IEOR 220 Instructor’s Lecture Schedule – First Five Weeks
- Model building, dynamic systems, linearity, difference equations, block diagrams, first order constant coefficient systems, homogeneous and particular solutions.
- Production and inventory systems examples, discounted cash flow, cobweb cycle, higher order systems, existence and uniqueness of solutions.
- Constant coefficient equations, homogeneous solutions, characteristic equation, boundary conditions, stability, particular solutions, undetermined coefficients, frequency response.
- Matrix difference equations and state space representation of systems. Homogeneous and particular solutions.
- System eigenvalues, diagonalization, dynamics of eigenvectors.
- Multiple eigenvalues, equilibrium analysis and stability, dominant eigenvectors.
- Positive systems – Frobenius-Perron theorem.
- Feedback control, design principles – compensation for lags, eigenvalue placement, observability and controllability.
- Linear systems with random inputs.
IEOR 231 Instructor’s Course Topics List
Prediction and Forecasting Models
- Formulation of Prediction Models. The Use of Influence Diagrams. Predictive Distributions. Binomial-Beta Priors, Poisson-Gamma Priors. Bayes Rule Applied to Influence Diagrams.
- Conditional and Unconditional Expectations, Median, Variances, Correlations. Prediction Intervals. Forecast Horizon. Updating and Revising Parameter Estimates, Predictive Distributions and Point Predictors.
- Examples: Rare Events – Pollution Exceedances, Nuclear Incidents, Exponential Times to Failures.
Influence Diagrams and Prediction Models
- Directed and Undirected Graphs. Inference. Prediction. Observable and Unobserable Random Variables, Absorption and Reversal Theorems.
- Multivariate Normal Influence Diagrams.
- Kalman Filter Models and State-Space Methods.
- Examples: Predicting Undetected Faults (“Bugs”) in Newly Developed Software.
Time Series Models, Box-Jenkins Methods
- Structure and Classification of ARMA. Stationary Linear Difference Equations – Autocorrelation, Partial Autocorrelation and Model Identification. Equivalent Autoregressive and Moving Average Models. Stationarity and Invertibility.
- ARIMA models. Non-stationary Correlated Random Walks.
- The Analysis of Forecast Errors. Autocorrelation Test for White Noise.
- Examples: ARIMA (0, 1, 1) – Exponential Smoothing and ARMA (p, q)
State-Space Models and Kalman Filters
- The Measurement and Observation Equation. Making Inferences about States from the Observation Equation.
- Level and Trend Change – Exponential Smoothing. Detecting Level Changes.
- Seasonal Models.
- Use of Kalman Filtering in Box-Jenkins Identification and Estimation.