İrem Tanrıverdi, iremt@metu.edu.tr — Monte Carlo methods are numerical techniques which rely on random sampling to approximate their results. Monte Carlo integration applies this process to the numerical estimation of integrals. Monte Carlo methods are a particularly attractive choice for the multidimensional integration problems common in computer graphics. Basics: Basic idea becomes clear from the…

SUMS AND MIXTURES — Sums and Mixtures Sums and mixtures of a random variable is a special type of transformation. Convolution: Basically, sums of independent random variables S= X₁+X₂+…+X𝚗 = ∑{i=1} X𝒾 For example; X ~ N(1, 5) Y ~ N(2, 3) Z = X + Y ~ N(3, 8)$ or; v ~𝛘²₂ u ~𝛘²₆ z =…

INVERSE TRANSFORMATION METHOD One of the basic tools required in computational statistics is to simulate random variables from specified probability distributions. To simulate drawing a random observation from a finite population, a method of generating random observations from a discrete uniform distribution is required. Therefore, a proper generator of uniform random numbers is…

REJECTION SAMPLING Remember that there are some techniques to generate random sample (numbers) from a distribution which are; – Inverse transform method – Acceptance-rejection method – Convolution method – Composition method We cannot use inverse transform method distributions which do not have closed from of CDF like normal, gamma, beta, etc. …

A statistical test provides a mechanism for making quantitative decisions about a process. The goal is to determine if there is sufficient evidence to “reject” an assumption or hypothesis about the process. To use statistical tests, processes must satisfied some conditions (assumptions). There is two types of tests which are…

Introduction Machine learning has become very popular nowadays. We use machine learning to make inferences about new situations using old data, and there are too many machine learning algorithms to do this. Linear Regression, Logistic Regression, Decision Tree, Naive Bayes, K-Means, and Random Forest have commonly used machine learning algorithms…