Questions tagged [intuition]

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

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Mean of geometric distribution is odds?

Context: I mean the $P(X=k)=(1-p)^k p$ not the $P(Y=k)=(1-p)^{k-1} p$. Apparently the mean of the 1st kind of geometric is $\frac{1-p}{p}$ instead of $\frac{1}{p}$ for the 2nd kind of geometric. I ...
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1 answer
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What does conditional independence mean semantically?

I've just spent the last 3 hours reading every post, question, Medium article, and textbook entry on conditional independence, and I still don't really understand it. Can somebody explain what it ...
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What exactly does the Box-Cox transformation do to a time series?

If I were to try and rephrase the argument in the original Box-Cox paper in my own words, I would say something like the following: given a model $$ y = x \beta , $$ if the residuals do not appear to ...
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2 votes
1 answer
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Why do we need a smaller sample size to detect a smaller proportion?

The plot below shows the sample size needed to detect a proportion with a precision 0.01 for various true proportions: This assumes an infinite population size, and the confidence intervals are fixed ...
1 vote
0 answers
52 views

Why PCA is invariant under rotation

Lets say that we have a matrix of variables (the columns are variables and rows are the observations) called X whenre X = [x1, x2, ...., xp] where ...
1 vote
0 answers
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Does the number of samples, as opposed to the sample size in each sample, matter for the Central Limit Theorem? [closed]

(1)So here is a formula that describes CLT I found at https://en.wikipedia.org/wiki/Central_limit_theorem. According to the first part of the explanation, n as in Xn describes the number of samples(i....
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1 vote
0 answers
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Why is my intuition about probability in this regard so flawed? [closed]

Take the following example: Take a sample from 100 people and measure their height. Assume that we know that height is approximately normally distributed, with a sample mean of 175 cm and sample ...
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12 votes
5 answers
2k views

What's complicated about regression to the mean?

Note: I am a bit of a novice when it comes to statistics and data analysis. Reading the chapter on regression to the mean in Kahneman's Thinking Fast and Slow, I came across the following passage: ...
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1 vote
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Intuition about the relation between joint distribution, marginal distribution, and conditional distribution

The wording "intuition" might be a bit imprecise. I want to discuss how we visualize in our head going from one to another among the joint PDF, marginal PDF, and conditional PDF. To make the ...
12 votes
5 answers
2k views

Is the exact value of any likelihood meaningless?

While reading about likelihood, I have heard that "the exact value of any likelihood is meaningless" why? So, because of that we may use the likelihood ratio. So, my question is, why the ...
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3 votes
1 answer
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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 ...
1 vote
1 answer
42 views

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
2 answers
319 views

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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1 vote
2 answers
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In a diff-in-diff or regression discontinuity research design, why is it important to describe why the counterfactual is a plausible one?

I've heard it mentioned that in difference-in-differences, regression discontinuity, or even in some other quasi-experimental research designs, that the counterfactual should be explained as a ...
3 votes
1 answer
92 views

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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2 votes
1 answer
55 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 ...
1 vote
0 answers
45 views

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 $\...
0 votes
0 answers
47 views

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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0 votes
2 answers
49 views

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 $\...
0 votes
0 answers
11 views

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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1 vote
0 answers
23 views

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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24 votes
7 answers
3k views

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
1 answer
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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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0 votes
2 answers
133 views

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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0 votes
0 answers
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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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2 votes
0 answers
90 views

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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0 votes
0 answers
20 views

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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1 vote
1 answer
40 views

Pairwise deletion and non-positive definite sample covariance matrix

So I have read that using pairwise deletion can lead to a non-positive definite matrix. However, I tried to find a source which showed this mathematically. Can someone point me to that? My intuition ...
4 votes
1 answer
217 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 ...
0 votes
0 answers
27 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 ...
1 vote
1 answer
125 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
75 views

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
0 answers
98 views

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}...
1 vote
0 answers
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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 ...
1 vote
1 answer
145 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 votes
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
53 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
51 views

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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0 answers
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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 ...
1 vote
1 answer
33 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
59 views

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
118 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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6 votes
2 answers
903 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 ...
0 votes
1 answer
50 views

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
43 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
152 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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