# Questions tagged [intuition]

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

254 questions
Filter by
Sorted by
Tagged with
533k views

### What is the meaning of p values and t values in statistical tests?

After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests. It ...
• 4,206
847k views

### Making sense of principal component analysis, eigenvectors & eigenvalues

In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues. I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like ...
• 12.9k
187k views

### How to understand degrees of freedom?

From Wikipedia, there are three interpretations of the degrees of freedom of a statistic: In statistics, the number of degrees of freedom is the number of values in the final calculation of a ...
• 18.3k
22k views

### What is meant by a "random variable"?

What do they mean when they say "random variable"?
• 2,108
73k views

### Maximum Likelihood Estimation (MLE) in layman terms

Could anyone explain to me in detail about maximum likelihood estimation (MLE) in layman's terms? I would like to know the underlying concept before going into mathematical derivation or equation.
• 1,579
19k views

• 2,087
51k views

### Cross-Validation in plain english?

How would you describe cross-validation to someone without a data analysis background?
• 12.1k
4k views

### Statistical interpretation of Maximum Entropy Distribution

I have used the principle of maximum entropy to justify the use of several distributions in various settings; however, I have yet to be able to formulate a statistical, as opposed to information-...
• 301
25k views

### Intuitive explanation of the bias-variance tradeoff?

I am looking for an intuitive explanation of the bias-variance tradeoff, both in general and specifically in the context of linear regression.
• 5,421
5k 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 ...
• 35.7k
38k views

### What is the difference between finite and infinite variance

What is the difference between finite and infinite variance ? My stats knowledge is rather basic; Wikipedia / Google wasn't much help here.
114k views

### Difference between standard error and standard deviation

I'm struggling to understand the difference between the standard error and the standard deviation. How are they different and why do you need to measure the standard error?
• 1,243
37k views

### Can you explain Parzen window (kernel) density estimation in layman's terms?

Parzen window density estimation is described as $$p(x)=\frac{1}{n}\sum_{i=1}^{n} \frac{1}{h^2} \phi \left(\frac{x_i - x}{h} \right)$$ where $n$ is number of elements in the vector, $x$ is a ...
• 1,528
11k views

### Why does shrinkage work?

In order to solve problems of model selection, a number of methods (LASSO, ridge regression, etc.) will shrink the coefficients of predictor variables towards zero. I am looking for an intuitive ...
44k views

### What is the role of the logarithm in Shannon's entropy?

Shannon's entropy is the negative of the sum of the probabilities of each outcome multiplied by the logarithm of probabilities for each outcome. What purpose does the logarithm serve in this equation? ...
• 2,503
21k views

### What is the intuition behind SVD?

I have read about singular value decomposition (SVD). In almost all textbooks it is mentioned that it factorizes the matrix into three matrices with given specification. But what is the intuition ...
• 1,199
10k views

### What kind of information is Fisher information?

Suppose we have a random variable $X \sim f(x|\theta)$. If $\theta_0$ were the true parameter, the the likelihood function should be maximized and the derivative equal to zero. This is the basic ...
• 3,823
55k views

### Intuitive explanation of unit root

How would you explain intuitively what is a unit root, in the context of the unit root test? I'm thinking in ways of explaining much like I've founded in this question. The case with unit root is ...
• 2,012
181k views

### How would you explain Markov Chain Monte Carlo (MCMC) to a layperson?

Maybe the concept, why it's used, and an example.
• 9,492
46k views

### Why do we need sigma-algebras to define probability spaces?

We have a random experiment with different outcomes forming the sample space $\Omega,$ on which we look with interest at certain patterns, called events $\mathscr{F}.$ Sigma-algebras (or sigma-fields) ...
• 24.6k
48k views

### Is there an intuitive explanation why multicollinearity is a problem in linear regression?

The wiki discusses the problems that arise when multicollinearity is an issue in linear regression. The basic problem is multicollinearity results in unstable parameter estimates which makes it very ... 39k views

### What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)?

I've read a lot about PCA, including various tutorials and questions (such as this one, this one, this one, and this one). The geometric problem that PCA is trying to optimize is clear to me: PCA ...
8k views

### Is there any intuitive explanation of why logistic regression will not work for perfect separation case? And why adding regularization will fix it?

