Monte Carlo integration

Python'da İstatistiksel Benzetim

Tushar Shanker

Data Scientist

Definite integration

Definite Integral

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

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

$\int_{1}^{2}x^{2}dx$
$x_{min} = 1, x_{max} = 2$
$\min(0, f_{min}(x)) = 0, f_{max}(x) = 4$
$\text{Overall Area} = 4$

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

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

$\text{Overall Area} \times \text{fraction} = 2.303$
$\text{Actual Answer} = 2.333$

Let's practice!

Python'da İstatistiksel Benzetim

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