1. uncertainty aleatoric uncertainty 偶然不确定性 epistemic uncertainty 认知不确定性 2. probability VS likelihood Pr(data|distribution); L(distribution|data); The likelihood function is unnormalized probability distribution describing uncertainty related to \tit…
PRML Chapter 2. Probability Distributions P68 conjugate priors In Bayesian probability theory, if the posterior distributions p(θ|x) are in the same family as the prior probability distributionp(θ), the prior and posterior are then called conjugate d…
PDF version PMF Suppose there is a sequence of independent Bernoulli trials, each trial having two potential outcomes called "success" and "failure". In each trial the probability of success is $p$ and of failure is $(1-p)$. We are obs…
2.1. Binary Variables 1. Bernoulli distribution, p(x = 1|µ) = µ 2.Binomial distribution + 3.beta distribution(Conjugate Prior of Bernoulli distribution) The parameters a and b are often called hyperparameters because they control the distribution of…
Targeted learning methods build machine-learning-based estimators of parameters defined as features of the probability distribution of the data, while also providing influence-curve or bootstrap-based confidence internals. The theory offers a general…
PDF version PDF & CDF The probability density function is $$f(x; \mu, \sigma) = {1\over\sqrt{2\pi}\sigma}e^{-{1\over2}{(x-\mu)^2\over\sigma^2}}$$ The cumulative distribution function is defined by $$F(x; \mu, \sigma) = \Phi\left({x-\mu\over\sigma}\ri…
PDF version PDF & CDF The probability density function of the uniform distribution is $$f(x; \alpha, \beta) = \begin{cases}{1\over\beta-\alpha} & \mbox{if}\ \alpha < x < \beta\\ 0 & \mbox{otherwise} \end{cases} $$ The cumulative distribu…
PDF version PDF & CDF The exponential probability density function (PDF) is $$f(x; \lambda) = \begin{cases}\lambda e^{-\lambda x} & x\geq0\\ 0 & x < 0 \end{cases}$$ The exponential cumulative distribution function (CDF) is $$F(x; \lambda) =…
PDF version PMF Suppose that a sample of size $n$ is to be chosen randomly (without replacement) from an urn containing $N$ balls, of which $m$ are white and $N-m$ are black. If we let $X$ denote the number of white balls selected, then $$f(x; N, m,…
PDF version PMF Suppose that independent trials, each having a probability $p$, $0 < p < 1$, of being a success, are performed until a success occurs. If we let $X$ equal the number of failures required, then the geometric distribution mass function…
PDF version PMF A discrete random variable $X$ is said to have a Poisson distribution with parameter $\lambda > 0$, if the probability mass function of $X$ is given by $$f(x; \lambda) = \Pr(X=x) = e^{-\lambda}{\lambda^x\over x!}$$ for $x=0, 1, 2, \cd…
PDF下载链接 PMF If the random variable $X$ follows the binomial distribution with parameters $n$ and $p$, we write $X \sim B(n, p)$. The probability of getting exactly $x$ successes in $n$ trials is given by the probability mass function: $$f(x; n, p) =…
Stat2.3x Inference(统计推断)课程由加州大学伯克利分校(University of California, Berkeley)于2014年在edX平台讲授. PDF笔记下载(Academia.edu) ADDITIONAL PRACTICE FOR THE FINAL In the following problems you will be asked to choose one of the four options (A)-(D). The options are sta…
Stat2.3x Inference(统计推断)课程由加州大学伯克利分校(University of California, Berkeley)于2014年在edX平台讲授. PDF笔记下载(Academia.edu) Summary Test of Hypotheses $$\text{Null}: H_0$$ $$\text{Alternative}: H_A$$ Assuming the null is true, the chance of getting data like the d…
Stat2.3x Inference(统计推断)课程由加州大学伯克利分校(University of California, Berkeley)于2014年在edX平台讲授. PDF笔记下载(Academia.edu) Summary Estimating population means and percents Sampling assumptions: Simple Random Sample (SRS) Large enough so that the probability histo…
Chapter 1.6 : Information Theory Chapter 1.6 : Information Theory Christopher M. Bishop, PRML, Chapter 1 Introdcution 1. Information h(x) Given a random variable and we ask how much information is received when we observe a specific value for thi…
听同事讲 Bayesian statistics: Part 2 - Bayesian inference 摘要:每天坐地铁上班是一件很辛苦的事,需要早起不说,如果早上开会又赶上地铁晚点,更是让人火烧眉毛.在城市里工作的人,很多是需要搭乘地铁上下班的,也包括同事M. 有一次M早上来得比较晚,进办公室以后就开始抱怨地铁又晚点了,而且同一周不只发生了一次.我说,作为 statistician,你就不能 predict 一下地铁会不会晚点吗?她说,"This is a very tricky prob…
CONTINUOUS RANDOM VARIABLES AND PDFS 连续的随机变量,顾名思义.就是随机变量的取值范围是连续的值,比如汽车的速度.气温.假设我们要利用这些參数来建模.那么就须要引入连续随机变量. 假设随机变量X是连续的,那么它的概率分布函数能够用一个连续的非负函数来表示,这个非负函数称作连续随机变量的概率密度函数(probability density function).并且满足: 假设B是一个连续的区间,那么: watermark/2/text/aHR0cDovL2Js…
https://github.com/lucasb-eyer/pydensecrf/blob/master/examples/inference.py 1.运行 先运行看看实现的结果: (deeplearning) userdeMBP:examples user$ python inference.py im1.png anno1.png out1.png Found a full-black pixel in annotation image, assuming it means 'unkno…
INDEX BAD EXAMPLE Improving Overall Performance Inserting Multiple Rows INSTEAD OF Inserting a Single Row Inserting Retrieved Data BAD EXAMPLE INSERT INTO Customers VALUES(NULL, 'Pep E. LaPew', '100 Main Street', 'Los Angeles', 'CA', ', 'USA', NULL,…
Keyword: Reject Inference Suppose there is a dataset of several attributes, including working conditions, credit history, and property, that have been provided by the bank. The sample classified the customers according to whether they paid off their…
Chapter 4. The class File Format Table of Contents 4.1. The ClassFile Structure 4.2. Names 4.2.1. Binary Class and Interface Names 4.2.2. Unqualified Names 4.2.3. Module and Package Names 4.3. Descriptors 4.3.1. Grammar Notation 4.3.2. Field Descript…
We consider two types of inference: finding the most likely state of the world consistent with some evidence computing arbitrary conditional probabilities. We then discuss two approaches to making inference more tractable on large , relational proble…
