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Stochastic Processes, Detection, and Estimation


The goal of this course was to develop analytical tools for the modeling and analysis of random phenomena and the application of these tools to a range of problems arising in engineering, manufacturing, and operations research. Emphasis was placed on hypothesis testing, confidence intervals, and nonparametric methods.

Course topics included:


  • MMSE/MAP/MLE Estimation

  • Cramer-Rao Bound

  • Vector Estimation

  • Bayes Linear Least Squares Estimation

  • Binary and M-Ary Hypothesis Testing

  • Asymptotic Analysis of Likelihood Ratio Tests

  • Composite Hypothesis Testing

  • Random Processes (RPs)

  • Stationarity/Moment Analysis of RPs

  • IID Processes

  • Markov Processes

  • Discrete Time Markov Chains

  • Bernoulli/Poisson/Wiener Processes

  • LSI Systems/WSS Processes

  • Power Spectral Density

  • Cross-Spectral Density & Optimal Estimation

  • (Non)Causal Wiener Filter

  • Discrete Wiener Filters


Stochastically Modeling MBE

Beyond examinations and problem sets, a final paper was also required for this course. I elected to write mine on stochastically modeling molecular beam epitaxy (MBE). A short video from my simulations can be seen below. It shows the simulated growth of one layer of a crystal lattice using MBE, where the black dots represent individual atoms. Islands can be seen nucleating.


Below this, the full paper is available for reading.

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