Questions tagged [intuition]

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

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What is the intuition behind the odds scale?

What is an intuitive explanation of the odds scale? In a logistic regression such as $$logit(p) = \beta_0 + \beta_1 x$$ we often interpret $\beta_1$ by looking at the odds ratio, $e^{\beta_1}$, which ...
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1 vote
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MLE of the Uniform Distribution

In a uniform distribution where $0\leq X \leq \theta$, the pdf is represented as $f(X|\theta) = \frac{1}{\theta}I(0\leq X \leq \theta)$, and the likelihood is $L(\theta) = \prod\frac{1}{\theta}I(0\leq ...
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4 votes
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Intuition for why mean of lognormal distribution depends on variance of normally distributed rv

Let $X\sim\mathcal{N}(\mu,\sigma^2)$, which is a normal distribution. Then, $\text{exp}(X)\sim\text{Lognormal}(\mu,\sigma^2)$, and its mean is $$ \mathbb{E}[\text{exp}(X)]=\text{exp}\left(\mu+\dfrac{\...
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Intuitive effect size (and CI) for one-way comparison of group means?

I'm a big fan of common language effect sizes (e.g. McGraw and Wong's CL or Cohen's U3 - "what proportion of group 1 are higher than the average for group 2"). I've been scrabbling around ...
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Why is each observation in a sample considered a random variable in linear regression?

I have the following excerpt in my statistics textbook: I am confused by the sentence: "Another way statisticians treat this model is that, assume $X_1...X_n$ are random variables, we make ...
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1 answer
38 views

Why does $\underset{\theta}{\arg\max }p_{\text{model}}(X;{\theta}) =\underset{\theta}{\arg\max} \prod_{i=1}^{m}p_{\text{model}}({x}^{(i)} ;\theta)$?

We have seen some definitions of common estimators and analyzed their properties. But where did these estimators come from? Rather than guessing that some function might make a good estimator and then ...
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Intuition for bandwidth and degrees of freedom in kernel smoothers

For Kernel smoothers such as local polynomial regression smoothers (the Nadaraya-Watson smoother), we consider $y = m(x) + \epsilon$, for $m(x)$ some smooth function we are trying to estimate and $\...
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Can you explain LINEAR in BLUE?

I have hard time understanding the LINEAR part. Found something like this: Linear property of OLS estimator means that OLS belongs to that class of estimators, which are linear in Y, the dependent ...
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2 answers
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Estimated vs. true expected value in $\chi^2$ test of independence of two categorical variables

Consider a $\chi^2$ test of independence of two categorical variables. In the test statistic, we have elements of the form $$ \frac{(\text{observed}_i-\text{expected}_i)^2}{\text{expected}_i}, $$ or $\...
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Pearson correlation coefficient as a measure of similarity between vectors? [duplicate]

I'm trying to understand, in layman's terms, what it is that pearson correlation coefficient is actually measuring and how it's used as a measure of similarity between two vectors. I don't have much ...
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Intuition Maximum likelihood [duplicate]

Can someone describe in simple words what the Intuition behind maximum likelihood estimation is and why it is so commonly used in statistics? Certainly, there are many other ways to estimate ...
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7 answers
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Explain in layperson's terms why predictive models aren't causally interpretable

Imagine that you are asked to infer some causal effect -- a change in an outcome $y$ in response to some variable $x$. But, the person asking for this directs you to use a predictive model to do so. ...
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1 vote
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Two basic questions about icp (iterative closest point) algorithm

I am trying to learn shape analysis and a part is learning icp. I have many confusions but for now I have two basic questions: Does the point clouds need to have the same number of points for icp? ...
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2 answers
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In permutation test, why do we take the proportion of sampled permutations with value equal or larger than the observed value?

The tutorial I followed explains permutation testing in an intuitive way. However, it has confused me in one specific part. Why do we take as p-value the proportion/probability of permutation with ...
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  • 101
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Intuition underyling kinds of time series that are typically additive or typically multiplicative with examples

What is the intuition underyling the kinds of time series that are typically additive or typically multiplicative? From what I understand, additive time series are such that variations on the trend ...
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Why do we try to "Reproduce" Hilbert Spaces in Statistics?

