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Probability Density Function (PDF) for Continuous Variables
Probability Density Function (PDF) for Continuous Variables
A PDF for a normal distribution.
RAI102-Review-20241115 Section 1: Introduction to Probability Theory 1.1 Understand the basic principles and concepts of probability theory. 1.1.5 Random Variables Figure2 ID: 14539 Module ID: 5945
Illustration of Conditional Probability Calculation
Illustration of Conditional Probability Calculation
Venn diagram with multiple arcs generated from a dataset.
RAI102-Review-20241115 Section 1: Introduction to Probability Theory 1.2 Understand the concept of conditional probability and its relevance in risk assessment. 1.2.1 Definition of Conditional Probability Figure 1 ID: 14541 Module ID: 5947
Independence of Events
Independence of Events
Venn diagram with multiple arcs generated from a dataset.
RAI102-Review-20241115 Section 1: Introduction to Probability Theory 1.2 Understand the concept of conditional probability and its relevance in risk assessment. 1.2.2 Deriving Conditional Probabilities Figure 4 ID: 14542 Module ID: 5947
Market Outcome Conditional Probability Distributions
Market Outcome Conditional Probability Distributions
Visual representation of prior, likelihood, and posterior distributions.
RAI102-Review-20241115 Section 1: Introduction to Probability Theory 1.2 Understand the concept of conditional probability and its relevance in risk assessment. 1.2.4 Applications in Risk Assessment Figure 2 ID: 14544 Module ID: 5947
Heat Map with Identified Risks
Heat Map with Identified Risks
A heatmap showing risk levels based on impact and likelihood with labeled risks.
RAI101-Review-20241115 1. Principles of Risk Management 1.3 Proficiency in assessing risk likelihood and impact. 1.3.1 Risk Assessment Techniques Figure 2 ID: 17356 Module ID: 7069
Common Assumptions in Risk Analysis Models
Common Assumptions in Risk Analysis Models
1.4.3 Assumptions in Models
RAI103-Review-20241115 Section 1: Introduction to Mathematical Modeling in Risk Analysis 1.4 Understanding the limitations and assumptions of mathematical models in risk analysis. 1.4.3 Assumptions in Models Figure 1 ID: 17593 Module ID: 7174
Arithmetic Mean of a Geometric Brownian Motion Process
Arithmetic Mean of a Geometric Brownian Motion Process
2.1.1 Arithmetic Mean as measure of central tendency
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.1 Understand the concept of central tendency and variability in data. 2.1.1 Arithmetic Mean as measure of central tendency Figure 2 ID: 14556 Module ID: 5953
Geometric Mean in Investment Returns
Geometric Mean in Investment Returns
2.1.2 Geometric Mean a measure of central tendency.
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.1 Understand the concept of central tendency and variability in data. 2.1.2 Geometric Mean a measure of central tendency. Figure 2 ID: 14557 Module ID: 5953
VaR and Expected Shortfall Illustration
VaR and Expected Shortfall Illustration
2.1.2 Tools for Assessing Market Risks
RAI101-Review-20241115 2. Financial Risks 2.1 Identification and assessment of market risks. 2.1.2 Tools for Assessing Market Risks Figure 1 ID: 17372 Module ID: 7072
Comparison of Means in Financial Analysis
Comparison of Means in Financial Analysis
2.1.3 Harmonic Mean as a measure of central tendency
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.1 Understand the concept of central tendency and variability in data. 2.1.3 Harmonic Mean as a measure of central tendency Figure 2 ID: 14558 Module ID: 5953
