Monte Carlo integration

Simulasi Statistik di Python

Tushar Shanker

Data Scientist

Definite integration

Definite Integral

Simulasi Statistik di Python

Monte Carlo integration

  • Calculate overall area.
  • Randomly sample points in the area.
  • Multiply the fraction of the points below the curve by overall area.
  • $f(x) = x^2$

X Squared

Simulasi Statistik di Python

Monte Carlo integration

  • Calculate overall area.
  • Randomly sample points in the area.
  • Multiply the fraction of the points below the curve by overall area.
Calculate Overall Area
  • $\int_{1}^{2}x^{2}dx$
  • $x_{min} = 1, x_{max} = 2$
  • $\min(0, f_{min}(x)) = 0, f_{max}(x) = 4$
  • $\text{Overall Area} = 4$
Simulasi Statistik di Python

Monte Carlo integration

  • Calculate overall area.
  • Randomly sample points in the area.
  • Multiply the fraction of the points below the curve by overall area.
Random Sampling

Random Sampling

Simulasi Statistik di Python

Monte Carlo integration

  • Calculate overall area.
  • Randomly sample points in the area.
  • Multiply the fraction of the points below the curve by overall area.
Fraction of Area
  • $\text{Overall Area} \times \text{fraction} = 2.303$
  • $\text{Actual Answer} = 2.333$ Fraction of Area
Simulasi Statistik di Python

Let's practice!

Simulasi Statistik di Python

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