Category Archives: Fundamentals

Statistical analysis

| February 15, 2014 12:39 pm |

Independent variable Dependent variable Analysis Categorical data Continuous data T-test Analysis of variance (ANOVA) Categorical […]

Bayesian model comparison

| December 6, 2013 5:45 pm |

Introduction In traditional statistics, when comparing two models, we often use the p-value, AIC, or […]

Metropolis-Hastings algorithm

| December 4, 2013 3:34 pm |

Introduction When conjugate or semi-conjugate prior distributions are used, the posterior distribution can be approximated […]

Group comparison

| November 21, 2013 11:02 am |

Problem definition We will compare the means of two groups. Consider the following sampling model for […]

Markov chain Monte Carlo Convergence Diagnostics

| November 14, 2013 8:30 pm |

Introduction The Markov chain Monte Carlo (MCMC) is one of the most popular methods of […]

Markov chain Monte Carlo (MCMC) and Gibbs Sampling

| August 26, 2013 1:49 am |

Introduction 베이지안 접근방식에서 가장 어려운 점은 추론 과정에서 다차원의 함수에 대해 integration을 요한다는 것이다. 여기서 […]

Conjugate prior

| June 30, 2013 5:27 pm |

Binomial distribution 이항 분포는 Bernoulli 시행을 $n$번 독립적으로 반복했을 때의 random variable $X$가 따르는 분포이다. […]

Bayesian statistics

| April 15, 2013 10:17 pm |

Introduction 고전통계학에서는 단순히 주어진 data information (likelihood)을 최대화하는 parameter $\hat{\theta}_{\text{MLE}}$를 취한다. 하지만 베이지안 통계학에서는 데이터와 […]

Expectation Maximization, EM

| April 12, 2013 6:43 pm |

Expectation-Maximization algorithm is used to estimate the underlying probability distribution of (observed) incomplete data. The term “incomplete […]

Singular Value Decomposition (SVD) and Low-Rank Approximation

| March 7, 2013 11:16 am |

Singular Value Decomposition, SVD In linear algebra, the singular value decomposition (SVD) is a factorization […]

Probability distribution

| March 1, 2013 6:38 pm |

Discrete probability distribution Bernoulli distribution $X \sim Bernoulli(\theta)$ Mean: $E[X] = \theta$ Variance: $Var[X] = […]

Elementary Linear Algebra

| February 27, 2013 6:45 pm |

Coefficient matrix The matrix $A$ in this equation is called the coefficient matrix of the system. […]