Notation refers to questions about statistical and mathematical notation.

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5
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1answer
225 views

Maximum Likelihood Formulation for Linear Regression

I have seen the following for maximum likelihood estimation (MLE) for linear regression in multiple sources, e.g. here: $$ \mathcal{D} \equiv \{(x_1, y_1), ..., (x_n, y_n)\} $$ I do not understand ...
0
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2answers
46 views

What is the mathematical symbol for a predicted value?

Take a simple linear regression $y = ax + b$. Here, $y$ is predicted. In my analysis I need to compare the predicted $y$s to the actual $y$s from my data set upon which the regression was built. What ...
19
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3answers
2k views

In machine learning, why are superscripts used instead of subscripts?

I'm taking Andrew Ng's course on Machine Learning through Coursera. For equations, superscripts are used instead of subscripts. For example, in the following equation $x^{(i)}$ is used instead of ...
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0answers
10 views

Should the arithmetic mean of a subset of population data be annotated as sample mean?

If I have population data, and I want to calculate the arithmetic mean of a subset of the population data (e.g. for a certain category of values within a certain range of $n$ observations), is the ...
1
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1answer
25 views

Notation in Markov Chain and MCMC literature

In the MC and MCMC literature one commonly finds statements of the following form (see e.g. Roberts & Rosenthal, 2004): $$ \int_{x \in \mathcal X} \pi(dx)P(x, dy) = \pi(dy). $$ What is the ...
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0answers
9 views

Express Normal Distributions with Integral Notation?

If possible, how would I be able to express some Normal Distribution using Integral notation if I had a distribution such that $$ \mu = 188 \text{ units} $$ $$ \sigma = 41 \text{ units} $$ And we ...
0
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1answer
22 views

Trouble plotting probability

I have a density function that can be written as follows: $$ f(r) = \frac{(1-r^2)^{\frac{n-4}{2}}}{\mathbf{B}\left(\frac{1}{2}, \frac{n-2}{2}\right)}$$ Where $\mathbf{B}$ is the beta function. I got ...
0
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1answer
27 views

Moving average process notation: negative or positive $\theta$s?

I noticed that sometimes the moving average process is written in two different ways. I would like to know which one is correct. $y_t = \epsilon_t + \theta \epsilon_{t-1}$ $y_t = \epsilon_t - ...
0
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1answer
27 views

How to report decision tree statistics?

I need to do a formal report with the results of a decision tree classifier developed in SPSS, but I don't know how. I know there are really well defined ways to report statistics such as mean and ...
0
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0answers
18 views

Estimating transition probabilities from a training set

if $a_{kl}$ is the maximum likelihood estimate for probability of the transition $k \rightarrow l$ and $A_{kl}$ is count of the number of times this transition occurs in the training set, What is ...
3
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0answers
27 views

Cumulant and moment names beyond variance, skewness and kurtosis

In physics, starting from position $x(t)$, one obtains rates of changes via derivatives with respect to time: velocity, acceleration, jerk, jounce (4th order). Some have proposed snap, crackle, pop ...
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1answer
43 views

Question on notation in Brownian motion

I' am reading about the zero set of Brownian motion from Introduction to Stochastic Processes by Lawler. Let $X_t$ be a Brownian motion and define the following random set: $Z=\{t:X_t=0\}$ ...
2
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1answer
90 views

Alternative notation for the arithmetic mean?

Is there any alternative to the convention of using an overline for denoting the arithmetic mean? In my opinion overlines are confusing. For instance, is $\overline{\mathbf{a}}$ a vector or a scalar? ...
3
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1answer
85 views

How to interpret this notation with a tilde?

The following convention is sometimes encountered in the text (here example from HMM statement, $\{X_n\}_{n \geq 1}$ is a Markov process): $$X_n \mid (X_{n-1} = x_{n-1}) \sim f(x_n \mid x_{n-1})$$ ...
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0answers
15 views

Is it usual to express mean Jaccard index be reported as an percentage?

I am presenting the results of a particular algorithm that for each test outputs a Bag (i.e. multiset), which I compare to a corresponding reference Bag. I am using two measures currently to describe ...
2
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0answers
25 views

notation in machine learning [duplicate]

When I am reading a machine learning book I came across the following notation $$||\theta||^2_2$$ What does the $||.||^2_2$ stand for? I know its magnitude but what is the 2,2 for?
2
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1answer
29 views

What does prime mean in the notation $k(x,x')$ in the context of kernels?

