MS&E 121

Introduction to Stochastic Modeling

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Course Topics

Review of Basic Probability and Statistics Concepts using Problem-based Focus

         Applications from: Health, Environment, Finance, Risk Assessment, Insurance

Managing Inventory

        Newsvendor model for perishable inventory

        Inventory systems with carry-over

        "Exploitation" vs "exploration"

Modeling Evolution of Uncertainty over Time (Markov Chains)

        Applications from: Queueing, biology, internet search, finance, physics

        Formulation

        Connection of Markov chain theory to linear algebra

        First-step analysis

        Equilibrium calculations

        Dynamic programming

Managing Congestion and Capacity
        Motivation
        The Poisson Process
        The M/M/1 Queue (M/M/s; M/M/infinity)
        The M/G/1 Queue
        Superposition Theorem
        Modeling abandonment and balking
        Customer vs System Performance Measures
        Little's Law
        Networks of Queues (Open and Closed)
        Kingman's Approximation for G/G/s Queues

Financial Forecasting
        Prediction
        Linear regression
        Autoregressive modeling
        In-sample vs out-of-sample testing

        Pitfalls of statistical modeling