I am trying to better understand why people are interested in "reproducing" Hilbert Spaces in Statistics and Machine Learning. I (think) understand the general idea behind Hilbert Spaces. ...
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Relation between the lattice points in ROC plot and different pairs of positive and negative classes

Suppose you have a classification problem and you get the following scores from your hypothesis: \begin{bmatrix} 0.87 & 0.30 & 0.40 & 0.10 & 0.23 & 0.70 & 0.90 & 0.60 \end{...
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1 vote
1 answer
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Practical consequences of wrong interpretation of confidence intervals

Can you give me a simple (but preferably common) example (or R/Python simulation) of what are practical consequences of wrong interpretation of frequentist confidence intervals? Especially when they ...
11 votes
4 answers
1k views

What is an intuitive interpretation for the softmax transformation?

A recent question on this site asked about the intuition of softmax regression. This has inspired me to ask a corresponding question about the intuitive meaning of the softmax transformation itself. ...
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4 votes
1 answer
144 views

Intuition for Wilks' theorem

I'm trying to wrap my head around why it is intuitive that (under certain conditions) the likelihood ratio statistic follows a chi-squared distribution, asymptotically. I've looked at the excellent ...
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0 answers
26 views

Different way to do PCA: overall comparison

Given a dataset PCA can be performed via 3 ways: Eigenvalue decomposition Singular value decomposition Non-linear iterative partial least-squares algorithm Can anyone shed light on comparative study ...
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1 vote
1 answer
69 views

Understanding numerical example of expectation maximization

I was trying to understand Expectation maximization algorithm. This is how it is defined in Andrew Ng's Stanford CS229 course: $$ \text{Repeat until convergence \{}\quad\quad\quad\quad\quad\quad\...
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2 votes
1 answer
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What does correlation formula really tell you?

The formula for correlation coefficient is as follows: $$\begin{align}\mathrm{corr} \left(\vec x, \vec y\right) = \frac{1}{n} \sum_{i=1}^n \frac{\left(x_i-\bar x\right)}{\sigma_x} \cdot \frac{\left(...
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2 votes
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What is the space that a class of probability distributions spans when T is a complete sufficient statistic?

There are a few good posts/notes (see here, and here) giving high level geometric intuition of a complete statistic ($E_{T}[g(T); \theta] = 0 \Rightarrow P(g(T)=0; \theta) = 1 \text{ almost everywhere}...
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An Intuitive Explanation of Multifractality in Financial Time Series

Can anyone please give an intuitive explanation of multifractality in financial time series? Most definitions I came across are either purely mathematical or not in relation to finance. As for the ...
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1 vote
1 answer
114 views

Central Limit Theorem - intuitive explanation without deep math [duplicate]

The Central Limit Theorem says that the distribution of the sample mean is approximately normal. Is there any intuitive explanation for why this should be so? I know it can be proven with deep math, ...
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0 answers
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Per-variable $p$-value in MLR and $p$-value in SLR

Suppose I fit a linear model Y ~ X1 + X2, and the output looks like ...
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1 vote
0 answers
48 views

Why to calculate $\mathbf{weighted}$ average of the leaf node impurities in decision trees? Why not to just add entropies up without weights?

In decision trees why do we calculate weighted average of entropies of each leaf when we calculate the entropy of target variable given some feature? The question is: "Why is it weighted average? ...
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2 votes
1 answer
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number and size of eigenvectors in PCA

As I understand, the size of eigenvector produced in PCA should be min{n,N}, where N=number of samples and n=dimension of each sample (Right?). However, I have seen in couple of cases that this size ...
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Intuitive explanation of Choquet Integral for data aggregation

I've recently stumbled upon this python package that implements Choquet integral as a way of aggregating data. Does anyone have an intuitive way of explaining how does this integral work in this case?
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Intuition for correlation of N≥3 dimensional Normal distribution

What is an intuitive way to think about the covariance matrix in an N≥3 dimensional Normal distribution? In two dimensions the covariance matrix can be visualized by plotting a region of constant ...
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1 vote
1 answer
32 views

Intuition: Variance of the sum of R.V's and correlation

I have many questions that seems basic to me but I just cannot wrap my head around it. Say we simulate 100 R.Vs that comes from a symmetric distribution with mean 0 $(X)$. Say we build another random ...
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3 votes
0 answers
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Relation between variance, square difference and CLT

NEW EDIT TO CLARIFY THE QUESTION My initial question was about why square difference was used instead of absolute value in the formula of the variance... But I ...
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3 votes
1 answer
110 views

How to explain intuitively to a lay audience that the variance is an unbiased estimator?

