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13 votes
11 answers
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When is it important for a practitioner to understand CIs?

I have a physician friend who asks me questions about stats. He gets confused about stuff, e.g., the definition of a confidence interval (CI) and its intricacies. For example, he finds the following ...
Yair Daon's user avatar
  • 2,634
2 votes
0 answers
46 views

Finding a specific reference on the construction of a confidence interval where by inspection we can see it does contain the parameter

I realise this is a long shot but I am trying to find a reference to a specific example of a construction of a confidence interval which I came across in the past. My memory on this is hazy and I may ...
8e9yQBKVlIDwoIVegfkJ's user avatar
7 votes
2 answers
127 views

Real-world example of quantile loss used for evaluation

We can use quantile loss (a.ka. tick or pinball loss) for training a model or for evaluating predictions. (It is helpful to distinguish the two clearly, e.g. as done here.) I am interested in the ...
Richard Hardy's user avatar
1 vote
2 answers
1k views

Support Vector Regression vs. Linear Regression

I am new to ML and I am learning the different algorithms one can use to perform regression. Keep in mind that I have a strong mathematical background, but I am new in the ML field. So I understand ...
kubo's user avatar
  • 145
3 votes
2 answers
54 views

Can using the IQR/Median help with this problem?

I have a set of data in tabular form which records the time it takes 500 people to bake a cake. Each person is assigned a single time: it may take Tom 30 minutes, or Mike 60 minutes to bake a cake. ...
Chips220 Swifty's user avatar
0 votes
0 answers
78 views

Practical examples of multiplicative regression model

Majority of the examples of multiple regression in practice is written as additive model. Can you give me some practical examples of a multiplicative regression model (i.e. a model that can be fitted ...
sitems's user avatar
  • 3,989
0 votes
0 answers
37 views

Natural Exponential family with polynomial partition function

Consider a natural exponential family: \begin{equation} f(x|\theta) = h(x) e^{ x \theta -A(\theta) } \end{equation} We assume that we are supported on $\mathbb{R}$ (i.e., $h(x)>0$ for $x \in \...
Lisa's user avatar
  • 131
0 votes
0 answers
27 views

Are all examples of normal distribution in nature only a consequence of CLT? [duplicate]

I have read that many bell curves we see in nature is just a consequence of the CLT, because those things are just the result of many small additive causes (e.g. human height). Then my question is: ...
sitems's user avatar
  • 3,989
0 votes
1 answer
68 views

Example consistency of functions

I know that as long as the population moments exist and the data are identically distributed the raw sample moments, the central sample moments and the sample quantiles are consistent. This concept of ...
Marie's user avatar
  • 3
0 votes
1 answer
112 views

Variance of truncated normal distribution [closed]

I am trying to calculate the variance of a truncated normal distribution, var(X | a < X < b), given the expected value and variance of the unbound variable X. I believe I found the corresponding ...
ajj's user avatar
  • 3
3 votes
1 answer
971 views

What are balanced and orthogonal designed experiments?

I have recently started studying Designed Experiments and have have come across non-rigorous definitions of "balanced" and "orthogonal" experiments and would be interested in ...
FD_bfa's user avatar
  • 243
3 votes
1 answer
57 views

Is there a statistic such that for large sample sizes $a_n (\hat{\theta} - \theta) \sim N(0, \Sigma)$ approximately but $a_n \neq n^{1/2}$?

Various central limit theorems are of the form $a_n(\hat{\theta}-\theta)\sim N(0, \Sigma)$ approximately as $n \to \infty$ and usually $a_n = n^{1/2}$. Are there central limit theorems for statistics ...
cgmil's user avatar
  • 1,373
1 vote
0 answers
327 views

What is a good introductory guide to Bayesian MCMC Analysis in R?

I am trying to perform Bayesian Analysis in R, using of Monte Carlo Markov Chains to calculate the probability of, in a set of data, there being a gaussian peak at a certain location $x_0$ (my 'target'...
1 vote
1 answer
48 views

Accuracy failure example

I am trying to understand the functioning of accuracy and I need a practical example. This is what I understood: it gets the average correctness of the predictions and in some cases its result can be ...
hellomynameisA's user avatar
1 vote
0 answers
111 views

Computing an Exponential Moving Average

According to the Wikipedia page on moving averages, "This is also why sometimes an EMA is referred to as an $N$-day EMA. Despite the name suggesting there are $N$ periods, the terminology only ...
user345010's user avatar
1 vote
0 answers
20 views

Example of a parametric family of distributions that always has dependence on among its variables

Inspired by this question, I would like an example of a parametric family of distributions such that there is dependence for all choices of parameters. The family could be infinite or finite, but I ...
Galen's user avatar
  • 9,381
6 votes
3 answers
1k views

A realistic example of a non identifiable model?

