CME308: Stochastic Methods in Engineering

Handouts

Notes

In an effort to clean up the notes, please direct all notes about errata to nickwest+308corrections@stanford.edu. 

The dates below represent the latest update to the file.
1. Course Description [22 March 2009]
2. A Review of Basic Probability and Statistics [13 April 2009]
Topics: 1. Probability: The Basics    2. Conditional Probability    3. Independence    4. Discrete Random Variables    5. Continuous Random Variables    6. Sums of Random Variables    7. Expectations    8. Summary Statistics    9. Conditional Expectation    10. Important Discrete RVs    11. Important Continuous RVs    12. Examples    13. Maximum Likelihood Estimation    14. Method of Moments    15. Bayesian Statistics
3. The Central Limit Theorem, Law of Large Numbers and Monte Carlo Methods [13 April 2009]
Topics: 1. Computer Experimentation and Simulation     2. Performance Engineering: SSQ     3. Discrete-Event Simulation    4. Generating Non-Uniform RVs    5. Generating Uniform RVs    6. Convergence of the MC Method    7. Strong Laws of Large Number    8. Rate of Convergence in MC Method    9. Characteristic Functions    10. Proof of the Central Limit Theorem    11. More on the MC Method    12. Error Bars for MC    13. The Boot Strap    14. More Complex MC Computations    15. The Delta Method and Small Noise Approximations    16. Kernel-based Density Estimation    17. Return to the Bootstrap
4. Conditional Probability and the Prediction Problem [22 March 2009]
Topics: 1. Conditional Probability     2. Conditional Probability for Random Variables     3. Reliability Modeling    4. The Calculus Based View of Conditional Expectation     5. Conditional Expectations and Prediction Theory     6. Affine Prediction
5a.

 Linear Stochastic Models
 [21 April 2009]
Topics: 1. Least Squares     2. Linear Regression Models with Gaussian Residuals     3. Linear Regression Models with non-Gaussian Residuals    4. Data Transformations    5. Multiple Linear Regressions    6. The Correlation Model    7. Modeling Deterninistic Dynamical Systems via Differential Equations   8. Linear Difference Equations of pth Order   9. Stochastic Linear Difference Equations of pth Order   10. Stability Properties of the Autoregressive Sequence   11. Stationary Version of a Stable Autoregressive Sequence   12. Prediction for Autoregressive Sequences   13. Parameter Estimation for Gaussian Autoregressive Sequences    14. Parameter Estimation for Autoregressive Sequences with non-Gaussian Residuals  

5b.
 Linear Regressions and Least Squares
This was written as a new version to replace the old version above.
 [1 June 2009]
Topics: 1. The Method of Least Squares     2. Basic Linear Regression Model     3. Weighted Least Squares    4. Data Transformations    5. Applying Linear Regression in the Presence of Nonnormality    6. The Bootstrap for Regression Problems    7. Regression Models with Randomness in the Independent Variable   8. Multiple Linear Regressions   9. Bayesian Linear Regression   10. Lasso Regression   11. Logistic Regression

6.
 Gaussian Random Variables [21 May 2009]  
Topics: 1. Random Variables in R-d     2. Gaussian Random Variables in R-d     3. Gaussian Process    4. Gaussian Random Fields    5. Parameter Estimation for Gaussian Models  
7. State-Space Models and the Kalman Filter
 [2 June 2009]
Topics: 1. State-Space Models     2. Partially Observed State-Space Models     3. The Innovations Sequence    4. Derivation of the Kalman Filter
8.
 Markov Chains (2007 version with more graphs) [12 May 2009]

Topics: 1. Non-Linear Stochastic Recursions    2. The Markov Property    3. Examples of Markov Chains    4. Computing the Distributions of the Markov Chain at Time n    5. Computing Conditional Expectations     6. First Transition Analysis     7. More on First Transitions     8. Further Examples of First Transition Analysis     9. Steady-State Equilibrium     10. Stationary Distributions for Finite State Markov Chains     11. Infinite State Space MCs     12. Regenerative Structure     13. Transience vs. Recurrence     14. Law of Large Numbers for Recurrent MCs     15. A Proof of Thm 8.7     16. Positive Recurrent MCs     17. The Central Limit Thm for MCs     18. Monte Carlo Computations of Steady-State Quantities     19. Time-Reversed MCs     20. Birth-Death MCs     21. Detailed Malance and Reversibility     22. Reversible MCs     23. Bayesian Statistics     24. Markov Chain Monte Carlo     25. The Metropolis Algorithm     26. Convergence to Stationarity     27. Coupling     28. Recurrence of MCs on a General State Space     29. Stochastic Lyapunov Functions
9.
 Optimization and Stochastic Control for Markov Chains
 [21 May 2009]
Topics: 1. Finite-Dimensional Parameter Optimization    2. Stochastic Control    3. Optimal Stopping  

10.
 Diffusions and Stochastic Differential Equations
 [21 May 2009]
Topics: 1. Stochastic Differential Equations    2. Brownian Motion    3. Stochastic Integrals    4. Infinitesimal Drift and Variance    5. Computing Expectations    6. Multi-dimensional Diffusions  


11. Markov jump process(continuous-time Markov chains) [2 June 2009]  

References:

A First Course in Stochastic Processes by S. Karlin and H. Taylor
Introduction to Stochastic Processes by E. Cinlar
Stochastic Processes by Hoel, Port, and Stone

  
A1.
 A Primer on Advanced Probability [22 March 2009]
Topics: 1. Expectations    2. Inequalities    3. Weak Convergence    4. Convergence in Probability    5. Convergence in Mean    6. Almost Sure Convergence    7. Relationship between Types of Convergence    8. Interchanging Limits and Expectations    9. Transforms
A Review of Basic Probability [22 March 2009]
This is a set of notes from Prof. Glynn's undergraduate class MSandE 121.
A2.
 Taylor Approximation and the Delta Method
 [28 April 2009]
Topics: 1. Taylor Approximation    2. The Delta Method    3. Second-Order Delta Method    4. Multivariate Delta Method

Practice Finals

CME 308 Final 2006-2007 [Solutions]
CME 308 Final 2007-2008 [Solutions]

CME 308 Final 2008-2009