Median of a Geometric Brownian Motion Process
Median of a Geometric Brownian Motion Process
2.1.4 Median as a measure of central tendency.
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.1 Understand the concept of central tendency and variability in data. 2.1.4 Median as a measure of central tendency. Figure 2 ID: 14559 Module ID: 5953
Mode of a Geometric Brownian Motion Process
Mode of a Geometric Brownian Motion Process
2.1.5 Mode as a measure of central tendency
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.1 Understand the concept of central tendency and variability in data. 2.1.5 Mode as a measure of central tendency Figure 1 ID: 14560 Module ID: 5953
Range of a Geometric Brownian Motion output
Range of a Geometric Brownian Motion output
2.2.1 Range
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.2 Learn how to calculate and interpret measures of dispersion. 2.2.1 Range Figure 1 ID: 14561 Module ID: 5955
Standard Deviation of a Geometric Brownian Motion Process
Standard Deviation of a Geometric Brownian Motion Process
2.2.3 Standard Deviation
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.2 Learn how to calculate and interpret measures of dispersion. 2.2.3 Standard Deviation Figure 2 ID: 14563 Module ID: 5955
Interquartile Range of a Geometric Brownian Motion Process
Interquartile Range of a Geometric Brownian Motion Process
2.2.4 Interquartile Range (IQR)
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.2 Learn how to calculate and interpret measures of dispersion. 2.2.4 Interquartile Range (IQR) Figure 2 ID: 14564 Module ID: 5955
Distribution of Cyber Security Risks
Distribution of Cyber Security Risks
A bar chart showing cyber security risks across departments
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.3 Explore different methods of data visualization for risk analysis. 2.3.1 Bar Charts Figure 1 ID: 14566 Module ID: 5957
Risk Assessment Heat Map
Risk Assessment Heat Map
A risk heat map showing likelihood vs impact
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.3 Explore different methods of data visualization for risk analysis. 2.3.2 Heat Maps Figure 1 ID: 14567 Module ID: 5957
Identifying Correlations Through Scatter Plots
Identifying Correlations Through Scatter Plots
2.3.3 Scatter Plots
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.3 Explore different methods of data visualization for risk analysis. 2.3.3 Scatter Plots Figure 1 ID: 14568 Module ID: 5957
Box Plots for Three Categories of Variables
Box Plots for Three Categories of Variables
A box plot showing the distribution of values by category.
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.3 Explore different methods of data visualization for risk analysis. 2.3.5 Box Plots Figure 1 ID: 14570 Module ID: 5957
LCR and NSFR Components - Bank Example
LCR and NSFR Components - Bank Example
Bar chart showing components of LCR and NSFR.
RAI101-Review-20241115 2. Financial Risks 2.3 Strategies for managing liquidity risks 2.3.5 Stress testing and scenario analysis Figure 2 ID: 17385 Module ID: 7074
Risk Analysis Visualization Example
Risk Analysis Visualization Example
Bar chart comparing risk levels across different departments.
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.4 Understand the importance of graphical representation in data analysis. 2.4.4 Facilitates Data Presentation Figure 1 ID: 14574 Module ID: 5959
Types of Graphs and Charts
Types of Graphs and Charts
2.5.2 Effective Data Presentation Techniques
RAI102-Review-20241115 Section 2: Descriptive Statistics 2.5 Gain proficiency in summarizing and presenting data effectively. 2.5.2 Effective Data Presentation Techniques Figure 1 ID: 14577 Module ID: 5961
Evolution of Asset Prices with GBM Model
Evolution of Asset Prices with GBM Model
Geometric Brownian Motion of Asset Prices
RAI103-Review-20241115 Section 3: Stochastic Models for Risk Analysis 3.1 Understanding the principles of stochastic modeling 3.1.1 Introduction to Stochastic Modeling Figure 1 ID: 17626 Module ID: 7190
Continuous and Discrete Probability Functions
Continuous and Discrete Probability Functions
3.1.1 Probability Distributions in Risk Analysis
RAI102-Review-20241115 Section 3: Probability Distributions for Risk Analysis 3.1 Understand the concept of probability distributions and their significance in risk analysis. 3.1.1 Probability Distributions in Risk Analysis Figure 1 ID: 14581 Module ID: 5963
Characteristics of Stochastic Processes
Characteristics of Stochastic Processes
Characteristics of Stochastic Processes
RAI103-Review-20241115 Section 3: Stochastic Models for Risk Analysis 3.1 Understanding the principles of stochastic modeling 3.1.2 Stochastic Processes Figure 2 ID: 17627 Module ID: 7190
VaR and Expected Shortfall Illustration
VaR and Expected Shortfall Illustration
3.1.3 Appplications in Risk Assessment
RAI102-Review-20241115 Section 3: Probability Distributions for Risk Analysis 3.1 Understand the concept of probability distributions and their significance in risk analysis. 3.1.3 Appplications in Risk Assessment Figure 1 ID: 14584 Module ID: 5963
Markov Chain Process
Markov Chain Process
Markov Chain Process
RAI103-Review-20241115 Section 3: Stochastic Models for Risk Analysis 3.1 Understanding the principles of stochastic modeling 3.1.3 Markov Chains Figure 3 ID: 17628 Module ID: 7190
Poisson (Events) and Exponential (Event Arrival-Time) Process Illustrations
Poisson (Events) and Exponential (Event Arrival-Time) Process Illustrations
Illustration of Poisson and Exponential processes.
