Details for Selected Courses

IEOR 220 Instructor’s Lecture Schedule – First Five Weeks

  1. Model building, dynamic systems, linearity, difference equations, block diagrams, first order constant coefficient systems, homogeneous and particular solutions.
  2. Production and inventory systems examples, discounted cash flow, cobweb cycle, higher order systems, existence and uniqueness of solutions.
  3. Constant coefficient equations, homogeneous solutions, characteristic equation, boundary conditions, stability, particular solutions, undetermined coefficients, frequency response.
  4. Matrix difference equations and state space representation of systems. Homogeneous and particular solutions.
  5. System eigenvalues, diagonalization, dynamics of eigenvectors.
  6. Multiple eigenvalues, equilibrium analysis and stability, dominant eigenvectors.
  7. Positive systems – Frobenius-Perron theorem.
  8. Feedback control, design principles – compensation for lags, eigenvalue placement, observability and controllability.
  9. Linear systems with random inputs.
  10. Review.

IEOR 231 Instructor’s Course Topics List

Prediction and Forecasting Models

  1. Formulation of Prediction Models. The Use of Influence Diagrams. Predictive Distributions. Binomial-Beta Priors, Poisson-Gamma Priors. Bayes Rule Applied to Influence Diagrams.
  2. Conditional and Unconditional Expectations, Median, Variances, Correlations. Prediction Intervals. Forecast Horizon. Updating and Revising Parameter Estimates, Predictive Distributions and Point Predictors.
  3. Examples: Rare Events – Pollution Exceedances, Nuclear Incidents, Exponential Times to Failures.

Influence Diagrams and Prediction Models

  1. Directed and Undirected Graphs. Inference. Prediction. Observable and Unobserable Random Variables, Absorption and Reversal Theorems.
  2. Multivariate Normal Influence Diagrams.
  3. Kalman Filter Models and State-Space Methods.
  4. Examples: Predicting Undetected Faults (“Bugs”) in Newly Developed Software.

Time Series Models, Box-Jenkins Methods

  1. Structure and Classification of ARMA. Stationary Linear Difference Equations – Autocorrelation, Partial Autocorrelation and Model Identification. Equivalent Autoregressive and Moving Average Models. Stationarity and Invertibility.
  2. ARIMA models. Non-stationary Correlated Random Walks.
  3. The Analysis of Forecast Errors. Autocorrelation Test for White Noise.
  4. Examples: ARIMA (0, 1, 1) – Exponential Smoothing and ARMA (p, q)

State-Space Models and Kalman Filters

  1. The Measurement and Observation Equation. Making Inferences about States from the Observation Equation.
  2. Level and Trend Change – Exponential Smoothing. Detecting Level Changes.
  3. Seasonal Models.
  4. Use of Kalman Filtering in Box-Jenkins Identification and Estimation.