Demos

• A QMCPy Quick Start
  • References
• Welcome to QMCPy
  • Importing QMCPy
  • Important Notes
• Integration Examples using QMCPy package
  • Keister Example
  • Arithmetic-Mean Asian Put Option: Single Level
  • Arithmetic-Mean Asian Put Option: Multi-Level
  • Keister Example using Bayesian Cubature
• QMCPy for Lebesgue Integration
  • Sample Problem 1
  • Sample Problem 2
  • Sample Problem 3
  • Sample Problem 4
• Scatter Plots of Samples
  • IID Samples
  • LD Samples
  • Transform to the True Distribution
  • Shift and Stretch the True Distribution
  • Plots samples on a 2D Keister function
• A Monte Carlo vs Quasi-Monte Carlo Comparison
  • Vary Absolute Tolerance
  • Vary Dimension
• Quasi-Random Sequence Generator Comparison
  • General Usage
  • QMCPy Generator Times Comparison
• Importance Sampling Examples
  • Game Example
  • Asian Call Option Example
  • Importance Sampling MC vs QMC
• NEI (Noisy Expected Improvement) Demo
  • Goal
  • Computation of the QEI quantity using qmcpy
• QEI (Q-Noisy Expected Improvement) Demo for Blog
  • Problem setup
  • Computation of the qEI quantity using qmcpy
  • GP model definition (kernel information) and qEI definition
  • Demonstrate the concept of qEI on 2 points
  • Choose some set of next points against which to test the computation
• Basic Ray Tracing
• A closer look at QMCPy’s Sobol’ generator
  • Basic usage
  • Randomize with digital shift / linear matrix scramble
  • Support for graycode and natural ordering
• Custom Dimensions
  • Custom generating matricies
  • Skipping points vs randomization
• Some True Measures
  • Mathematics
  • Imports
  • 1D Density Plot
  • 2D Density Plot
  • 1D Expected Values
  • Importance Samling with a Single Kumaraswamy
  • Importance Sampling with 2 (Composed) Kumaraswamys
  • Can we Improve the Keister function?
• Comparison of multilevel (Quasi-)Monte Carlo for an Asian option problem
• Control Variates in QMCPy
  • Setup
  • Problem 1: Polynomial Function
  • Problem 2: Keister Function
  • Problem 3: Option Pricing
• Elliptic PDE
  • 1. Problem definition
  • 2. Single-level methods
  • 3. Multilevel methods
  • 4. Convergence tests
• Gaussian Diagnostics
  • Example 1: Exponential of Cosine
  • Example 2: Random function
  • Example 3a: Keister integrand: npts = 64
  • Example 3b: Keister integrand: npts = 1024
• ML Sensitivity Indices
  • Load Data
  • Importance of Decision Tree Hyperparameters
  • Bayesian Optimization of Hyperparameters
  • Best Decision Tree Analysis
• Vectorized QMC
  • LD Sequence
  • Simple Example
  • BO QEI
  • Bayesian Logistic Regression
  • Sensitivity Indices
• Vectorized QMC (Bayesian)
  • LD Sequence
  • Simple Example
  • BO QEI
  • Bayesian Logistic Regression
  • Sensitivity Indices
• UM-Bridge with QMCPy
  • Imports
  • Start Docker Container
  • Problem Setup
  • Model Evaluation
  • Automatically Approximate the Expectation
  • Parallel Evaluation
  • Shut Down Docker Image
• Random Lattice Generators Are Not Bad
  • Lattice Declaration and the gen_samples function
  • Integration
• Challenges in Developing Great QMC Software
  • Import the necessary packages and set up plotting routines
  • Here are some plots of Low Discrepancy (LD) Lattice Points
  • Beam Example Plots
  • Beam Example Computations
• Purdue University Colloquim Talk
  • Import the necessary packages and set up plotting routines
  • Here are some plots of IID and Low Discrepancy (LD) Points
  • Beam Example Figures
  • Beam Example Computations
• Genz Function in Dakota and QMCPy
• Monte Carlo for Vector Functions of Integrals
  • Monte Carlo Problem
  • Python Setup
  • Discrete Distribution
  • True Measure
  • Integrand
  • Stopping Criterion
  • Vectorized Stopping Criterion