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Numerical Analysis - Simulation -

Numerical Analysis - Simulation -. Hanyang University Jong-Il Park. Modeling. Modeling and fitting. unmodeled World. modeled World. modeling. observed data. model parameters. fitting. Modeling - complexity. Eg. Computer graphics. Simulation. Simulation. Synthetic data. model.

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Numerical Analysis - Simulation -

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  1. Numerical Analysis- Simulation - Hanyang University Jong-Il Park

  2. Modeling • Modeling and fitting unmodeled World modeled World modeling observed data model parameters fitting

  3. Modeling - complexity Eg. Computer graphics

  4. Simulation Simulation Synthetic data model data generation ※varying fitting ◦ Data generation Random number generation • Uniform distribution • Gaussian distribution NR in C chap. 7

  5. General procedure of random number generation 1. Determine the probability density function(pdf) - uniform, Gaussian, Poisson, Gamma,... 2. Generate a RN with uniform distribution eg. Call ran1() in NR in C. 3. Generate a RN with an arbitrary pdf using the RN of 2. - Transformation method, Rejection method... eg. Call gasdev() in NR in C for Gaussian distribution

  6. Generating an arbitrary pdf(I) • Transformation method

  7. Generating an arbitrary pdf(II) • Rejection method

  8. Synthetic data generation • Flow diagram of synthetic data generation Mix Random number generation yideal y pdf of x Contaminated data = practical data model noise a Random number generation Determined x pdf of noise • pdf of x : uniform, Gaussian, ...; probability • Determined x : x1,x2,...,xN given • yideal : no noise • y : contaminated data • pdf of noise : uniform, Gaussian, ... • Mixer : additive, multiplicative, ...

  9. Homework #6 • Programming on Random Number Generation: (1) Uniform distribution in [a,b], (2) Gaussian distribution with mean=m, standard deviation=s. - Generate 1000 samples and draw a histogram for each distribution (a=-4, b=1, m=0.5, s=1.5). - Repeat the same job with varying the number of samples. (eg. 100, 10000, 100000) - Discuss the shape of the histograms in terms of the number of samples. Refer to Ch. 7, NR in C. [Due: Nov. 5]

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