Questions tagged [intuition]

Questions that seek a conceptual or non-mathematical understanding of statistics.

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40 views

Intuitive explanation on “Generalization ” [closed]

I recently worked on Generalization of Gradients. If I'm asked to find Generalization of Gradients or for Dirichlet distribution, etc. I'll do it correctly like a machine. But I didn't understand it. ...
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1answer
31 views

Intuition behind m-out-of-n bootstrap

I am trying to get some intuition on why m-out-of-n bootstrap works but haven't been able to find good explanation. I would really appreciate any input on this. I think I do understand what bootstrap ...
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0answers
21 views

Properties of the diff of a sorted uniformly generated set

I am studying a set of uniformly generated points, more concretely the distance between the points. When the set is unsorted the histrogram shows it is normally distributed and that matches my ...
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7answers
2k views

Intuitive explanation of “Statistical Inference”

What is the cleanest, easiest way to explain someone the concept of Inference? What does it intuitively mean? How would you go to explain it to the layperson, or to a person who has studied a very ...
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0answers
22 views

What are the appropriate ways of performing model selection? [closed]

I am reading up on model selection and ran into some intresting questions that I would like to understand to build intuition on the topic. My questions were: What are the appropriate ways of ...
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1answer
24 views

Intuition behind the use of multiple attention heads

Consider this introduction to attention layers with the main description below. I understand attention layers as learnable soft query retrieval operators that act on a "K-V store" of vectors....
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1answer
22 views

How to Compare Variances?

I have a dataset which contains height and weight variables. The mean and variance for height are 165 cm and 25 cm. The mean and variance for weight are 70 kg and 16 kg. How to compare variances of ...
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0answers
9 views

Beta distribution meaning? [duplicate]

I am trying to understand what is the meaning of Beta distribution. I can try compare it to classical probability of event that when I throw the dice it will be let's say 1, that is 1/6. Btw also try ...
36
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6answers
3k views

Debunking wrong CLT statement

The central limit theorem (CLT) gives some nice properties about converging to a normal distribution. Prior to studying statistics formally, I was under the extremely wrong impression that the CLT ...
0
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1answer
19 views

Intuition behind spectral density of time series

Is there any intuition behind the spectral density $f(\lambda)$ of a time series, where $$ f(\lambda)= \frac{1}{2\pi}\sum_{h=-\infty}^{+\infty}{e^{-ih\lambda}\gamma(h)}, -\infty < \lambda < \...
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0answers
37 views

How to explain a Box Plot?

Assuming that I'm able to augment their knowledge about boxplot I can give the below insights for box plot ...
6
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3answers
240 views

Permutation tests and exchangeability [duplicate]

Permutation tests assume exchangeability of the response/observations under the null hypothesis. In what practical situations is this clearly violated? When is it unproblematic? Edit/additional ...
2
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1answer
79 views

Intuitive explanation of “invariance”

...assuming that I'm able to augment their knowledge about variance in an intuitive fashion Understanding "variance" intuitively and about covariance How would you explain covariance to ...
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3answers
106 views

Foundations behind Linear Regression / Statistical Modelling

I've always struggled with the foundations behind the concept of modelling (and specifically regression) - what is random, what is not, what we are modelling. I think I have a grasp of it - but I'd ...
35
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4answers
2k views

Intuitive explanation of Kolmogorov Smirnov Test

What is the cleanest, easiest way to explain someone the concept of Kolmogorov Smirnov Test? What does it intuitively mean? It's a concept that I have difficulty in articulating - especially when ...
0
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1answer
48 views

Interpretation for changes in a $\chi^2$'s density as $k$ increases

The chi-square's density becomes more regular as $k$ increases: $k=1$ unbounded, convex $k=2$ bounded, convex $k=3$ close to 0 near 0, unbounded positive slope $k=4$ close to 0 near 0, bounded ...
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2answers
62 views

What is an intuitive way for choosing the right Statistical test?

In my Statistics class, we just talked about Statistical tests. So far I’ve been understanding the material, okay, but now I’m very confused. I get that Statistical tests are used in hypothesis ...
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5answers
2k views

Can someone explain the importance of mean stationarity in time series?