I admit it's a very specific question, but what is meant by the notation $'$ in Bishop's book Pattern Recognition and Machine Learning? I'd always thought it's a transpose, but this marked by a ...
9
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2answers
176 views

What exactly does $\dot\sim$ notation mean?

What does $\dot\sim$ notation (dot over tilde) mean, in the context like $x \mathrel{\dot\sim} \mathcal N(0,1)$? Turns out it is easier to find how to typeset it correctly: tex.SE explains that one ...
3
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2answers
174 views

What is the meaning of super script 2 subscript 2 within the context of norms?

I am new to optimization. I keep seeing equations that have a superscript 2 and a subscript 2 on the right-hand side of a norm. For instance, here is the least squares equation min $ ||Ax-b||^2_2$ I ...
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0answers
32 views

Is Weight Matrix Wij from neuron j to i or from i to j?

I have a question about the Weight matrix from a Neural network. I see different notations for this. I see some publications (e.g. This stanford page) with: Notation 1: $W^{(l)}_{ij}$ denotes ...
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1answer
62 views

What does this gated recurrent unit notation mean?

I'm trying to replicate the algorithm found in this paper: http://arxiv.org/abs/1506.07285. And I'm struggling to understand the notation of equation 3 on page 4, which is given as: Is z(c,m,q) a ...
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0answers
21 views

Notation: multivariate expectation

Can someone please explain the meaning behind the multivariate expectation notation used in Econometric Analysis 5th edition by William Greene, page 42? Below is a summary of the arguments justifying ...
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0answers
36 views

What is the intuition behind this pmf/pdf abstraction?

When the writer wishes to show a sum/integration that applies similarly to both pmfs and pdfs, they write it like this: $\quad \int (whatever)\ dF_X(x) $ Such that this becomes either $\sum_x ...
4
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1answer
125 views

Notation for CDF of the binomial distribution

The CDF for $X \sim \operatorname{Bin}(n,p)$ is $I_{1-p}(n-k,1+k)$. What does the $I$ mean?
0
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1answer
52 views

Does $S$ and $s$ mean different things in statistics regarding standard deviation?

In some contexts when denoting sample standard deviation, I notice a capital $S$ and sometimes a small $s$. I also notice this in the same standard textbook. Do they mean different things in context ...
2
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1answer
75 views

Notation for ordinary and ridge regression

I'm trying to obtain an estimator $f(x)=y$ where $x \in \mathbb{R}^{D_1}$ and $y \in \mathbb{R}^{D_2}$, both are column vectors. So my training set $X$ and $Y$ are data matrices of size $D_1 \times ...
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1answer
48 views

What is the right notation for degree of freedom — v or $\nu$?

How to denote the df (degree of freedom), particularly for $t$, $F$ and $\chi^2$ distributions in hypothesis testing? Some references state it as the English letter $v$ such as this one, and in ...
3
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1answer
118 views

What do “$i$” and “$j$ ” subscript mean in statistics?

I'm just curious about what the meaning of $i$ and $j$ subscript in statistic formula. I think $i$ means individual and $j$ means higher level unit in a multilevel frame work. How did statisticians ...
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0answers
18 views

Clarification on statistical notation of mutual information

The following is a definition from a textbook about information theory: Definition: The conditional mutual information of random varaibles X and Y given Z is defined by $I(X;Y|Z) = ...
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2answers
52 views

notation for point estimation in “All of Statistics” by Larry Wasserman

I'm currently reading All of Statistics by Larry Wasserman. The question is about the Delta Method, page 160 in the pdf (I have a hard copy, there it's page 133). The authors defines $\hat{\theta}$ or ...
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1answer
69 views

About $s_x$ and $s_y$

What does $s_x$ and $s_y$ mean (e.g., in the picture below)? Is it a specific value from a column? For instance if you have a table ...
0
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1answer
34 views

Does $X$ (a random variable) usually refer to the population or the sample? [duplicate]

Like the title says, does $X$ (a random variable) usually refer to the population or the sample?
5
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2answers
67 views

Notation for possible values of a random variable

Let $X$ be a discrete random variable that can take the values $1, 2, \textrm{and}\ 3$. What is the conventional way to write this mathematically? Is it just $X\in\{1,2,3\}$ or should I somehow write ...
0
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1answer
23 views

Notation related to probability spaces

Let $A$ and $B$ be events in the probability space $(\Omega, \mathcal{F}, \mathcal{P})$. How would I write that events $A$ and $B$ both occur and event $A$ occurs with probability $0.5$ ...
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0answers
51 views

Hypothesis testing – abusing notation or am I missing something?

