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Stochastic Processes, Detection, and Estimation

Introduction

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.

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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

Paper

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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