RAI103-Review-20241115 Section 3: Stochastic Models for Risk Analysis 3.1 Understanding the principles of stochastic modeling 3.1.4 Poisson Processes Figure 1 ID: 17629 Module ID: 7190
SDE Components in Risk Analysis
SDE Components in Risk Analysis
Illustration of a simple SDE dXt=μXtdt+σXtdWt with μ=0.05 * Δt and σ=0.07 * √Δt.
RAI103-Review-20241115 Section 3: Stochastic Models for Risk Analysis 3.1 Understanding the principles of stochastic modeling 3.1.5 Stochastic Differential Equations Figure 1 ID: 17630 Module ID: 7190
Gaussian Distributions with Different Parameters
Gaussian Distributions with Different Parameters
Gaussian distributions with different parameters
RAI102-Review-20241115 Section 3: Probability Distributions for Risk Analysis 3.2 Learn about common probability distributions such as normal, binomial, and exponential. 3.2.1 Normal Distribution Figure 1 ID: 14586 Module ID: 5965
Probability Density / Mass profiles of the Normal, Binomial and Poisson Distributions
Probability Density / Mass profiles of the Normal, Binomial and Poisson Distributions
Comparison of Normal, Binomial, and Poisson Distributions
RAI103-Review-20241115 Section 3: Stochastic Models for Risk Analysis 3.2 Knowledge of probabilistic models used in risk analysis. 3.2.1 Understanding Probability Distributions Figure 1 ID: 17631 Module ID: 7192
Binomial Distribution PMF for Different Parameters
Binomial Distribution PMF for Different Parameters
Binomial Distribution PMF for different parameters
RAI102-Review-20241115 Section 3: Probability Distributions for Risk Analysis 3.2 Learn about common probability distributions such as normal, binomial, and exponential. 3.2.2 Binomial Distribution Figure 1 ID: 14587 Module ID: 5965
Exponential Distribution PDF for Different Rate Parameters
Exponential Distribution PDF for Different Rate Parameters
Exponential Distribution PDF for different rate parameters
RAI102-Review-20241115 Section 3: Probability Distributions for Risk Analysis 3.2 Learn about common probability distributions such as normal, binomial, and exponential. 3.2.3 Exponential Distribution Figure 1 ID: 14588 Module ID: 5965
Assessing Capital Adequacy with LDA
Assessing Capital Adequacy with LDA
Horizontal layout of histogram, line chart, and product chart with centered plus and equal signs.
RAI101-Review-20241115 3. Non-Financial Risks 3.2 Recognition and assessment of business and operational risks. 3.2.5 Quantitative assessment of operational risks. Figure 3 ID: 17402 Module ID: 7077
Beta Distribution PDF for Various Parameters
Beta Distribution PDF for Various Parameters
Beta Distribution PDF for various parameters
RAI102-Review-20241115 Section 3: Probability Distributions for Risk Analysis 3.3 Explore the properties and characteristics of different distributions. 3.3.1 Beta Distribution Figure 1 ID: 14591 Module ID: 5967
Lognormal Distribution PDF for Various Parameters
Lognormal Distribution PDF for Various Parameters
Lognormal Distribution PDF for different parameters
RAI102-Review-20241115 Section 3: Probability Distributions for Risk Analysis 3.3 Explore the properties and characteristics of different distributions. 3.3.2 LogNormal Distribution Figure 1 ID: 14592 Module ID: 5967
Poisson Distribution PMF for Different λ Values
Poisson Distribution PMF for Different λ Values
Poisson Distribution PMF for different lambda values
RAI102-Review-20241115 Section 3: Probability Distributions for Risk Analysis 3.3 Explore the properties and characteristics of different distributions. 3.3.3 Poisson Distribution Figure 1 ID: 14593 Module ID: 5967
Student's T-Distribution PDF for Different Degrees of Freedom
Student's T-Distribution PDF for Different Degrees of Freedom
Student's T-Distribution PDF for different degrees of freedom
RAI102-Review-20241115 Section 3: Probability Distributions for Risk Analysis 3.3 Explore the properties and characteristics of different distributions. 3.3.4 Student-T Distribution Figure 1 ID: 14594 Module ID: 5967
Uniform Distribution PDF and CDF
Uniform Distribution PDF and CDF
Uniform Distribution PDF and CDF
RAI102-Review-20241115 Section 3: Probability Distributions for Risk Analysis 3.3 Explore the properties and characteristics of different distributions. 3.3.5 Uniform Distribution Figure 1 ID: 14595 Module ID: 5967
Inversion from Standard Normal Cumulative Distribution Function (CDF)
Inversion from Standard Normal Cumulative Distribution Function (CDF)
PDF, CDF, and Inverse-CDF visualization of a normal distribution with random draws.
