probabilities
29 Discrete random variables
30 Continuous random variables
31 Mixed random variables (also known as mixed discretecontinuous random variables)
32 Audit point: Ignoring mixed random variables
33 Cumulative probability distribution function
34 Audit point: Ignoring impact spread
35 Audit point: Confusing money and utility
36 Probability mass function
37 Probability density function
38 Sharpness
39 Risk
40 Mean value of a probability distribution (also known as the expected value)
41 Audit point: Excessive focus on expected values
42 Audit point: Misunderstanding ‘expected’
43 Audit point: Avoiding impossible provisions
44 Audit point: Probability impact matrix numbers
45 Variance
46 Standard deviation
47 Semivariance
48 Downside probability
49 Lower partial moment
50 Value at risk (VaR)
51 Audit point: Probability times impact
Some types of probability distribution
52 Discrete uniform distribution
53 Zipf distribution
54 Audit point: Benford’s law
55 Nonparametric distributions
56 Analytical expression
57 Closed form (also known as a closed formula or explicit formula)
58 Categorical distribution
59 Bernoulli distribution
60 Binomial distribution
61 Poisson distribution
62 Multinomial distribution
63 Continuous uniform distribution
64 Pareto distribution and power law distribution
65 Triangular distribution
66 Normal distribution (also known as the Gaussian distribution)
67 Audit point: Normality tests
68 Nonparametric continuous distributions
69 Audit point: Multimodal distributions
70 Lognormal distribution
71 Audit point: Thin tails
72 Joint distribution
73 Joint normal distribution
74 Beta distribution
Auditing the design of business prediction models
75 Process (also known as a system)
76 Population
77 Mathematical model
78 Audit point: Mixing models and registers
79 Probabilistic models (also known as stochastic models or statistical models)
80 Model structure
81 Audit point: Lost assumptions
82 Prediction formulae
83 Simulations
84 Optimization
85 Model inputs
86 Prediction formula structure
87 Numerical equation solving
88 Prediction algorithm
89 Prediction errors
90 Model uncertainty
91 Audit point: Ignoring model uncertainty
92 Measurement uncertainty
93 Audit point: Ignoring measurement uncertainty
94 Audit point: Best guess forecasts
95 Prediction intervals
96 Propagating uncertainty
97 Audit point: The flaw of averages
98 Random
99 Theoretically random
100 Real life random
101 Audit point: Fooled by randomness (1)
102 Audit point: Fooled by randomness (2)
103 Pseudo random number generation
104 Monte Carlo simulation
105 Audit point: Ignoring real options
106 Tornado diagram
107 Audit point: Guessing impact
108 Conditional dependence and independence
109 Correlation (also known as linear correlation)
110 Copulas
111 Resampling
112 Causal modelling
113 Latin hypercube
114 Regression
115 Dynamic models
116 Moving average
Auditing model fitting and validation
117 Exhaustive, mutually exclusive hypotheses
118 Probabilities applied to alternative hypotheses
119 Combining evidence
120 Prior probabilities
121 Posterior probabilities
122 Bayes’s theorem
123 Model fitting
124 Hyperparameters
125 Conjugate distributions
126 Bayesian model averaging
127 Audit point: Best versus true explanation
128 Hypothesis testing
129 Audit point: Hypothesis testing in business
130 Maximum a posteriori estimation (MAP)
131 Mean a posteriori estimation
132 Median a posteriori estimation
133 Maximum likelihood estimation (MLE)
134 Audit point: Best estimates of parameters
135 Estimators
136 Sampling distribution
137 Least squares fitting
138 Robust estimators
139 Overfitting
140 Data mining
141 Audit point: Searching for ‘significance’
142 Exploratory data analysis
143 Confirmatory data analysis
144 Interpolation and extrapolation
145 Audit Point: Silly extrapolation
146 Cross validation
147 R^{2} (the coefficient of determination)
148 Audit point: Happy history
149 Audit point: Spurious regression results
150 Information graphics
151 Audit point: Definition of measurements
152 Causation
Auditing and samples
153 Sample
154 Audit point: Mixed populations
155 Accessible population
156 Sampling frame
157 Sampling method
158 Probability sample (also known as a random sample)
159 Equal probability sampling (also known as simple random sampling)
160 Stratified sampling
161 Systematic sampling
162 Probability proportional to size sampling
163 Cluster sampling
164 Sequential sampling
165 Audit point: Prejudging sample sizes
166 Dropouts
167 Audit point: Small populations
Auditing in the world of high finance
168 Extreme values
169 Stress testing
170 Portfolio models
171 Historical simulation
172 Heteroskedasticity
173 RiskMetrics variance model
174 Parametric portfolio model
175 Backtesting
176 Audit point: Risk and reward
177 Portfolio effect
178 Hedge
179 BlackScholes
180 The Greeks
181 Loss distributions
182 Audit point: Operational loss data
183 Generalized linear models
Congratulations
Useful websites
Index


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