I have data for the concentration of several chemicals in the milk of 10000 cows and have to explain to policymakers and the lay public (i.e. people with no or limited knowledge of statistics) that ...
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5 votes
2 answers
492 views

Intuition for why LDA is a special case of naive Bayes

The naive Bayes classifier assumes the regressors to be mutually independent, while linear discriminant analysis (LDA) allows them to be correlated. James et al. "An Introduction to Statistical ...
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0 votes
1 answer
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Understanding the Importance of "Sufficiency" within Statistics

I am trying to better understand what it means to be a "sufficient statistic". "In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown ...
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0 votes
0 answers
37 views

How do total rewards considered in reinforcement learning setting?

I am new to reinforcement learning and struggling to understand the basic concept of how the reward is calculated. Let's say I have 10 users. At each time step, different news articles are recommended ...
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2 votes
1 answer
119 views

Empirical Implications of Unbiased Estimators

I am familiar with the layperson explanation of an unbiased estimator as follows: if we repeat an experiment under identical conditions many times, the average value of the estimate will be close to ...
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2 votes
0 answers
19 views

How would you explain inference conditional on cross-sectional fixed effects to a layman?

The goal is to infer $\partial y / \partial x$, $x \in \mathbf{X}$. You observe individuals $i$ over time $t$. The model is $$ y_{it} = \mathbf{X}_{it}\beta + \epsilon_{it} $$ You can rewrite $$ \...
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1 vote
1 answer
31 views

Intuition for hypergeometric variance?

I'm trying to learn the major facts about a bunch of probability distributions, hypergeometric included. I can use the commonalities between it and a binomial to my advantage for thinking through some ...
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3 votes
1 answer
166 views

What's the intuition behind the canonical link function in GLM?

I have already read the answer from What is the difference between a “link function” and a “canonical link function” for GLM but I think my question is different from this one. I am watching the MIT ...
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0 answers
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What causes probability distributions to equalize?

To my understanding: Flipping a coin has a discrete 1/2 probability to be heads or tails, and every iteration of that trial resets the probability back to 1/2. So, it could be heads every time, or, ...
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1 vote
1 answer
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Understanding "Kalman Filter" intuitively

What is the cleanest, easiest way to explain to someone the concept of "Kalman Filter"? What does it intuitively mean? It's a concept that I have difficulty articulating - especially when ...
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  • 2,391
0 votes
0 answers
33 views

split in linear in multi-head attention

i just learned about transformer and until today i still got confused about somethings. after reading this article one and two there are 2 things i dont understand if in the case is 8 head attention, ...
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6 votes
0 answers
66 views

Explaining conditioning number in statistics to non-statisticians

I work these days as a statistician and a lot of what I do is evaluating design of experiments; I started this job less than a year ago, after getting a PhD in mathematical statistics. I remember once ...
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8 votes
1 answer
273 views

Definition of heavy-tailed distribution

I'm reading about heavy-tailed distributions, the definition states that: The distribution of a real-valued random variable $X$ is said to have a heavy right tail if the probabilities $\mathbb{P}(X &...
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7 votes
2 answers
294 views

Intuition behind Weibull distribution?

I don't understand the physical meaning of Weibull distribution's $k$ parameter. Here is a simplified formula of cumulative probability function of Weibull in the simplest form: $$p(\xi \geq x) = e^{-(...
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3 votes
2 answers
138 views

Intuition behind SEM latent variables not being actual variables

There are essentially two ways, to my knowledge, to put together a number of numerical items that are all meant to quantify one abstract notion. One can average the items and create a composite score. ...
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6 votes
4 answers
238 views

What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadditivity

In a business situation, management keeps a reserve of money for a 'rainy day' just in case costs are more than expected. The 90th percentile ($Q_{90}$ in the following) might be an indicator of how ...
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1 vote
1 answer
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Which of these two experiment designs converges faster?

This is an abstract question, an attempt at roughly heuristicking an answer that would otherwise take significant cost and data to answer. If the "fuzziness" of the question makes it a bad ...
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