Questions tagged [intuition]

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

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6answers
2k 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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1answer
9 views

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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2answers
28 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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0answers
10 views

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 ...
2
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0answers
29 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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0answers
16 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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1answer
51 views

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 ...
10
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4answers
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. ...
4
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1answer
81 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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0answers
23 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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1answer
24 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\...
2
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1answer
53 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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0answers
69 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}...
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0answers
14 views

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
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1answer
56 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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0answers
5 views

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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0answers
37 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? ...
2
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1answer
40 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 ...
0
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0answers
23 views

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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0answers
30 views

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
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1answer
24 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 ...
3
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0answers
54 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 ...
3
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1answer
102 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 ...
5
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2answers
189 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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1answer
40 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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0answers
33 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 ...
2
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1answer
81 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 ...
2
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0answers
17 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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1answer
30 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 ...
2
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1answer
84 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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0answers
89 views

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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1answer
101 views

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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0answers
26 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, ...
5
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0answers
55 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 ...
8
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1answer
145 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 &...
7
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2answers
208 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^{-(...
3
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2answers
84 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. ...
4
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2answers
138 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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1answer
20 views

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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0answers
24 views

Conceptual Question about Interactions

I have a question that are conceptual and statistical in nature. It might seem elemental but I am unable to find any clear answers online so I was hoping to find them here! They pertain to ...
2
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1answer
231 views

What is meant by divergence in statistics?

I have learned about the Intuition on the Kullback-Leibler (KL) Divergence as how much a model distribution function differs from the theoretical/true distribution of the data. The two most important ...
1
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1answer
38 views

Is it harder to estimate the variance of a Gaussian compared to its mean?

In various ML talks I keep hearing that variance estimation is harder than mean estimation but I never really get why the above statement is correct. Is there a theoretical argument or a published ...
2
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0answers
33 views

Calculating the standard error for the ratio of 2 random variables?

I have 2 40x10 matrices, $X$ and $Y$. Each row represents a sample, and each column represents a different trial. Its OK to assume that $X$ and $Y$ are random normal variables if that's relevant. I ...
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1answer
96 views

What is intuition behind the product rule of probability and independent events? [duplicate]

I just bumped into a simple question. Let's say I want to compute the probability of taking both Math and Science courses (i.e., $P(M \cap S)$) given this information: Total class size is 10; 7 ...
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0answers
30 views

Applications of the Weibull and Reversed Weibull distribution

I'm trying to get some intuition for the GEV distributions. As I understand, the GEV distributions derive from the limiting maximum distributions, one of which is the Type III distribution, also ...
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1answer
71 views

Intuitive explanation behind the statistical interpretation of regularization

I understand that using regularization is equivalent to finding a MAP estimate. I am wondering why using a Gaussian prior (for example) is better at preventing overfitting than using the uniform prior....
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0answers
40 views

Intution about the memoryless property of geometric distribution [duplicate]

I was watching the video about the memoryless property of geometric distribution. Here is an excerpt from the video. $$\begin{aligned} P(X \geq x+y \mid X \geq x) &=\frac{P(X \geq x+y, X \geq x)}...
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1answer
35 views

A question about the information content in the entropy formula

One intuition in the entropy definition is that there is an inverse relationship between the information content of an event and its probability. This makes sense since learning an event which has a ...
0
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1answer
54 views

Is it taboo to take the standard deviation of a very small list of numbers?

I read through a similar question: Is it meaningful to calculate standard deviation of two numbers? However, this was largely focusing on error bars. If I have five numbers, let's say: ...
3
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1answer
78 views

Question about Instrumental variables, endogeneity, and correlated errors

I have seen his notation to describe the Instrumental Variable framework, and I wish to make sure I understand it. Y is the dependent variable, x is treatment, and z is the instrument: $y = f(x,\...

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