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Questions tagged [definition]

This tag indicates questions about definitions of statistical terms. Use a more general tag [terminology] for questions on statistical parlance that are not specifically about definitions.

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1answer
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Are the law of iterated expectation and the law of total expectations the same?

On the Wikipedia page of the Law of total expectations it is said that The proposition in probability theory known as the law of total expectation, the law of iterated expectations, the tower rule, ...
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0answers
12 views

Geisser's definition of nonstochastic prediction

Does anyone have Geisser, 1993, "Predictive Inference: An Introduction." Chap- man and Hall, London. MR1252174? I am interested in the definition on page 31 for "nonstochastic prediction," but unable ...
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0answers
33 views

How can you say that a set of probability distributions have the same distribution without also saying that their parameters are the same? [duplicate]

Suppose that I want to talk about a couple of sets of probability distributions. The first set is a collection of gamma distributions that all have different parameters and the second set is a ...
2
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2answers
103 views

Why is the risk equal to the empirical risk when taking the expectation over the samples?

From Understanding Machine Learning: From theory to algorithms: Let $S$ be a set of $m$ samples from a set $Z$ and $w^*$ be an arbitrary vector. Then $\Bbb E_{S \text{ ~ } D^m}[L_S(w^*)] = L_D(w^*)...
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0answers
6 views

Definition for lifted inference

What is the definition for lifted inference? As per my current knowledge, lifted inference is an inference technique that uses the rules of first-order logic. Is it true?
2
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1answer
71 views

What does it mean to generate a random variable from a distribution when random variable is a function?

I am looking at a reference for sampling from a distribution, and the first step of the so-called algorithm states:http://www.columbia.edu/~ks20/4703-Sigman/4703-07-Notes-ARM.pdf Generate a random ...
0
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1answer
20 views

Noise and Outliers in DBSCAN

Why are noise and outliers treated as the same concept in DBSCAN (density-based spatial clustering of applications with noise)?
3
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1answer
53 views

How to call this frequentist interval estimate that is neither a prediction interval nor a confidence interval

This question is inspired by Confidence Interval on a random quantity?. That question introduces an interesting concept for a type of interval that is neither a prediction nor a confidence interval (...
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0answers
11 views

definition of integrated- and- exponential autocorrelation time

I understand them (to an extent) both seperately, but i was reviewing my notes from class and my verbal definition is effectively stating the same thing in different words. I have: integrated: ...
1
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2answers
43 views

What are the predictor variables in a neural network?

In a linear regression model, the predictor or independent (random) variables or regressors are often denoted by $X$. The related Wikipedia article does, IMHO, a good job at introducing linear ...
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3answers
70 views

What comes after the geometric mean?

The geometric mean is a multiplicative alternative to the arithmetic mean, which we could call additive mean, thereby calling the geometric mean multiplicative mean. My question is the following: what ...
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2answers
25 views

What does it mean to condition on a variable B in causal models?

Given the causal model $A \rightarrow B \rightarrow C$, then $A$ and $C$ are independent conditioned on $B$. What does this mean?
0
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1answer
25 views

What does it mean for a variable to block a path between other two variables?

What does it mean for a variable $Z$ to "block" the path between variables $X$ and $Y$ in a causal model? What is the formal definition of a "block", and how can I intuitively understand this concept? ...
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1answer
30 views

What is the definition of the geometric mean of a random variable?

I am not sure if my question is a bit stupid but I haven't found any definition online although searching for hours; So here is the thing: The geometric mean(GM) of an (iid) sample drawn from some ...
3
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0answers
41 views

P-value: Fisherian vs. contemporary frequentist definitions

I am trying to see if I understand the definition of $p$-value as used by Sir R. A. Fisher and the one used today by frequentist statisticians (not sure how to call it better). $p$-value according ...
5
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3answers
823 views

What is the precise definition of “performance” in machine learning?

In machine learning, people usually refer to the "performance of a model" or "performance of an optimizer". What is the exact definition of "performance"? What would be the "performance of an ...
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0answers
24 views

Dot subscript summation notation used in design of experiments

Context I couldn't find a clear explanation of this on this site, and thought that it might be of use. I have provided part of the answer, which anyone is welcome to build from. I'm not sure how to ...
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0answers
18 views

Example of a problem with structured output labels

I'm studying SSVM (Structured SVMs). On my book is stated that Structured SVM is an extension of the SVM, in which Each sample is assigned to a structured output label z ∈ K, e.g. partitions, ...
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0answers
9 views

Definition of a 'design adaptive' fit?

When studying non-parametric regression, I've been told that local linear fitting is often better than local constant fitting at the job of estimating regression functions because local linear fitting ...
2
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1answer
48 views

Typo or change of interpretation in loss function in the Bayesian Choice textbook?

In the proof of the following proposition, the posterior loss depends on a prior distribution $\pi$, while in the derivation it depends on the parameter $\theta$. Should the posterior loss function be ...
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2answers
225 views

What is the name for the complement of accuracy?

I have a metric that is defined as $1 - Accuracy$ and I need a name for it. Is there a scientific name for the complement of accuracy?
0
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1answer
22 views

What is the definition of layer in neural network?

What is the precise definition of layer in neural network? Are things like concatenate functions, activations, batch normalizations, skip connections considered as layers?
0
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1answer
25 views

Name of functional part of a pdf after removing proportionality constants?

Let $f(x;\theta)$ be probability density function. Suppose that this pdf contains a proportionality constant $c$, so that $f(x;\theta) = c\cdot g(x;\theta)$, where $g$ is an integrable function. Is ...
0
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1answer
35 views

Frequentist definition of probability and prediction?

The frequentist definition of probability states that: The probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to ...
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1answer
83 views

VC dimension of sine family is infinite?