In a number of statistics books and references you can find formulas such as: $P\,(result~|~H_0)$ (Bortz, p. 114) $P\,(reject~H_0\;|\;H_0~valid)$ (Wikipedia - Statistical hypothesis testing) and ...
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0answers
27 views

Are the $\text{P}$ and $\Pr$ operators equivalent?

I have seen both used to represent probability. Are they interchangeable?
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1answer
221 views

constant $\times$ distribution

I know that if $U\sim\chi^2(k)$ then $aU\sim \Gamma(k/2,2a)$ for $a>0$. But i read about the estimator and its distribution $$\hat{\sigma}_k^2=\frac{1}{2k}\sum_{i=1}^k ...
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2answers
122 views

What does it mean 'A random variable is a function'?

I have sometimes seen the formulas such that $\operatorname{Var}(aX+b)=a^2\operatorname{Var} X$ and $EX^2=\sum_{x=0}^nx^2\binom{n}{x}p^x(1-p)^{n-x}$. But how do we define $aX+b$ and $X^2$ if, say ...
3
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2answers
474 views

What does this notation mean?

Could anybody tell me what is this model? What does it mean? $$\Delta Y = C + a(Y_{t-1} + bX_{t-1}) + c\Delta Y_{t-1} + d\Delta X_{t-1} + \varepsilon_t$$ Where $\Delta$ is the differencing operator, ...
1
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1answer
27 views

Wilcoxon Rank-Sum Test $H_1$ notation

This notation is from Nonparametric Statistical Inference, 5th ed., by Gibbons and Chakraborti. On p. 290, it states: Wilcoxon (1945) proposed a test where we accept the one-sided location ...
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1answer
74 views

Notation for constant random variables?

Suppose $X$ is a random variable. Now, suppose I want to add a constant random variable to $X$. Should I denote the constant by a lower- or upper-case letter? So $X+A$ or $X+a$?
2
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1answer
44 views

Notation - gradients

I am reading Friedman's paper on stochastic gradient boosting - and saw as per below the following set of formulas. Purely from a notation perspective - why do we write $F(x)$ = $F_{m-1}(x)$ outside ...
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0answers
19 views

Meaning of $\psi$ in regard to $p$-value distributions

In Combining dependent P-values by Kost & McDermott, the notation $\psi$ is used in a way that I am not familiar with. Relevant passge: 2.1. Known Variance. Let ...
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1answer
82 views

About the $X\sim \mathcal{N}$ notation

If a random variable $X$ has mean $\mu_{X}$ and variance $\sigma_{X}^{2}$, and follows a normal distribution, it may be written as $X\sim \mathcal{N}(\mu_{X},\sigma_{X}^{2})$. Suppose $Y$ is also ...
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0answers
42 views

Math notation for bayesian hierarchical models with covariance matrix with LKJ priors

I am fitting a simple hierarchical bayesian gaussian model of the form: $$ Y = b_0 + b_1 X_1 + b_2 X_2 + e $$ $$ b_{0:2} \sim N(\theta_{0:2}, \sigma_{0:2}) $$ $$ \sigma_{0:2} \sim Gamma(.001 , .001) ...
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6answers
652 views

How is the notation $X\sim N(\mu,\sigma^2)$ read?

How is the notation $X\sim N(\mu,\sigma^2)$ read? Is it $X$ follows a normal distribution? Or $X$ is a normal distribution? Or perhaps $X$ is approximately normal.. What if there are several ...
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0answers
1k views

What is the difference between x-bar and X-bar?

I'm reading "Statistics: Principles and Methods" by Johnson and Bhattacharyya (7th edition). I know x-bar is sample mean, mu is population mean, s^2 is sample variance, σ^2 is population variance, s ...
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1answer
24 views

Notation - brackets

How should i interpret the square brackets [] in the third formula per below?
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0answers
22 views

how can I interpret this notation?

I was wonder if anyone could interpret this in words "Under the Gaussian process prior, these functions depend on the model solely through its predictive mean function ...." Thank you in-advance !
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2answers
67 views

Does ARIMA(0,1,11)4 exist?

I have, without luck, searched to find what an ARIMA model that is differenced once, and has two moving average terms (one at lag 1 and one at lag 4) is called. The equation for what I am asking for ...