RAI103-Review-20241115 Section 3: Stochastic Models for Risk Analysis 3.4 Interpretation of probabilistic results for risk decision-making 3.4.1 Extracting Values from Probability Distributions Figure 1 ID: 17641 Module ID: 7196
Confidence Interval Development Visualization
Confidence Interval Development Visualization
Regression with error bands.
RAI103-Review-20241115 Section 3: Stochastic Models for Risk Analysis 3.4 Interpretation of probabilistic results for risk decision-making 3.4.2 Understanding Confidence Intervals for Risk Analysis Figure 2 ID: 17642 Module ID: 7196
Monte Carlo Illustration - 100 Scenarios - $50 Stock Price (mu = 5%, sigma = 10%) 1 Year Horizon
Monte Carlo Illustration - 100 Scenarios - $50 Stock Price (mu = 5%, sigma = 10%) 1 Year Horizon
Monte Carlo Simulation of a Stock Price over 1 Year Horizon
RAI103-Review-20241115 Section 3: Stochastic Models for Risk Analysis 3.4 Interpretation of probabilistic results for risk decision-making 3.4.4 Decison Support through Monte Carlo Simulation Figure 1 ID: 17644 Module ID: 7196
Evolution of Distribution Shape Over Time
Evolution of Distribution Shape Over Time
temp_max distribution analysis with density curves
RAI102-Review-20241115 Section 3: Probability Distributions for Risk Analysis 3.5 Gain proficiency in analyzing data using probability distributions. 3.5.4 Interpreting Data Using Probability Distributions Figure 2 ID: 14604 Module ID: 5971
Value at Risk (VaR) Evaluation using Normal Distribution
Value at Risk (VaR) Evaluation using Normal Distribution
Value at Risk (VaR) Evaluation
RAI102-Review-20241115 Section 3: Probability Distributions for Risk Analysis 3.5 Gain proficiency in analyzing data using probability distributions. 3.5.5 Advanced Techniques in Probability Distributions Figure 2 ID: 14605 Module ID: 5971
Comparative Analysis of Sampling Methods - Credit Scores Data
Comparative Analysis of Sampling Methods - Credit Scores Data
4.1.3 Sampling Techniques in Data Analysis
RAI102-Review-20241115 Section 4: Sampling and Estimation 4.1 Understand the importance of sampling in data analysis 4.1.3 Sampling Techniques in Data Analysis Figure 1 ID: 14608 Module ID: 5973
Monte Carlo simulation for Optimal Investment Portfolio
Monte Carlo simulation for Optimal Investment Portfolio
Monte Carlo simulation for portfolio optimization
RAI103-Review-20241115 Section 4: Optimization Techniques for Risk Management 4.3 Application of optimization techniques to improve risk mitigation strategies. 4.3.4 Utilizing Monte Carlo Methods Figure ID: 17664 Module ID: 7205
Constructing Confidence Intervals - Credit Score Data Sample
Constructing Confidence Intervals - Credit Score Data Sample
4.4.2 Constructing Confidence Intervals
RAI102-Review-20241115 Section 4: Sampling and Estimation 4.4 Understand how to estimate population parameters and construct confidence intervals. 4.4.2 Constructing Confidence Intervals Figure 2 ID: 14622 Module ID: 5979
Accurate Inference Process
Accurate Inference Process
A scatterplot showing the impact and probability of different scenarios.
