# Statistics

Hypothesis testing in statistics

Basics of statistics

Survival probabilities

Monte Carlo method is a fantastic numerical integration method

Useful when centering a vector around its mean

Betweenness centrality of a node $v$ is measurement of how likely the shortest path between two …

Given a graph with adjacency matrix $\mathbf A$, the eigenvector centrality is $$\mathbf e_u = …$$ c_u = \frac{ \lvert (v_1,v_2)\in \mathcal E: v_1, v_2 \in \mathcal N(u) \rvert}{ \color{red}{d_n …

Node degree of a node $u$ $$d_u = \sum_{v\in \mathcal V} A[u,v],$$ where $A$ is the adjacency …

The Weisfeiler-Lehman kernel is an iterative integration of neighborhood information. We initialize …

Likelihood is not necessarily a pdf

Jensen’s inequality shows that $$f(\mathbb E(X)) \leq \mathbb E(f(X))$$ for a concave …

Ask for valid confidence: “Valid”: validate for test data, train data, or the …

analysis of variance

The conditional probability table is also called CPT

Arcsine Distribution The PDF is $$\frac{1}{\pi\sqrt{x(1-x)}}$$ for $x\in [0,1]$. It can also be …

Two categories with probability $p$ and $1-p$ respectively. For each experiment, the sample space is …

Beta Distribution Interact {% include extras/vue.html %} ((makeGraph))

The number of successes in $n$ independent events where each trial has a success rate of $p$. PMF: …

By generalizing the Bernoulli distribution to $k$ states, we get a categorical distribution. The …