The intuition tag has no wiki summary.
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0answers
26 views
Derivation of the pdf of the Beta distribution [duplicate]
$$
f(x)= \frac{x^{(\alpha−1)} * (1−x)^{(\beta−1)}}{\mathcal B(\alpha,\beta)}
$$
Questions:
How can we derive this famous pdf?
What is the intuitive meaning of the Beta distribution? (Please ...
1
vote
1answer
37 views
what is the intuition behind stationarity condition for AR(p) process?
i get that you have to find the roots of the characteristic polynomial but can someone explain the intuition behind the roots must be outside the unit circle? what is a unit circle?
before anyone ...
-2
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0answers
26 views
*Effective* statistical and probability resources [duplicate]
My question is as follow. I want to develop a greater intuitive understanding of probability and stats. I find that most of the available resources are books, which fall in two bins:
textbooks, ...
1
vote
2answers
28 views
Poker shared cards change odds
I wrote a poker simulator for seven card texas hold 'em, and I found a counter-intuitive result:
If player A starts with a pair of aces against player B who has a random hand, I get a different %win ...
2
votes
1answer
143 views
Understanding OLS regression slope formula
I understand the intuition behind the OLS model: to minimize the squared residuals. Is there a way, however, to interpret the formula for the slope of the regression line intuitively? That is $m = ...
1
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0answers
90 views
Intuition behind tensor product interactions in GAMs (MGCV package in R)
Generalized additive models are those where
$$ y = \alpha + f_1(x_1) + f_2(x_2) + e_i$$
for example. the functions are smooth, and to be estimated. Usually by penalized splines. MGCV is a package ...
4
votes
2answers
390 views
Intuition and uses for coefficient of variation
I'm currently attending the An Introduction to Operations Management course in Coursera.org. At some point in the course, the professor started to deal with variation in the operations' time.
The ...
7
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1answer
139 views
Frequentist statistics references for someone well versed in modern probability theory
Coming from a rigorous background in analysis and modern probability theory, I find Bayesian statistics straightforward and easy to understand, and frequentist statistics incredibly confusing and ...
2
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0answers
326 views
Geometric intuition for why an outer product of two vectors makes a correlation matrix? [closed]
I understand that the outer product of two vectors, say representing two detrended time series, can represent a cross-correlation (well covariance) matrix.
I also know that the inverse of a ...
10
votes
2answers
407 views
Geometric interpretation of penalized linear regression
I know that linear regression can be thought as "the line that is vertically closest to all the points":
But there is another way to see it, by visualizing the column space, as "the projection at ...
3
votes
1answer
171 views
Geometrical interpretation of correlation of a variable and the residual
I came across this blog post about least angle regression, and at a point he says:
Find the variable $x_1$ most correlated with the residual. (Note that the variable most correlated with the ...
14
votes
4answers
268 views
The operation of chance in a deterministic world
In Steven Pinker's book Better Angels of Our Nature, he notes that
Probability is a matter of perspective. Viewed at sufficiently close
range, individual events have determinate causes. Even a ...
26
votes
3answers
1k 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 ...
1
vote
3answers
953 views
Why is a deterministic trend process not stationary?
I am confused on why a simple trend process is not stationary. Consider the following process:
$Y_t = a + bt + \epsilon_t$
The variance is clearly constant. However, the mean $bt$ is dependent on ...
5
votes
1answer
290 views
What is the intuition behind the score function?
Wikipedia tells us that the score plays an important role in the Cramér–Rao inequality. It also phrases out the definition:
$$V = \frac{\partial}{\partial \theta} \log{L(\theta; X)}$$
However, I ...
5
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2answers
856 views
Why is the Poisson distribution chosen to model arrival processes in Queueing theory problems?
When we consider Queueing theory scenarios where individuals arrive to a serving node and queue up, usually a Poisson process is used to model the arrival times. These scenarios come up in network ...
2
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1answer
137 views
Plain English explanation of Bernoulli mixture models?
Not exactly the most accessible explanation can be found here, but I'm looking for something more intuitive, examples of applications and so on.
Help is much appreciated.
24
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6answers
7k views
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 ...
20
votes
5answers
3k views
Understanding “variance” intuitively
What is the cleanest, easiest way to explain someone the concept of variance? What does it intuitively mean? If one is to explain this to their mom or child how would one go about it?
It's a concept ...
4
votes
1answer
115 views
PDF for a function of random variables
If $g=f(x,y)$ is a function of independent random variables $x$ and $y$ then how do we arrive at the expression for the probability density function of $g$,
$$f_G(g) = \iint ...
10
votes
2answers
299 views
Intuitive explanation for density of transformed variable?
Suppose $X$ is a random variable with pdf $f_X(x)$. Then the random variable $Y=X^2$ has the pdf
$f_Y(y)=\left\{\begin{array}{ll}\frac{1}{2\sqrt{y}}\left(f_X(\sqrt{y})+f_X(-\sqrt{y})\right) & y ...
17
votes
1answer
748 views
Intuition behind why Stein's paradox only applies in dimensions $\ge 3$
Stein's Example shows that the maximum likelihood estimate of $n$ normally distributed variables with means $\mu_1,\ldots,\mu_n$ and variances $1$ is inadmissible (under a square loss function) iff ...
3
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1answer
66 views
How do I tell when and why to use specific statistical measures?
I've taken a few probability classes and now understand how to calculate some statistical measures like mean and confidence intervals. What I don't know is the what, when, and why of using these ...
14
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2answers
397 views
Statistics, war stories, data intuition
I think it is fair to say statistics is an applied science so when averages and standard deviations are calculated it is because someone is looking to make some decisions based on those numbers. Part ...
28
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5answers
2k views
What intuitive explanation is there for the central limit theorem?
In several different contexts we invoke the central limit theorem to justify whatever statistical method we want to adopt (e.g., approximate the binomial distribution by a normal distribution). I ...
10
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1answer
325 views
Intuition for higher moments in circular statistics
In circular statistics, the expectation value of a random variable $Z$ with values on the circle $S$ is defined as
$$
m_1(Z)=\int_S z P^Z(\theta)\textrm{d}\theta
$$
(see wikipedia).
This is a very ...
31
votes
8answers
2k 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 ...
9
votes
1answer
241 views
E-M, is there an intuitive explanation?
The E-M procedure appears, to the uninitiated, as more or less black magic. Estimate parameters of an HMM (for example) using supervised data. Then decode untagged data, using forward-backward to ...
8
votes
2answers
752 views
How to understand a convolutional deep belief network for audio classification?
In "Convolutional deep belief networks for scalable unsupervised learning of hierarchical representations" by Lee et. al.(PDF) Convolutional DBN's are proposed. Also the method is evaluated for image ...
14
votes
6answers
2k views