RAI102-Review-20241115 Section 4: Sampling and Estimation 4.5 Gain proficiency in drawing meaningful inferences from sample data. 4.5.2 Types of Inferences Figure 2 ID: 14627 Module ID: 5981
Skewing Inversion from Standard Normal Distribution Function
Skewing Inversion from Standard Normal Distribution Function
Demonstration of skewing a normal distribution using beta distribution
RAI103-Review-20241115 Section 5: Simulation Modeling for Risk Analysis 5.1 Understanding the principles of simulation modeling for risk analysis 5.1.2 Probability Distributions in Simulation Modeling Figure 1 ID: 17677 Module ID: 7212
Qualitative Risk Scale
Qualitative Risk Scale
Risk Likelihood Scale Table
RAI101-Review-20241115 5. Techniques for Non-Financial Risk Analysis 5.1 Understanding qualitative risk assessment methods for non-financial risks. 5.1.2 Qualitative Risk Analysis Figure 2 ID: 17448 Module ID: 7087
Statistical Analysis of Simulation Results
Statistical Analysis of Simulation Results
Statistical Analysis of Simulation Results
RAI103-Review-20241115 Section 5: Simulation Modeling for Risk Analysis 5.4 Interpretation of simulation results for risk-informed decision-making. 5.4.2 Statistical Analysis of Simulation Results Figure 1 ID: 17692 Module ID: 7218
Risk Analysis Dashboard Example
Risk Analysis Dashboard Example
Risk Analysis Dashboard
RAI103-Review-20241115 Section 5: Simulation Modeling for Risk Analysis 5.4 Interpretation of simulation results for risk-informed decision-making. 5.4.5 Communicating and Applying Simulation Insights Figure 2 ID: 17695 Module ID: 7218
Example Correlation Coefficients
Example Correlation Coefficients
Scatterplots showing positive, negative, and no-correlation scenarios for two variables.
RAI102-Review-20241115 Section 6: Correlation and Regression Analysis 6.1 Understand the concepts of correlation and regression in data analysis. 6.1.1 Correlation in data analysis Figure 1 ID: 14656 Module ID: 5993
Example of a Correlation Matrix
Example of a Correlation Matrix
6.1.5 Interpreting correlation and regression results
RAI102-Review-20241115 Section 6: Correlation and Regression Analysis 6.1 Understand the concepts of correlation and regression in data analysis. 6.1.5 Interpreting correlation and regression results Figure 1 ID: 14660 Module ID: 5993
KRI Monitoring Mechanism Example
KRI Monitoring Mechanism Example
A simple bar chart with embedded data.
RAI101-Review-20241115 6. Integration of Risk Management Principles and Practices 6.2 Integration of risk management principles into decision-making 6.2.5 Continuous Monitoring and Review Figure 2 ID: 17481 Module ID: 7093
Simple and Multiple Linear Regression Depictions
Simple and Multiple Linear Regression Depictions
6.3.1 Linear Regression
RAI102-Review-20241115 Section 6: Correlation and Regression Analysis 6.3 Explore the different types of regression analysis and their applications. 6.3.1 Linear Regression Figure 1 ID: 14666 Module ID: 5997
Logistic Regression Fits
Logistic Regression Fits
6.3.2 Logistic Regression
RAI102-Review-20241115 Section 6: Correlation and Regression Analysis 6.3 Explore the different types of regression analysis and their applications. 6.3.2 Logistic Regression Figure 1 ID: 14667 Module ID: 5997
Normalized Residuals Patterns and Correlation Results
Normalized Residuals Patterns and Correlation Results
Scatterplots showing correlation with different residuals.
