Questions tagged [intuition]

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

Filter by
Sorted by
Tagged with
6
votes
1answer
77 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 &...
5
votes
2answers
98 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^{-(...
2
votes
2answers
38 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
votes
2answers
121 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 ...
0
votes
1answer
16 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 ...
0
votes
0answers
22 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
votes
1answer
60 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
vote
1answer
31 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
votes
0answers
29 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 ...
1
vote
1answer
69 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 ...
0
votes
0answers
18 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 ...
1
vote
1answer
66 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....
0
votes
0answers
26 views

Intution about the memoryless property of geometric distribution

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)}...
1
vote
1answer
32 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
votes
1answer
40 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
votes
1answer
72 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,\...
1
vote
1answer
18 views

Understanding the decomposed matrices in Singular Value Decomposition [duplicate]

I am trying to get some intuition regarding the U and V matrices in SVD ($M=UEV^T$). I think these are orthonormal basis vectors, but I am struggling to get an intuition if they represent anything ...
1
vote
1answer
22 views

Intuition or proof for combinatorial function in binomial distribution

For a the probability of a binomial distribution with n trials, the probability of k successes where Prob(success) = p is (n Choose k) * p^k * (1-p)^(n-k). I understand that we have to multiply p^k * ...
0
votes
1answer
37 views

statistical regression vs machine learning regression [duplicate]

I was trying to understand the difference between statistical regression VS machine learning regression. My background is from Economics and learned regression from statistical point of view for the ...
0
votes
0answers
25 views

Intuition for reasoning between Quasi-poisson and Negative Binomial regression

I am aware of the several similar questions existing here (like this, this or this), but my question is slightly different and remains after going through most of those posts. Specifically, my ...
4
votes
3answers
143 views

Population covariance, are these two formulas equivalent?

For the population covariance, you can write it as: $$\sigma_{x,y} = \frac{\sum_i(x_i-\bar{x})(y_i-\bar{y})}{N},$$ where $N$ is the population size. I think you can also write it in terms of expected ...
0
votes
0answers
16 views

What about the covariance formula makes it obvious that it is about 'linear' associations? [duplicate]

The covariance (and correlation) are described as the strength of a linear association between variables. Is there a way to see where the 'linear' part comes from in the formula?
1
vote
1answer
25 views

Is there an intuition about the matrix operations in the exponent of the multivariate normal distribution?

In the exponent of the multivariate distribution, there are 2 vectors and a square matrix multiplied together to get a scalar result: $$(\mathbf{x} - \mu)^{\text{T}}\Gamma^{-1}(\mathbf{x} - \mu)$$ ...
3
votes
3answers
91 views

Can we explain Bayesian method with intuitive manner?

I reckon that utilizing Bayesian method often produces counterintuitive results, but the example below seems counterintuitive in an extent too extreme for me. Suppose there is a specific disease and a ...
0
votes
1answer
26 views

Estimation with MCMC [closed]

I would like to ask some high-view questions about MCMC. I do not have a specific example, I just want to get a general intuitive idea. Suppose I have a data set $X$ and a rather complex model with ...
1
vote
1answer
44 views

Do more general specifications of Dickey Fuller lead to bias if true model is more parsimonious?

When I was studying econometrics I was taught that whenever in doubt it is always better to run more general specification both in terms of including drift term or trend term and including lags, as ...
1
vote
1answer
217 views

Intuitive explanation of Friedman's H-statistic

What is the cleanest, easiest way to explain someone, a non-STEM person the concept of Friedman's H-statistic? What does it intuitively mean? While exploring feature interaction I went through ...
3
votes
0answers
37 views

Intuition for hypothesis testing [duplicate]

I'm in the process of building an intuition for how hypothesis testing works and why we should use it. I'm not new to the topic — I've taken the usual introductory course in probability theory and ...
5
votes
2answers
55 views

Intuitive understanding of least squares slope formula

One formula for the least squares linear regression line with independent variable $X$ and response variable $Y$ is: $\hat{\beta} = \frac{Cov(X, Y)}{Var(X)}$ This formula screams deeper intuition but ...
0
votes
0answers
7 views

Why does the bootstrap method work to estimate a statistic? [duplicate]

I am a novice at statistics and recently learned about the bootstrap method. I am curious about why such a method works. Intuitively it feels like we are cheating since we are not collecting new ...
2
votes
1answer
31 views

Intuitively Assert Consistency

Consider a model $$\mathbf y=\beta_0+\mathbf x_1\beta_1+\mathbf x_2\beta_2+\mathbf e$$ and assume $\mathbb E[\mathbf e\mid\mathbf X]=0$. Under this scenario, the OLS estimator is a consistent ...
0
votes
2answers
45 views

Bayesian Probability of Zero?