From what I understand, the VC dimension of an hypothesis class is given by the maximum number of points in general position (or random) on the domain space that can be arbitrarily labeled by the ...
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1answer
97 views

The definitions of estimator and estimate

This example demonstrates the difference between a theoretical observation and a realized observation. A theoretical observation is a random variable with a probability distribution, while its ...
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1answer
25 views

Sampling from a finite sequence without replacement yields exchangeable sequences?

I have read (and re-read) the wikipedia article on Exchangeability https://en.wikipedia.org/wiki/Exchangeable_random_variables . The disconnect for me is that : after having sampled without ...
0
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1answer
39 views

What's the difference between outlier analysis and clustering?

What's the difference between outlier analysis and clustering? When clustering is done isn't that outliers (if exist) are also found? Sorry for this simple question.
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2answers
238 views

Is there a difference between Bayesian and Classical sufficiency?

The title pretty much says it all. I wonder whether there is any difference in the way Bayesians understand sufficiency vs. the way orthodox statistics understands sufficiency, or are they equivalent? ...
15
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1answer
1k views

Is supervised learning a subset of reinforcement learning?

It seems like the definition of supervised learning is a subset of reinforcement learning, with a particular type of reward function that is based on labelled data (as opposed to other information in ...
15
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3answers
2k views

Is there more than one “median” formula?

In my work, when individuals refer to the "mean" value of a data set, they're typically referring to the arithmetic mean (i.e. "average", or "expected value"). If I provided the geometric mean, people ...
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0answers
59 views

monotonic vs non monotonic models

I am reading this paper and it mentions monotonic and non monotonic functions. I only only what is monotonic and non monotonic function is, I do not really understand it in the scope of their ...
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0answers
62 views

Equivalence of sufficient statistics definitions [duplicate]

I'm reading about sufficient statistics, and have come across two definitions which seems unrelated, and I'm trying to understand their connection. The first definition is from Wikipedia A ...
1
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1answer
359 views

What is the difference between Cronbach's alpha and standardized Cronbach's alpha?

I found in the wiki article a definition of a standardized Cronbach's alpha but nothing is said what it is and about its relation to the original Cronbach's alpha: I found at What is Cronbach's ...
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0answers
51 views

Probit model specification

im writing a paper that involves using a probit regression, would this be a correct summary of what a probt model is and how it works?: "the probit specification is a binary-dependent model that ...
0
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1answer
25 views

Definition of forecasting period in time series

I am new to forecasting time series. The team that I am working with keep referring to forecasting period as lag. For example we have 20 month of data and we would like to create 5 month forecast. Is ...
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1answer
525 views

Size of the Hypothesis Space

(I'm asking the same question as the linked one, I simply don't have enough reputation to comment yet, but hopefully, this one will more clearly explain what me and the other asker both mean) Let's ...
1
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1answer
640 views

What's the definition of “Dynamic Regression Models”?

I am trying to learn about Dynamic Regression models. However, the sources on the topic is (relatively) few compared to other TS topics, and so I cannot really get a grasp of where to start. I really ...
2
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3answers
139 views

I need help clarifying the term forecast interval

I am reading Introduction to Time Series Analysis and Forecasting by Douglas Montgomery et al. They describe the term forecast interval as: The forecast interval is the frequency with which new ...
2
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0answers
18 views

Definition of stable distribution

In some places, I find the following definition of stable distribution: A distribution is said to be stable if a linear combination of two independent random variables with this distribution has ...
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0answers
35 views

Does a time series start at $t=0$?

I am a beginner in Time Series Analysis and I am reading something about the most simple processes like AR and MA. So far I understood that one wants to have the following result: The MA($\infty$)-...
8
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1answer
89 views

Alternate (?) definition of sample variance [duplicate]

The variance of a sample can be defined as $$s^2 = \frac{1}{2}\frac{1}{n(n-1)}\sum_{i}\sum_{j\ne i}\left(x_i - x_j\right)^2$$ Apart from the factor of $1/2$, this can be paraphrased verbally as ...
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3answers
436 views

What is the precise definition of unsupervised learning?

Let's look at a special case: Generative Adversarial Networks (GANs). (For those who don't know what a GAN is: for this purpose they are two neural networks that are trained using user generated ...
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0answers
45 views

question about correct interpretation of sufficiency [closed]

I am currently trying to understand the concept of sufficiency and I am trying to create my own example. Assume that we have a statistic$$T:(\mathscr X, \mathscr A, \mathscr P) \to (\mathbb{R}^2, B^2)...
1
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1answer
190 views

What does linear time series refer to?

In some papers or documents, "linear times series" seems to refer to a time series that can be modeled as a linear AR (auto-regressive) model. In other places, "linear time series" seems to refer to ...
8
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2answers
218 views

What is a probability distribution? [duplicate]

This is a very basic question, and maybe a silly one, but I'm struggling to understand the actual definition of a probability distribution. In Wasserman's "All of Statistics", for example, he says ...
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1answer
2k views
3
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1answer
432 views

What are soft policies in reinforcement learning?

What are soft policies in reinforcement learning? Do soft policies use soft-max function as $\pi(s, a)$ instead of deterministic policies?
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3answers
134 views

“Pragmatic” trials: what are they?

On twitter, a trialist Stuart Nicholls critiqued a recently published study by saying: Further to the very interesting paper by Dal-Re they flag several examples that question usage of the term ...
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1answer
31 views

Unsure about result given in lecture

I'm looking through my notes and something my lecture said seems off, just want to clarify. "Let $Z_1,\ldots, Z_n$ be iid N(0,1) random variables and let $\overline{Z}$ be their average. Then $\...