In regular regression, the expected value of Y | X is allowed to change. In fact we generally use regression when we want to model this change in conditional mean. I am not understanding why in time ...
6
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2answers
103 views

Intuition for why the (log) partition function matters?

I'm on a quest for the intuition behind the fact that theoretical introductions to approximate inference focus so much on the log partition function. Say we have a regular exponential family $$p(\...
1
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2answers
90 views

Central limit theorem seems counterintuitive given Law of large number

From what I understand, the Central limit theorem says the sample mean is distributed normally when sample number tends to infinity. However, the Law of large number says sample mean converges in ...
10
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2answers
395 views

Intuition behind Box-Cox transform

For features that are heavily skewed, the Transformation technique is useful to stabilize variance, make the data more normal distribution-like, improve the validity of measures of association. I am ...
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0answers
19 views

Intuitive explanation for spline convolution [duplicate]

What is spline convolution intuitively? When should use it? what is the motivation behind it?
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0answers
12 views

Regression using trig-computed terms for non-time series data sets

Follwing up from my recent post: How to construct this "prediction heatmap" assuming OLS (worked out example) , I want to build my intuition around model specification for the classic ...
8
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2answers
124 views

Does this interpretation $\phi'(x)=-x\phi(x)$ of the normal distribution have any significance?

For the standard normal distribution $\phi(x)$, we can see that $\phi'(x)=-x\phi(x)$. Put differently, $\frac{\mathrm{d}\ln(\phi(x))}{\mathrm{d} x}= -x $. I see this as the fall in the value of the ...
3
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0answers
55 views

Intuitively, why is the expectation of the score 0? [duplicate]

Given a probability model $p(x|\theta)$, the score function is typically defined as $\frac{d}{d\theta} \log p(x|\theta)$. The expectation $\mathbb{E}[\frac{d}{d\theta} \log p(X|\theta)]$ is zero ...
0
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1answer
24 views

When is uniform distribution have maximum entropy instead of normal distribution?

As far as I know, when we have just data and no constraints (other than probabilities must add up to 1), the distribution that gives maximum entropy is uniform distribution. But when we know mean and ...
2
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1answer
61 views

Intuition Behind Correlation Function in Kriging Models

I'm thinking and researching extensively to interpret the parameter $\theta$ (activeness parameter) in Gaussian correlation function in a Kriging model, namely as: $$ K(h;\theta)=exp(-h^2/(2\theta^2)) ...
3
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1answer
82 views

Can you explain ANOVA and its assumptions to a beginner?

I was about to start coding up an ANOVA test to study the differences in house prices between neighborhoods. I read that ANOVA is a great way to find out if there is significance difference in nominal ...
4
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1answer
80 views

Why is Kullback Leibler Divergence always positive?

I know there have been mathematical treatments of this question on here. What I'd like help with is my intuitive understanding though. Take the example given on Wikipedia: $$\begin{array}{|c|c|c|c|} \...
5
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4answers
148 views

Why highly correlated means higher variance?

I am reading the book Introduction to Statistical Learning and on page 183, the book states that Since the mean of many highly correlated quantities has higher variance than does the mean of many ...
4
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0answers
44 views

Why are $\mathbb{E}( \ln(x))$ and $\mathbb{E} ( \ln(1 - x))$ reasonable descriptions of knowledge about a beta distribution?

The max entropy philosophy states that given some constraints on the prior, we should choose the prior that is maximum entropy subject to those constraints. I know that the Beta($\alpha, \beta$) is ...
0
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1answer
98 views

How do I interpret mean absolute error (MAE) or mean absolute percentage error (MAPE) in layman words?

For example, I am predicting a score that can have value from 0 to 100. Lets assume MAPE = 10...
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0answers
29 views

How do I interpret RMSE in layman words? [duplicate]

For example, I am predicting a score that can have value from 0 to 100. The RMSE = 10. How ...
2
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1answer
43 views

Can anyone show how the concept of Identifiability is geometrically/intuitively presented?

