1. Bayesian statistics 一组独立同分布的数据集 X=(x1,-,xn)(xi∼p(xi|θ)),参数 θ 同时也是被另外分布定义的随机变量 θ∼p(θ|α),此时: p(X|α)=∫θp(X|θ)p(θ|α)dθ 2. 频率统计(frequentist statistics) 此时的 θ=(ψ,λ)(joint parameter,联合参数),其中 ψ 是真正的待求解的参数,λ 则是 nuisance parameter. L(ψ;X)=p(X|ψ)=∫λp(X|ψ,λ)p…

There are three popular metrics to measure the correlation between two random variables: Pearson's correlation coefficient, Kendall's tau and Spearman's rank correlation coefficient. In this article, I will make a detailed comparison among the three…

基本概念 样本空间: 随机试验E的所有可能结果组成的集合, 为E的样本空间, 记为S 随机事件: E的样本空间S的子集为E的随机事件, 简称事件, 由一个样本点组成的单点集, 称为基本事件 对立事件/逆事件: 若A并B=S, 且A交B=空, 则称A与B互为逆事件, A与B互为对立事件. A上面加一横即A的逆事件 频率: 在相同的条件下进行了n次试验, 事件A发生的次数为A的频数, 与n的比值成为A的频率 概率: 设E为随机试验, S是E的样本空间, 对于E的每一个事件A赋予一个实数, 记为P(A…

Bayes for Beginners: Probability and Likelihood 好好看,非常有用. 以前死活都不理解Probability和Likelihood的区别,为什么这两个东西的条件反一下就相等. 定义: Probability是指在固定参数的情况下,事件的概率,必须是0-1,事件互斥且和为1. 我们常见的泊松分布.二项分布.正态分布的概率密度图描述的就是这个. Likelihood是指固定的结果,我们的参数的概率,和不必为1,不必互斥,所以只有ratio是有意义的. 至…

https://www.quora.com/How-do-I-learn-mathematics-for-machine-learning   How do I learn mathematics for machine learning? Promoted by Time Doctor Software for productivity tracking. Time tracking and productivity improvement software with screenshots…

1.What is Maximum Likelihood? 极大似然是一种找到最可能解释一组观测数据的函数的方法. Maximum Likelihood is a way to find the most likely function to explain a set of observed data. 在基本统计学中,通常给你一个模型来计算概率.例如,你可能被要求找出X大于2的概率,给定如下泊松分布:X ~ Poisson (2.4).在这个例子中,已经给定了你泊松分布的参数 λ(2.4),…

One of the most fundamental concepts of modern statistics is that of likelihood. In each of the discrete random variables we have considered thus far, the distribution depends on one or more parameters that are, in most statistical applications, unkn…

Common sense reduced to computation - Pierre-Simon, marquis de Laplace (1749–1827) Inventor of Bayesian inference 贝叶斯方法的逻辑十分接近人脑的思维:人脑的优势不是计算,在纯数值计算方面,可以说几十年前的计算器就已经超过人脑了. 人脑的核心能力在于推理,而记忆在推理中扮演了重要的角色,我们都是基于已知的常识来做出推理.贝叶斯推断也是如此,先验就是常识,在我们有了新的观测数据后,就可以…

The Basics of Probability Probability measures the amount of uncertainty of an event: a fact whose occurence is uncertain. Sample space refers to the set of all possible events, denoted as . Some properties: Sum rule: Union bound: Conditional probabi…

1.Normal distribution In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and…