RAI102-Review-20241115 Section 6: Correlation and Regression Analysis 6.5 Gain proficiency in analyzing relationships and patterns in data using correlation and regression techniques. 6.5.1 Advanced understanding of correlation Figure 1 ID: 14676 Module ID: 6001
Components of Time Series Data
Components of Time Series Data
Time Series Components with Trend, Seasonality, Cyclical Patterns, and Random Fluctuations
RAI103-Review-20241115 Section 7: Time Series Forecasting Models for Risk Analysis 7.1 Understanding the principles of time series forecasting for risk analysis 7.1.3 Key components of time series forecasting Figure 1 ID: 17728 Module ID: 7234
Comparison of SMA, ES and ARIMA models on a sample dataset
Comparison of SMA, ES and ARIMA models on a sample dataset
Comparison of Time Series Models with Forecasts
RAI103-Review-20241115 Section 7: Time Series Forecasting Models for Risk Analysis 7.2 Knowledge of time series analysis techniques used in risk assessment. 7.2.1 Differentiating among time series techniques Figure 1 ID: 17731 Module ID: 7236
Common Types of Time Series Data Patterns in Risk Analysis
Common Types of Time Series Data Patterns in Risk Analysis
Time Series Components with Trend, Seasonality, Cyclical Patterns, and Random Fluctuations
RAI102-Review-20241115 Section 7: Time Series Analysis 7.2 Learn how to analyze and interpret time series data patterns. 7.2.1 Understanding Time Series Data Figure 3 ID: 14686 Module ID: 6005
Monthly Sales Data and Decomposition
Monthly Sales Data and Decomposition
7.2.2 Time Series Decomposition Techniques
RAI103-Review-20241115 Section 7: Time Series Forecasting Models for Risk Analysis 7.2 Knowledge of time series analysis techniques used in risk assessment. 7.2.2 Time Series Decomposition Techniques Figure 1 ID: 17732 Module ID: 7236
Seasonal Subseries Plots: Real Estate Prices and Variations Across Different Quarters
Seasonal Subseries Plots: Real Estate Prices and Variations Across Different Quarters
Seasonal Subseries Plots to Visualize Data Across Different Time Periods with Varying Levels and Variations
RAI102-Review-20241115 Section 7: Time Series Analysis 7.2 Learn how to analyze and interpret time series data patterns. 7.2.3 Interpreting Time Series Data Patterns Figure 1 ID: 14688 Module ID: 6005
Exponential Smoothing Techniques and Time Series Components
Exponential Smoothing Techniques and Time Series Components
7.2.4 Decompositon with Exponential Smoothing Techniques
RAI103-Review-20241115 Section 7: Time Series Forecasting Models for Risk Analysis 7.2 Knowledge of time series analysis techniques used in risk assessment. 7.2.4 Decompositon with Exponential Smoothing Techniques Figure 1 ID: 17734 Module ID: 7236
Random Forest Workflow
Random Forest Workflow
7.2.5 LSTM and Random Forest for Time Series and Risk Analysis
RAI103-Review-20241115 Section 7: Time Series Forecasting Models for Risk Analysis 7.2 Knowledge of time series analysis techniques used in risk assessment. 7.2.5 LSTM and Random Forest for Time Series and Risk Analysis Figure 1 ID: 17735 Module ID: 7236
Comparison of Exponential Smoothing Methods
Comparison of Exponential Smoothing Methods
Differentiated Exponential Smoothing Methods Applied to Synthetic Time Series Data
RAI102-Review-20241115 Section 7: Time Series Analysis 7.3 Explore different time series forecasting techniques and their applications. 7.3.2 Exponential Smoothing Methods Figure 2 ID: 14692 Module ID: 6007
ARIMAX Forecast for Portfolio Returns
ARIMAX Forecast for Portfolio Returns
ARIMAX Risk Analysis for Portfolio Returns
RAI103-Review-20241115 Section 7: Time Series Forecasting Models for Risk Analysis 7.3 Application of time series forecasting models to predict risk trends. 7.3.3 Advanced forecasting with exogenous variables Figure 2 ID: 17738 Module ID: 7238
Residual Analysis Plots
Residual Analysis Plots
Residual Analysis Plots
RAI103-Review-20241115 Section 7: Time Series Forecasting Models for Risk Analysis 7.4 Interpretation of time series forecasts for risk-informed decision-making. 7.4.1 Understanding Time Series Forecasts Figure ID: 17741 Module ID: 7240
Comparison of Moving Average, Exponential Smoothing, and Trend Line Applied to Synthetic Time Series Data
Comparison of Moving Average, Exponential Smoothing, and Trend Line Applied to Synthetic Time Series Data
Comparison of Moving Average, Exponential Smoothing, and Trend Line Applied to Synthetic Time Series Data
RAI102-Review-20241115 Section 7: Time Series Analysis 7.4 Understand how to identify trends and make future projections based on time series data. 7.4.2 Identifying Trends in Time Series for Risk Analysis Figure 2 ID: 14697 Module ID: 6009
Comparison of Unconditional and Conditional Delinquency Rate Forecasts
Comparison of Unconditional and Conditional Delinquency Rate Forecasts