Given the definition of statistical model identifiability : identifiable iff $P_\theta = P_{\theta'} \implies \theta = \theta' ~~ \forall \theta, \theta' \in \Theta$ we can see that, for example, $X \...
Antonello's user avatar
  • 403
1 vote
1 answer
648 views

Downward slope but Spearman correlation coefficient is positive and vice versa

Why the slope and the Rho value not the same? For examples, graph H-DSI shows downward slope but the Rho value is positive (P value=0.9603; r=0.009867). Hope someone can explain it. Thank you. H DSI ...
Mei's user avatar
  • 13
8 votes
1 answer
105 views

Is there a real example in which a correlation finally leads to the discovery of a non-trivial causal relationship?

More specifically, I am wondering if there is such an example satisfying the following criteria: The example happened after 1888, it would be better to be after 1900—I think few people have the ...
Eli4ph's user avatar
  • 181
0 votes
0 answers
18 views

Examples of correlated Xs with opposite effect on Y [duplicate]

Could someone give me a simple real life example of how two things can be positively correlated, but they have different (opposite) effects on a third variable? I encountered this scenario and I'm ...
Laura's user avatar
  • 1
4 votes
2 answers
571 views

Symmetric distribution with finite Mean but no Variance

Is there a symmetric continuous distribution that has a finite mean, but no variance? What I've found so far: For instance the Pareto distribution satisfies everything but the symmetry, so I was ...
flawr's user avatar
  • 583
2 votes
1 answer
157 views

concrete example of degenracy

I was reading on degeneracy. Can someone give concrete example of following definition. A kernel $h$ is symmetric if it is invariant under permutations of its inputs. $S_m$ be symmetric group ...
manifold's user avatar
0 votes
3 answers
1k views

Real-life example in which Markov chain Monte Carlo is desirable? [duplicate]

A typical introduction to the Metropolis--Hastings algorithm, and hence to Markov chain Monte Carlo techniques in general, starts with the following assumptions on some probability distribution $P(x)$ ...
Mr. Palomar's user avatar
1 vote
0 answers
99 views

Kwiatkowski–Phillips–Schmidt–Shin (KPSS) and Augmented Dickey–Fuller (ADF) Tests

I have been searching for a sample usage of the KPSS and ADF tests, however I can only find pages reporting examples using R or Python. The mathematical definition of the KPSS test also seems to be ...
98418's user avatar
  • 11
2 votes
1 answer
4k views

How to use missForest in R for test data imputation?

I want to use the R missForest() function at work to perform missing value imputation. However, after reading up on the algorithm more, I can't decide how to impute ...
Liam Morgan's user avatar
6 votes
2 answers
142 views

On the difference between the main effect in a one-factor and a two-factor regression

Consider a linear regression (based on least squares) on two predictors including an interaction term: $$Y=(b_0+b_1X_1)+(b_2+b_3X_1)X_2$$ $b_2$ here corresponds to the conditional effect of $X_2$ when ...
Arnaud Mortier's user avatar
2 votes
1 answer
203 views

Statistics/Data Science: Real world example for a donut destribution?

I'm looking for different real world examples for donut distribution (in the statistic meaning). https://i.sstatic.net/VrGq4.jpg For the most other distributions, I found good examples. But for this ...
Clemens Drolshagen's user avatar
1 vote
0 answers
36 views

Am I understanding correctly the Maximum Entropy concept using a sentence?

In the sentence "The house is white", each word carries a different amount of information. If I remove the "The" from the sentence, almost nothing happens: you are still able to ...
perep1972's user avatar
3 votes
0 answers
129 views

Examples of positive definite periodic covariance matrices

My aim is to find a few examples of positive definite covariance matrices $\pmb{R} = \{R(s,t)\}_{s,t=1}^n$ that satisfy $$R(s,t) = R(s+T, t+T),~~~1\leq s,t \leq n-T,$$ where $T$, $1\leq T\leq n-1$, is ...
Joy's user avatar
  • 323
2 votes
1 answer
31 views

Question about latent variables in Co-integration Regression

I have a question about cointegration regression models as follows: Is it common to have latent variables or regressors with measurement error in the cointegrating regression model? Is it highly ...
Sarah's user avatar
  • 103
3 votes
1 answer
739 views

Two random variables not correlated with normal distribution, whose sum is normal but which are not independent

The example based on the Rademacher distribution of two random variables, $X$ and $Y$, normally standard distributed, not correlated, but not independent, is well known. Additionally, in this example ...
G al Cubo's user avatar
1 vote
1 answer
129 views

Example of random process with negative variation

I study about random processes. Let us have $\{X_1, X_2, \dots X_n\}$ observations. I learned, that in stationary time series the sample autocovariance function is defined as $$ \widehat{γ}(h)= \...
martina's user avatar
  • 121
1 vote
2 answers
188 views

Instructive example for using machine learning to predict continuous variable?

Arguably, the MNIST or titanic examples are probably the most common and instructive examples of classification problems solved using machine learning. Are there any 'iconic' examples of machine ...
1 vote
0 answers
32 views

What scenario corresponds to choosing the "true distribution" $p$ in $\textsf{KL}(p\parallel q)$?