I've been reading a few different philosophical papers/books which have mentioned a "Bayesian belief". Within these texts I've been basically inferring that within the Bayesian theorem, ...
0
votes
0answers
48 views

intuition behind asymmetry of Poisson distribution

Today I've learned that the probability of the number of independent random events occurring in a fixed interval of time can be modeled with the Poisson distribution. When thinking about it my ...
0
votes
0answers
18 views

Intuition behind Vapnik-Chervonenkis Symmetrization lemma

I am trying to get a good understanding of what Vapnik-Chervonenkis Symmetrization Lemma really says, since it comes up quite often. First, we consider the empirical process : $$f\mapsto ({\mathbb {P}...
0
votes
0answers
21 views

Covariance vs Correlation Definition [duplicate]

I am having a tough time understanding the difference between both terms. Could someone please clear up what both terms mean and in the process of doing so, explain the difference between them?
3
votes
1answer
55 views

Probability on different time scales

I just finished reading "Fooled by Randomness" by Nassim Taleb. He, inter alia, gives the following example to prove one of his points: A 15% return with 10% volatility per annum translates ...
2
votes
0answers
27 views

Intuitive interpretation of the covariance matrix

I am trying to get a "feel" for the covariance matrix. I know that $v_iCov(X)v_j$ gives the covariance between $X$ projected along $v_i$ and $v_j$. I'm curious if there's a similar intuitive ...
0
votes
0answers
15 views

Intuition of Condition of (weak) Stationarity in multivariate case

This may be a duplicate. I am trying to get an intuitive idea about the condition for stationarity. I think I got a fair idea of stationarity as a concept (from this and other sources on internet) but ...
1
vote
0answers
29 views

Intuition for Hotelling's T^2 Test

I have been learning about Hotelling's $T^2$ test from Multivariate Statistics: Old School. The test is given by $T^2 = \nu\cdot\text{trace}(\bf{W}^{-1}\bf{B})$. The author shows that in the case of ...
2
votes
0answers
22 views

Intuition behind the degrees of freedom in ridge regression

I'm reading through the ESL book and I'm on the part of ridge regression where the effective degrees of freedom are defined $$ df(\lambda) = tr(X(X'X + \lambda I)^{-1}X') = \sum_{j=1}^p{\frac{d_j^2}{...
0
votes
0answers
16 views

Why does consistency of cluster robust standard error depend on the number of clusters?

I've seen many hand wavy explanations about it, but when I read White's book for the original reference, the math is too dense. Could someone help me derive this result in terms of the asymptotic ...
1
vote
1answer
58 views

Econometrics meaning of structural versus regression model

I want to make sure my understanding is correct. Particularly in econometrics, when authors write down a model: $Y_i = \beta_0 + \beta_1 X_i + \epsilon$ Can I think of this as a 'structural model'- or ...
0
votes
2answers
177 views

Assumption of linearity between variables and log odds in logistic regression

I know that in logistic regression we assume a linear relationship between the independent variables and the logits. Can you explain why is this a reasonable assumption?
0
votes
0answers
10 views

Question about consistent estimators and asymptotic distributions

Lets say you have an estimator that is consistent, and you do not have any information on the asymptotic distribution, what can you do with such an estimator? Also when using aysmptotic distribtuions, ...
1
vote
1answer
65 views

Understanding maximum likelihood estimation

I am told the method of maximum likelihood says we should use the model that assigns the greatest probability to the data we have observed; formally, the maximum likelihood estimator is found by ...
4
votes
2answers
126 views

Interpretation of multivariate conditional gaussian function form?

I've been reading over this Multivariate Gaussian conditional proof, trying to make sense of how the mean and variance of a gaussian conditional was derived. I've come to accept that unless I allocate ...
8
votes
3answers
309 views

Why does a function being smoother make it more likely?

I am currently studying the textbook Gaussian Processes for Machine Learning by Carl Edward Rasmussen and Christopher K. I. Williams. Chapter 1 Introduction says the following: Given this training ...
1
vote
1answer
149 views

Is it really appropriate to say “standard deviation” is variation or dispersion

Question I have been struggling to convince myself that SD (standard deviation) is about variation or dispersion. Standard deviation From Wikipedia, the free encyclopedia In statistics, the standard ...
3
votes
0answers
701 views

A new strain of covid-19 is 70% more infectious/transmissible. What does that mean and how has it been estimated/measured? [closed]

70% in the media https://www.dailymail.co.uk/news/article-9070683 Prime Minister Boris Johnson told a Downing Street briefing that early analysis showed the new strain could increase the reproductive ...
3
votes
2answers
195 views

Fixed effects vs the dummy variables themselves: structural vs practical equation

I have a question about if there is a substantive difference between a fixed effect and the way we estimate them (e.g., dummy variables). Are the estimated dummy variables the fixed effect, or do they ...

1
2 3 4 5
14