频率主义（Frequentism）与贝叶斯主义（Bayesianism）的哲学辨异与实践（Python仿真）

2024-04-06 22:21:34

对概率的认识

两者的根本不同在于对概率的认识：

frequentists
probabilities are fundamentally related to frequencies of events.
Bayesians,
probabilities are fundamentally related to our own knowledge about an event.

频率

We’ll start with the classical frequentist maximum likelihood approach.

P(D|Ftrue)

P(\mathcal{D}|F_{true})

dlogLdFtrue=0

\frac{d\log\mathcal{L}}{dF_{true}}=0

贝叶斯

The Bayesian approach, as you might expect, begins and ends with probabilities.
It recognizes that what we fundamentally want to compute is our knowledge of the parameters in question, i.e. in this case,

P(Ftrue|D)=P(Ftrue)P(D|P(Ftrue))P(D)

P(F_{true}|\mathcal{D})=\frac{P(F_{true})P(\mathcal{D}|P(F_{true}))}{P(\mathcal{D})}

P(Ftrue|D)P(F_{true}|\mathcal{D})中的D\mathcal{D} 表示数据或者抽象地说我们掌握的知识，
P(Ftrue)P(F_{true})，模型的先验知识，which encodes what we knew about the model prior to the application of the data D\mathcal D。

Note that this formulation of the problem is fundamentally contrary to the frequentist philosophy, which says that probabilities have no meaning for model parameters like Ftrue.
Nevertheless, within the Bayesian philosophy this is perfectly acceptable.

noninformative prior like the flat prior

It turns out that in many situations, a truly noninformative prior does not exist!

Frequentism can often be viewed as simply a special case of the Bayesian approach for some (implicit) choice of the prior: a Bayesian would say that it’s better to make this implicit choice explicit, even if the choice might include some subjectivity.

Photon counts: the Bayesian approach

For a one parameter problem like the one considered here, it’s as simple as computing the posterior probability P(Ftrue|D)P(F_{true}|\mathcal{D}) as a function of FtrueF_{true}: this is the distribution reflecting our knowledge of the parameter FtrueF_{true}.

But as the dimension of the model grows, this direct approach becomes increasingly intractable. For this reason, Bayesian calculations often depend on sampling methods such as Markov Chain Monte Carlo (MCMC).

This maximum likelihood value gives our best estimate of the parameters μ\mu and σ\sigma governing our model of the source. But this is only half the answer: we need to determine how confident we are in this answer, that is, we need to compute the error bars on μ\mu and σ\sigma.

频率主义（Frequentism）与贝叶斯主义（Bayesianism）的哲学辨异与实践（Python仿真）相关推荐

机器学习领域中各学派划分（符号主义、频率主义、贝叶斯主义、连接主义）
前言如果你对这篇文章感兴趣,可以点击「[访客必读 - 指引页]一文囊括主页内所有高质量博客」,查看完整博客分类与对应链接. 在机器学习领域中,算法数量可谓是数不胜数,若只关注每个算法本身,将各个算法 ...
机器学习领域中各学派划分——符号主义、频率主义、贝叶斯主义、连接主义核心思想和理论
机器学习领域中各学派划分--符号主义.频率主义.贝叶斯主义.连接主义文章目录机器学习领域中各学派划分--符号主义.频率主义.贝叶斯主义.连接主义符号主义频率主义贝叶斯主义连接主义符号主义 ...
贝叶斯优化调参-Bayesian optimiazation原理加实践
随着机器学习用来处理大量数据被广泛使用,超参数调优所需要的空间和过程越来越复杂.传统的网格搜索和随即搜索已经不能满足用户的需求,因此方便快捷的贝叶斯优化调参越来越受程序员青睐. 1.贝叶斯优化原理介绍 ...
科研工具-R-META分析与【文献计量分析、贝叶斯、机器学习等】多技术融合实践
Meta分析是针对某一科研问题,根据明确的搜索策略.选择筛选文献标准.采用严格的评价方法,对来源不同的研究成果进行收集.合并及定量统计分析的方法,最早出现于"循证医学",现已广泛应 ...
java mllib 算法_朴素贝叶斯算法原理及Spark MLlib实例(Scala/Java/Python)
朴素贝叶斯算法介绍: 朴素贝叶斯法是基于贝叶斯定理与特征条件独立假设的分类方法. 朴素贝叶斯的思想基础是这样的:对于给出的待分类项,求解在此项出现的条件下各个类别出现的概率,在没有其它可用信息下,我 ...
朴素贝叶斯应用之在手写数字识别的实践
文章目录引言朴素贝叶斯朴素贝叶斯法的学习与分类朴素贝叶斯法的参数估计极大似然估计贝叶斯估计实战朴素贝叶斯图片预处理图片数据化模型训练模型预测其他说明 Reference 引言 ...
【机器学习】贝叶斯算法详解 + 公式推导 + 垃圾邮件过滤实战 + Python代码实现
文章目录一.贝叶斯简介二.贝叶斯公式推导三.拼写纠正案例四.垃圾邮件过滤案例 4.1 问题描述 4.2 朴素贝叶斯引入五.基于朴素贝叶斯的垃圾邮件过滤实战 5.1 导入相关库 5.2 邮件数 ...
BPR贝叶斯个性化推荐算法—推荐系统基础算法（含python代码实现以及详细例子讲解）
BPR贝叶斯个性化排序算法一.问题导入二.显示反馈与隐式反馈 2.1 显式反馈与隐式反馈基本概念 2.2 显式反馈与隐式反馈的比较 2.3 显式反馈与隐式反馈的评价方法 2.3.1 显式反馈数据模 ...
德国坦克问题及频率学派与贝叶斯学派
转载:Tony's blog: 德国坦克问题及频率学派与贝叶斯学派 (tonysh-thu.blogspot.com) 这是一个看起来很基础很简单的经典问题:假设所有的德国坦克是从1开始按自然数递增编 ...

最新文章

热门文章