I understand that when you think about changing $q$ in the Kullback-Leibler divergence $\textsf{KL}(p\parallel q)$, this corresponds to trying to find the distribution that minimizes information loss ...
mimuller's user avatar
  • 111
1 vote
2 answers
816 views

What are 3 easy, real-world examples for high, medium and low correlation?

I understand what correlation means on paper (as in: given high, positive correlation, then, if A is high, B is likely to be high, too). However, the classification into "high", "medium" and "low" ...
FirefoxMetzger's user avatar
1 vote
1 answer
212 views

Example of a Markov Process with observable states?

I have a pretty good handle on Hidden Markov Models, but I can't think of any examples of a Markov process with a directly observable state. Any examples?
infinitely_improbable's user avatar
5 votes
2 answers
186 views

Teaching (very elementary) statistical modelling

I've been asked to contribute some lectures (or parts of lectures) to a course on "Mathematical Modelling", from a statistical perspective. This is to a rather mixed group of Mathematics ...
2 votes
1 answer
2k views

Numerical Example of Independent Component Analysis

Can somebody explain ICA(Independently Component Analysis) with a small practical example over here. I have seen lot of programs and libraries written and you can just apply that to your data to find ...
Edison's user avatar
  • 435
1 vote
1 answer
487 views

where can I find advanced stats questions and answers like the example below?

I am at the beginning of an advanced stats course and I am looking to practice some questions beyond the few which are given in class. below are a few examples from our first assignment. I am looking ...
1 vote
0 answers
30 views

How to use parameters to calculate a value which will be used for a statistical analysis?

I am confused on a basic statistics concept. Also, my terminology may be a bit off as well; I am a novice. I will be as simple and concise as possible. Hopefully, this scenario gets to the core of my ...
Nicholas Hayden's user avatar
1 vote
1 answer
3k views

Power function of a test,example

Consider a population with the pdf $N(\theta,1)$ where $\theta$ is unknown and hypothesis $H_0:\theta=5.5$ and $H_1:\theta=8$.Suppose that $\bar{X}=\frac{1}{9}\sum_{i=1}^9 X_i.$Reject $H_0$ iff $\bar{...
user2925716's user avatar
3 votes
3 answers
196 views

Under torture, the data may yield false confessions. Examples?

My statistics teacher repeated the statement "Under torture, the data may yield false confessions" several times, but without giving a concrete example of what it means. Can you give some good ...
8 votes
1 answer
1k views

Model with admissible estimator(s) that are not the Bayes estimator for any choice of prior?

Every Bayes estimator is admissible, to the best of my knowledge. (Related questions - 1,2.) I recall my professor mentioning once during a lecture that, at least as rough intuition, the converse is ...
Chill2Macht's user avatar
  • 6,369
1 vote
0 answers
35 views

What is the probability of Jack finding Sam at the last bar?

Jack and Sam are friends. It is Saturday and Sam forgot his phone home. Jack knows that there is a 2/3 probability that Sam goes to a party. There are 10 clubs in town and all have an equal ...
power_uP's user avatar
7 votes
2 answers
8k views

Smarter example of biased but consistent estimator?

I am trying to get an intuitive understanding of why there exists biased but consistent estimator. Suppose $X_i \sim \mathcal{N}(\mu, 1)$. One example I came across is this: $$W_n(X_1,\cdots,X_n) = ...
3x89g2's user avatar
  • 1,716
2 votes
1 answer
794 views

Regression example for one-dimensional input

For some educational purposes, I need a realistic regression example where the input space is one-dimensional, i.e. $x\in\mathbb{R}$. I do not want to use any dummy approaches such as simulation from ...
Karel Macek's user avatar
  • 2,856
1 vote
1 answer
678 views

Difference between instance-based and example-based Learning

I've read both the terms instance-based and example-based learning in some contexts, e. g. instance-based learning for label ranking and example-based for general text classification tasks. Is there ...
Julian L.'s user avatar
  • 115
6 votes
1 answer
2k views

Negative autocorrelation in linear regressions : examples and consequences

I am wondering if there are classical (or not so classical) examples of negative autocorrelation in a regression model. To expalin the context : I am explaining OLS limitations, heterosckedasticity ...
Anthony Martin's user avatar
0 votes
0 answers
4k views

Real world practical Outliers/Anomalies

I want to have some real life and practical examples for anomalies that can be expressed like a scenario. For example in a country following left-hand driving, a vehicle moving in a wrong direction ...
maliks's user avatar
  • 201
1 vote
0 answers
78 views

What are the first historical examples of meta-analysis?

I am researching the history of meta-analysis, and have found several interesting scholarly sources, going O'Rourke to Hedges, just to name two recent ones. On top of these authoritative sources, I ...
Giuseppe Biondi-Zoccai's user avatar