We have many good discussions about perfect separation in logistic regression. Such as, Logistic regression in R resulted in perfect separation (Hauck-Donner phenomenon). Now what? and Logistic ...
• 33.9k
7k views

### What is the intuition behind defining completeness in a statistic as being impossible to form an unbiased estimator of $0$ from it?

In classical statistics, there is a definition that a statistic $T$ of a set of data $y_1, \ldots, y_n$ is defined to be complete for a parameter $\theta$ it is impossible to form an unbiased ...
• 2,225
7k views

### The Monty Hall Problem - where does our intuition fail us?

From Wikipedia : Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who ...
13k views

### What is the distribution of $R^2$ in linear regression under the null hypothesis? Why is its mode not at zero when $k>3$?

What is the distribution of the coefficient of determination, or R squared, $R^2$, in linear univariate multiple regression under the null hypothesis $H_0:\beta=0$? How does it depend on the number ...
• 96.4k
12k views

### What's so 'moment' about 'moments' of a probability distribution?

I KNOW what moments are and how to calculate them and how to use the moment generating function for getting higher order moments. Yes, I know the math. Now that I need to get my statistics knowledge ...
• 13.9k
21k views

### Can someone explain the concept of 'exchangeability'?

I see the concept of 'exchangeability' being used in different contexts (e.g., bayesian models) but I have never understood the term very well. What does this concept mean? Under what circumstances ...
• 815
22k views

### Why does the correlation coefficient between X and X-Y random variables tend to be 0.7

Taken from Practical Statistics for Medical Research where Douglas Altman writes in page 285: ...for any two quantities X and Y, X will be correlated with X-Y. Indeed, even if X and Y are ...
• 1,357
7k views

### Seeking certain type of ARIMA explanation

This may be hard to find, but I'd like to read a well-explained ARIMA example that uses minimal math extends the discussion beyond building a model into using that model to forecast specific cases ...
• 11.7k
15k views

### Understanding distance correlation computations

As far as I understood, distance correlation is a robust and universal way to check if there is a relation between two numeric variables. For example, if we have a set of pairs of numbers: ...
• 365
2k 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 ...
• 2,491
2k views

### Odds made simple

I am having some trouble in understanding odds, and I would like just a basic explanation for how to interpret them. I have found various posts related to odds but most of them are more complex than ...
• 151
98k views

### Numerical example to understand Expectation-Maximization

I am trying to get a good grasp on the EM algorithm, to be able to implement and use it. I spent a full day reading the theory and a paper where EM is used to track an aircraft using the position ...
• 2,503
7k views

### Idea and intuition behind quasi maximum likelihood estimation (QMLE)

Question(s): What is the idea and intuition behind quasi maximum likelihood estimation (QMLE; also known as pseudo maximum likelihood estimation, PMLE)? What makes the estimator work when the actual ...
• 57.6k
2k views

### Choosing the number of bootstrap resamples

Say we have the following sample and we are trying to estimate the variance of the sample mean of the population. X = [0, -1, 2, 10, -3] If I take an increasing ...
• 3,598
31k views

### Why is the CDF of a sample uniformly distributed

I read here that given a sample $X_1,X_2,...,X_n$ from a continuous distribution with cdf $F_X$, the sample corresponding to $U_i = F_X(X_i)$ follows a standard uniform distribution. I have ...
18k views

• 3,823
15k views

### Intuitive explanation of convergence in distribution and convergence in probability

What is the intuitive difference between a random variable converging in probability versus a random variable converging in distribution? I've read numerous definitions and mathematical equations, ...
• 1,173