ARIMA and ARIMAX Model Application with Flat Delinquency Rate and Unemployment Rate
RAI102-Review-20241115 Section 7: Time Series Analysis 7.4 Understand how to identify trends and make future projections based on time series data. 7.4.3 Making Future Projections based on Time Series Data Figure 1 ID: 14698 Module ID: 6009
Example of Risk Management KPIs in Bullet Chart
Example of Risk Management KPIs in Bullet Chart
Example of highlighting bars above a marker value
RAI101-Review-20241115 7. Risk Management Frameworks 7.4 Integration of risk management frameworks into organizational processes. 7.4.4 Communication and Reporting Figure 2 ID: 17515 Module ID: 7100
Forecast Scenarios Comparison
Forecast Scenarios Comparison
Forecast Scenarios Comparison
RAI103-Review-20241115 Section 7: Time Series Forecasting Models for Risk Analysis 7.4 Interpretation of time series forecasts for risk-informed decision-making. 7.4.5 Communicating Forecast Findings Effectively Figure 1 ID: 17745 Module ID: 7240
Comparison of Time Series Data Sectioning across Model Evaluation Techniques
Comparison of Time Series Data Sectioning across Model Evaluation Techniques
Comparison of different cross-validation and backtesting techniques applied to synthetic time series data
RAI102-Review-20241115 Section 7: Time Series Analysis 7.5 Gain proficiency in using time series analysis for risk forecasting and prediction. 7.5.2 Advanced techniques for Time Series model evaluation Figure 1 ID: 14702 Module ID: 6011
Kalman Filter on Uptrending and Seasonal Data
Kalman Filter on Uptrending and Seasonal Data
Noise Reduction Techniques: Kalman Filter Examples
RAI103-Review-20241115 Section 7: Time Series Forecasting Models for Risk Analysis 7.5 Addressing of challenges and utilizing benefits of using time series forecasting in risk analysis. 7.5.2 Noise reduction techniques in time series modeling Figure ID: 17747 Module ID: 7242
Differenced Data Visualization
Differenced Data Visualization
Time Series Data Transformations
RAI103-Review-20241115 Section 7: Time Series Forecasting Models for Risk Analysis 7.5 Addressing of challenges and utilizing benefits of using time series forecasting in risk analysis. 7.5.3 Data quality considerations for time-series forecasting Figure 2 ID: 17748 Module ID: 7242
Comparison of Structural Breaks, Outliers, and Regime Switches in Time Series Data
Comparison of Structural Breaks, Outliers, and Regime Switches in Time Series Data
Comparison of Structural Breaks, Outliers, and Regime Switches in Time Series Data
RAI102-Review-20241115 Section 7: Time Series Analysis 7.5 Gain proficiency in using time series analysis for risk forecasting and prediction. 7.5.5 Advanced Topics in Time Series Analysis Figure 1 ID: 14705 Module ID: 6011
Monte Carlo Simulation Results
Monte Carlo Simulation Results
Monte Carlo Simulation for High Risk Loan Portfolio - 100 Scenarios across 12 Months
RAI103-Review-20241115 Section 8: Advanced Topics in Mathematical Modeling for Risk Analysis 8.1 Exploration of advanced mathematical modeling techniques for risk analysis. 8.1.1 Application of Monte Carlo Simulation Figure 1 ID: 17751 Module ID: 7245
Comparison of Risk Distributions
Comparison of Risk Distributions
Comparison of Normal, Student-t, Lognormal, and Gumbel Distributions
RAI103-Review-20241115 Section 8: Advanced Topics in Mathematical Modeling for Risk Analysis 8.1 Exploration of advanced mathematical modeling techniques for risk analysis. 8.1.2 Development of Stochastic Models Figure 2 ID: 17752 Module ID: 7245
Bayesian Network for Operational Risk Assessment in Economic Downturns
Bayesian Network for Operational Risk Assessment in Economic Downturns
8.1.3 Bayesian Networks
RAI102-Review-20241115 Section 8: Bayesian Methods 8.1 Understand the principles of Bayesian inference and probabilistic modeling. 8.1.3 Bayesian Networks Figure 1 ID: 14708 Module ID: 6013
Flood Risk Projections for US South-East
Flood Risk Projections for US South-East
Flood Risk Projections for Southern States
RAI103-Review-20241115 Section 8: Advanced Topics in Mathematical Modeling for Risk Analysis 8.1 Exploration of advanced mathematical modeling techniques for risk analysis. 8.1.5 Climate risk forecasting with time series models Figure 2 ID: 17755 Module ID: 7245
Sequential Monte Carlo Visualization
Sequential Monte Carlo Visualization
Economic Forecasting with Sequential Monte Carlo (50 Samples)
RAI103-Review-20241115 Section 8: Advanced Topics in Mathematical Modeling for Risk Analysis 8.2 Understanding emerging trends in mathematical modeling for risk assessment. 8.2.1 Advanced Monte Carlo Simulation Techniques Figure 4 ID: 17756 Module ID: 7247
Prior and Posterior Exponential Distributions in Hazard Modeling
Prior and Posterior Exponential Distributions in Hazard Modeling
Visual representation of prior, likelihood, and posterior hazard rate distributions.
