Notation refers to questions about statistical and mathematical notation.

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Is my notation here reasonable? (basic probability)

Disclaimer: this is a homework problem, but I'm not asking for the answer I already have it. What I'm wondering is if a specific way of writing part of the problem is correct or not. I have other ways ...
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0answers
15 views

What description fits this this learning scenario, is this a form of active learning?

A system is involved in dialog with a human partner. The system has a model of a problem domain and knows mappings between words an concepts. The human has its own model of the problem domain and ...
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1answer
81 views

Is it okay to write the square of expectation of a random variable $X$ as $\mathbb{E}^2(X)$?

Is this notation accepted when I write $\text{Var}(X)=\mathbb{E}(X^2)-\mathbb{E}^2(X)$?
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9 views

Scaling parameters to lie in unit hypercube — how to understand this notation?

I am attempting to emulate a simulation in a paper I am reading. The model includes two parameters $\theta_1,\theta_2$. These parameters are scaled to lie in the unit hypercube. That is, where the ...
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1answer
32 views

Question on Kernel function notation and rationale

Say I have the following kernel function: $$K(u) = \frac{15}{16}(1-u^2)^2\ 1_{(|u|\leq1)}$$ As I understand, $u$ denotes some absolute distance parameter for each observation $x_i$ from a given ...
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29 views

What does $S$ mean in this standard deviation estimate

What does $S$ mean in estimates like $$s^2 = \frac{S(x_1^2)}{n} - \left(\frac{S(x_1)}{n}\right)^2 = \frac{S(x_1^2)}{n} - \frac{S(x_1^2)}{n} - 2\frac{S(x_1 x_2)}{n^2}$$ (for context look "The probable ...
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1answer
32 views

Understanding Matrix and Vector Notation

I am trying to understand the Matrix and Vector Notations on page 2 here: (the page is also pasted below, to make it easier to explain the problem). Problem: For equation (2), I think it should be $\...
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9 views

Standard notation to indicate certain distributions

On a figure that I wish to annotate to indicate what prior distributions were used in an analysis, I need a shorter way of indicating a $\text{Cauchy}(0, \sigma)$ distribution and saving just 3 or 4 ...
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1answer
35 views

Why is the expected value of y written as E(y|x)?

The expected value of the simple linear regression model $y = \beta_0 + \beta_1x + \epsilon$ is typically written as $E(y|x) = \beta_0 + \beta_1x$. Why is it written as $E(y|x)$ instead of just $E(y)$?...
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1answer
19 views

Numbers in reporting one way ANOVA

In reporting data for a one way ANOVA what do all the numbers in the following stand for? $F (1, 24) = 44.4$, $p < .01$.
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29 views

Name of maximum of integrated likelihood?

What do people call the maximum of the integrated likelihood function (i.e. marginal likelihood function)? This is, suppose that $x_i\stackrel{iid}{\sim} f(\vert\theta)$, $\theta=(\alpha,\beta)$, and ...
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1answer
44 views

What is the meaning of the notation $P_\theta()$, where a probability has a subscript Greek letter?

What does theta subscript imply in e.g. this case: $$ P_\theta(T(x)=t) = 0 $$
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0answers
32 views

Ratio symbol in multiple regression

I am running a multiple regression of the following form: Ratio Y = X0 + Ratio X1 + Ratio X2 I was wondering if there would be a symbol I could use for the 'Ratio'? I found a similar type of ...
13
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3answers
1k views

In statistics, should I assume $\log$ to mean $\log_{10}$ or the natural logarithm $\ln$?

I'm studying statistics and often come across formulae containing the log and I'm always confused if I should interpret that as the standard meaning of ...
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1answer
25 views

What does the notation 1{T = 1} mean?

Here's a screenshot: This is from Evaluating Continuous Training Programs Using Generalized Propensity Scores by Jochen Cluve, Hilmar Schneider, Arne Ulendorff and Zhong Zhao. I understand from the ...
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0answers
96 views

Katz Backoff help calculating alpha

$Pkatz(z|x,y) =$ $P'(z|x,y), if C(x,y,z) > 0$ $α(x,y)Pkatz(z|y), else if C(x,y) > 0$ $P'(z), otherwise.$ $Pkatz(z|y) =$ $P'(z|y),ifC(y,z)>0$ $α(y)P' (z), otherwise.$ $$P'(...
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1answer
76 views

Transpose or lack of transpose in the $\hat y=X\hat \beta$ regression equation

$$\large \hat y = X\,\hat\beta \tag 1$$ seems to be (?) the most commonly encountered expression of the ordinary least square projection. The actual values of the "dependent" variable differ from the ...
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32 views

Translating lmer syntax with fixed effects, covariate and random intercepts in a “conventional” or standardised way

I have the following lmer() syntax: lmer(Y ~ A*B*C + COV + A:COV + B:COV + C:COV + (1|A:BLOCK)) where ...
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0answers
18 views

Problems in notations in a paper on Bayesian space-time models

Suppose I have been given some process $Y$. Let $Y(s,t)$ denote the value of process at location $s$ and time $t$. For my experiment, I consider a model described as - $$Y(s,t) = \mu(s) + M(t;\beta(s)...
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1answer
27 views

Dummy variable notation

Consider the following linear regression model that only consists of dummy variables:$$Y_{i}=\beta_{0}+\beta_{1}D_{1i}+\beta_{2}D_{2i}+\epsilon_{i}$$ whereby $i$ denotes individual, $D_{1i}$ is an ...
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1answer
28 views

Meaning of “T-vector of time series values”?

I am currently studying a paper on Hierarchical Bayesian space-time models. In that, we have denoted $Y(s,t)$ to be the process of interest ate location $s$ and time $t$ in a gridded space-time. $Y(s, ...
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1answer
28 views

Terminology: Vector, attributes, and matrices in a dataset

I am confused about the terms "vectors", "attributes", and "matrix" when applied to a dataset. I know that attributes are the features or columns of the dataset, and the matrix is $N \times M$ data ...
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1answer
34 views

What do the angular parentheses in $\langle g_n \rangle^2$ mean?

I am reading this paper. At the first part it says $\langle g_n \rangle=0$ and $\langle g_{n} \rangle ^2=1$. I know that $\langle x \rangle$ is used in physics to refer to the mean. So, the second ...
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1answer
48 views

Why is F used for an unspecified distribution?

I'm taking a linear regression course in university right now, and my professor often uses the notation F to refer to a generic, unspecified distribution with the given mean and variance. For example, ...
5
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1answer
289 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 ...
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2answers
132 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 ...
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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 $x_i$...
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0answers
18 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 ...
2
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1answer
41 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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14 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 ...
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1answer
23 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
34 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
81 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 ...
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21 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 ...
5
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91 views

Higher-order cumulant and moment names beyond variance, skewness and kurtosis

In physics or mathematical mechanics, starting from position $x(t)$, one obtains rates of change via derivatives with respect to time: velocity, acceleration, jerk, jounce (4th order). Some have ...
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1answer
57 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
121 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
101 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
22 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
27 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
36 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 $^{T}$....
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2answers
217 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 ...
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2answers
342 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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1answer
58 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
93 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
29 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
40 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
143 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?
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1answer
175 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
89 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 ...