The motivation for this question comes from the following: When I was studying statistics for the first time long ago, no one presented the mathematical concepts behind linear regression, like the one ...
1
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3answers
66 views

Bayes Theorem: How to get an intuition for it? [duplicate]

I have taken a handful of statistics/ data science-oriented courses. And to this day, I feel like I grasp the underlying concept but I do not comprehend the in-depth understanding. I am asking this ...
1
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1answer
86 views

Intuition behind Weight of Evidence and Information Value formula

In credit scoring models, we use Weight of Evidence to create bins for continuous variables and Information value to filter out important variables. \begin{align} \text{WoE:} \qquad &\ln \frac{\...
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0answers
14 views

An lms estimator that is biased?

We have a free falling body, and its motion has parameters $\theta_0$, $\theta_1$ and $\theta_2$. Its position (in time t) is given by $\theta_0 + \theta_1 * t + \theta_2 * t^2$ The values $\theta_0$...
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2answers
22 views

ANOVA Conceptual understanding [duplicate]

I am trying to understand ANOVA. When we look at the null hypothesis we are trying to make a statement about the means. But what we indeed calculate is the variances, and make statements about the ...
1
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0answers
44 views

Intuitive explanation of Gaussian Process Regression

How would you intuitively explain the idea behind Gaussian Process Regression to someone unfamiliar with stochastic processes? Especially the point where you discuss modeling covariance, choice of ...
0
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0answers
24 views

What is the math behind predict() in e1071 for SVM? [duplicate]

I have no math or computer science training. When I run predict(svm,data,type="class") R spits out a prediction of 1 or 0 for each row of data. What is it doing ...
0
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1answer
64 views

The meaning of margin of error in a real life example?

I guess I almost understand the concept of confidence intervals and confidence levels with two real life examples. I still have some difficulties to understand "margin of error". Image that, in a ...
3
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3answers
146 views

How to construct this “prediction heatmap” assuming OLS (worked out example)

The following visual certainly delivers in terms of eye candy: There was no details on the model specification, but let's just assume its something like: $$price = \beta_{0} + \beta_{1} x_{surface} +...
0
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0answers
14 views

Outside of making machine learning work better, what do z-scores do and what do they mean intuitively?

My Own Research: I've read all the Wikipedia articles I could find on z-score and standardizing variables. I've also searched Cross validated using terms like "intuitive meaning of z-score" and "Why ...
1
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0answers
18 views

What is repetition in ANOVA?

I came across an explanation here, which states It’s whether you are replicating (i.e. duplicating) your test(s) with multiple groups. With a two way ANOVA with replication , you have two groups and ...
1
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0answers
34 views

Why would a Bayesian want to maximize expectation? [closed]

A Frequentist interprets probability as an estimate of how frequent an event is giving that we can repeat the experiment many times. It is natural for them to try to maximize the expected utility ...
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0answers
20 views

Connection between the two expressions of fisher information

I've seen two major expressions for the fisher information: $$I_{\mathbf{X}}(\theta) = \mathbb{V}ar(\ell'(\theta|\mathbf{X}))$$ where $\ell(\theta)$ is the log-likelihood function for $\mathbf{X}$...
1
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1answer
50 views

In the context of likelihood, why is the log-density considered to be more “natural” than the density?

Working through some notes and it says that one of the reasons for using the log-likelihood rather than the likelihood is that the "log-likelihood is a the more "natural" and relevant quantity" in ...
3
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2answers
48 views

Understanding sufficient statistics geometrically

Consider the distribution $\mathcal{P} = \mathcal{N}(\mu, 1)$, where the variance is known but the mean is unknown. Let $X_1,X_2\sim P$ i.i.d. In this case $T = X_1+X_2$ is a sufficient statistic. I ...
9
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2answers
2k views

What's the intitution behind contrastive learning or approach?

Maybe a noobs query, but recently I have seen a surge of papers w.r.t contrastive learning (a subset of semi-supervised learning). Some of the prominent and recent research papers which I read, which ...
1
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0answers
28 views

Intuition behind the coordinate descent convergence

I am looking at the page 6 of the slides about Coordinate Descent of Geoff Gordon and Ryan Tibshirani at the Carnegie Mellon University. They are dealing with the the Coordinate Descent algorithm ...

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