RAI102-Review-20241115 Section 8: Bayesian Methods 8.2 Learn how to apply Bayesian methods in data analysis and decision-making. 8.2.3 Bayesian Modeling in Insurance and Healthcase Figure 2 ID: 14713 Module ID: 6015
Demonstrating K-means Clustering and Random Forest Classification
Demonstrating K-means Clustering and Random Forest Classification
Generated samples with K-means clustering and Random Forest classification
RAI103-Review-20241115 Section 8: Advanced Topics in Mathematical Modeling for Risk Analysis 8.2 Understanding emerging trends in mathematical modeling for risk assessment. 8.2.3 Integration of data minding and Big Data analytics Figure 3 ID: 17758 Module ID: 7247
Infectious Disease Spread Simulation
Infectious Disease Spread Simulation
Agent-based model showing disease spread
RAI103-Review-20241115 Section 8: Advanced Topics in Mathematical Modeling for Risk Analysis 8.2 Understanding emerging trends in mathematical modeling for risk assessment. 8.2.5 Agent-Based Modeling for Complex Risk Scenarios Figure 2 ID: 17760 Module ID: 7247
Risk Factor Sensitivity Depiction with Tornado Diagrams
Risk Factor Sensitivity Depiction with Tornado Diagrams
8.4.3 Evaluating uncertainties and assumptions in the modeling results
RAI103-Review-20241115 Section 8: Advanced Topics in Mathematical Modeling for Risk Analysis 8.4 Interpretation of complex modeling results for decision-making in risk scenarios. 8.4.3 Evaluating uncertainties and assumptions in the modeling results Figure 2 ID: 17768 Module ID: 7251
Probability Density Functions (PDFs) of Typical Distributions
Probability Density Functions (PDFs) of Typical Distributions
9.1.1 Identifying risk factors
RAI101-Review-20241115 9. Case Studies and Real-World Examples 9.1 Analysis of real-world case studies in risk management. 9.1.1 Identifying risk factors Figure 2 ID: 17542 Module ID: 7106
Survival Function, Hazard Rate, and Cumulative Hazard Rate
Survival Function, Hazard Rate, and Cumulative Hazard Rate
Survival Function, Hazard Rate, and Cumulative Hazard Rate Visualization
RAI102-Review-20241115 Section 9: Risk Analysis Techniques 9.1 Gain insights in applying survival analysis for risk assessment. 9.1.1 Introduction to survival analysis and hazard rates Figure 1 ID: 14731 Module ID: 6023
Survival Function and Hazard Rate Depictions - Credit and Operational Risk
Survival Function and Hazard Rate Depictions - Credit and Operational Risk
Survival Functions and Hazard Rates for Credit and Operational Risks
RAI102-Review-20241115 Section 9: Risk Analysis Techniques 9.1 Gain insights in applying survival analysis for risk assessment. 9.1.2 Calculating hazard rates for risk assessment Figure 1 ID: 14732 Module ID: 6023
Survival and Hazard Rate Visualizations for a Hypothetical Loan Portfolio
Survival and Hazard Rate Visualizations for a Hypothetical Loan Portfolio
Credit Risk Analysis: Survival and Hazard Rates
RAI102-Review-20241115 Section 9: Risk Analysis Techniques 9.1 Gain insights in applying survival analysis for risk assessment. 9.1.5 Applications of hazard rates in Risk Management Figure 1 ID: 14735 Module ID: 6023
Random Sampling from Normal PDF Demonstrating LLN Convergence
Random Sampling from Normal PDF Demonstrating LLN Convergence
9.2.2 Fundamentals of Monte Carlo simulations
RAI102-Review-20241115 Section 9: Risk Analysis Techniques 9.2 Learn about advanced statistical tools and models used in risk analysis. 9.2.2 Fundamentals of Monte Carlo simulations Figure 2 ID: 14737 Module ID: 6025
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