Questions that seek a conceptual or non-mathematical understanding of statistics.
This tag is for questions that seek a conceptual or non-mathematical understanding of statistics.
Questions tagged [intuition]
720 questions
1229
votes
27 answers
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 a machine. But I didn't understand it. I didn't…
claws
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607
votes
12 answers
What is the difference between "likelihood" and "probability"?
The wikipedia page claims that likelihood and probability are distinct concepts.
In non-technical parlance, "likelihood" is usually a synonym for "probability," but in statistical usage there is a clear distinction in perspective: the number that…
Douglas S. Stones
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527
votes
15 answers
What is the intuition behind beta distribution?
Disclaimer: I'm not a statistician but a software engineer. Most of my knowledge in statistics comes from self-education, thus I still have many gaps in understanding concepts that may seem trivial for other people here. So I would be very thankful…
ffriend
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393
votes
11 answers
Explaining to laypeople why bootstrapping works
I recently used bootstrapping to estimate confidence intervals for a project. Someone who doesn't know much about statistics recently asked me to explain why bootstrapping works, i.e., why is it that resampling the same sample over and over gives…
Alan H.
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315
votes
13 answers
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 statistic that are free to vary.
Estimates of…
Tim
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280
votes
16 answers
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 seems that students easily learn how to perform the…
Sharpie
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262
votes
10 answers
How would you explain covariance to someone who understands only the mean?
...assuming that I'm able to augment their knowledge about variance in an intuitive fashion ( Understanding "variance" intuitively ) or by saying: It's the average distance of the data values from the 'mean' - and since variance is in square units,…
PhD
- 13,429
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261
votes
11 answers
How would you explain Markov Chain Monte Carlo (MCMC) to a layperson?
Maybe the concept, why it's used, and an example.
Neil McGuigan
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204
votes
17 answers
Intuitive explanation for dividing by $n-1$ when calculating standard deviation?
I was asked today in class why you divide the sum of square error by $n-1$ instead of with $n$, when calculating the standard deviation.
I said I am not going to answer it in class (since I didn't wanna go into unbiased estimators), but later I…
Tal Galili
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186
votes
8 answers
What intuitive explanation is there for the central limit theorem?
In several different contexts we invoke the central limit theorem to justify whatever statistical method we want to adopt (e.g., approximate the binomial distribution by a normal distribution). I understand the technical details as to why the…
user28
182
votes
4 answers
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) are made up of events to which a probability…
Antoni Parellada
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166
votes
5 answers
How to intuitively explain what a kernel is?
Many machine learning classifiers (e.g. support vector machines) allow one to specify a kernel. What would be an intuitive way of explaining what a kernel is?
One aspect I have been thinking of is the distinction between linear and non-linear…
hashkey
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160
votes
9 answers
Bottom to top explanation of the Mahalanobis distance?
I'm studying pattern recognition and statistics and almost every book I open on the subject I bump into the concept of Mahalanobis distance. The books give sort of intuitive explanations, but still not good enough ones for me to actually really…
jjepsuomi
- 5,207
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125
votes
9 answers
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 information coming from a radar. Honestly, I don't…
arjsgh21
- 2,403
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118
votes
3 answers
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 that I know (little, by the way) that the unit root…
Lucas Reis
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