The theory tag has no wiki summary.
-2
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1answer
17 views
Standard deviation of game results about predictions from a rating system
I'm very in to Sports analysis and am keen to look at finessing my analysis models that I have worked up (I don't have a great maths background, I've just done a little bit of reading).
Standard ...
1
vote
0answers
27 views
Equivalence of with and without replacement sampling
After some heavy reordering and canceling of factorials, I discovered that the following experiment is approximately equivalent for $m \ll n < N$ if conducted with or without replacement:
In ...
5
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1answer
35 views
Average case analysis of learning algorithms
Typically analysis of learning algorithms is in the worst-case setting, for example regret bounds in online learning, or generalisation error bounds in classification. Whilst worst case performance is ...
7
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2answers
75 views
Best bandit algorithm?
The most well-known bandit algorithm is upper confidence bound (UCB) which popularized this class of algorithms. Since then I presume there are now better algorithms. What is the current best ...
8
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2answers
69 views
In boosting, why are the learners “weak”?
See also a similar question on stats.SE.
In boosting algorithms such as AdaBoost and LPBoost it is known that the "weak" learners to be combined only have to perform better than chance to be useful, ...
7
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7answers
1k views
What theories should every statistician know?
I'm thinking of this from a very basic, minimal requirements perspective. What are the key theories an industry (not academic) statistician should know, understand and utilize on a regular basis?
A ...
7
votes
1answer
50 views
What are alternatives to VC-dimension for measuring the complexity of neural networks?
I have come across some basic ways to measure the complexity of neural networks:
Naive and informal: count the number of neurons, hidden neurons, layers, or hidden layers
VC-dimension (Eduardo D. ...
9
votes
3answers
281 views
Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, and when is it a bad one?
In what circumstances would you want to, or not want to scale or standardize a variable prior to model fitting? And what are the advantages / disadvantages of scaling a variable?
4
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1answer
94 views
Why efficiency matters?
Suppose we are trying to estimate the quantity $\theta$ and we have that the estimator $\hat\theta_n$. Suppose it is efficient, i.e. is variance is the smallest among certain class of other possible ...
3
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2answers
185 views
Difference between bias-variance dilemma and overfitting
I'm wondering what difference it makes whether we talk about bias-variance dilemma where fitting a regression line to the given dataset reduces bias and increases variance or whether we talk about ...
3
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4answers
263 views
What exactly does 'representative sample' refer to?
When reading passages like the following:
Based on a representative sample of 88 recent raids, we show that the Turkana sustain costly cooperation in combat at a remarkably large scale, at ...
7
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4answers
304 views
Can one leave out data from research because it is not significant?
I've encountered this sentence while reading an article on sciencemag.org.
In the end, responses from just 7600 researchers in 12 countries were included because the remaining data were not ...
7
votes
3answers
361 views
What does “unbiasedness” mean?
What does it mean to say that "the variance is a biased estimator".
What does it mean to convert a biased estimate to an unbiased estimate through a simple formula. What does this conversion do ...
15
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3answers
342 views
What is the curse of dimensionality?
Specifically, I'm looking for references (papers, books) which will rigorously show and explain the curse of dimensionality. This question arose after I began reading this white paper by Lafferty and ...
6
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4answers
538 views
Probability theory books for self-study
Are there any good books that explain important concepts of probability theory like probability distribution functions and cumulative distribution functions?
Please avoid referring books like ...
6
votes
2answers
333 views
Will quantum computing allow new statistical techniques?
I just read that you can now buy a quantum computer (albeit that there has only been one sold so far!).
Will quantum computing have any applications in statistics?
{edit - for the purposes of the ...
3
votes
2answers
188 views
Theory on discriminant analysis in small sample size conditions
I see a similarity between a problem I'm working on and Linear (or Quadratic) Discriminant Analysis when the sample size is smaller than $p+1$.
I'm interested in theory bounding the generalization ...
2
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0answers
184 views
How to come up with research questions in statistical theory? [closed]
(I think this question is appropriate as a community wiki? If not, please close it, no hard feelings.)
Does anybody have links to webpages/PDF files of advice for grad students in statistical theory ...
2
votes
1answer
221 views
Calculating the transfer entropy in R
The transfer entropy, from information theory, is an effective way to measure the one-way information dependence between two variables. A nice high-level summary is here:
...
5
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2answers
180 views
Interpreting p-values associated with correlation measurements
The "Introductory Statistics with R" book contains a section that deals with correlations (section 6.4 in the second edition). The book shows Pearson, Spearman and Kendall correlation coefficients ...
10
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4answers
551 views
Readable introduction to measure theory
I'm interested in learning more about nonparametric Bayesian (and related) techniques. My background is in computer science and I have never taken a course on measure theory or probability theory. Can ...
4
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2answers
346 views
Is there a relationship between the median of a function of random variables and the function of the median of random variables?
Background
notation: RV= random variable, $\mu=$ mean $m=$ median
Jensen's Inequality considers the relationship between the mean of a function of an RV and the function of the mean of an RV.
If ...
2
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1answer
653 views
Statistics Proof that $E[(X-Y)^2] = 0$
If X and Y are standardized variables and are perfectly positively correlated with respect to each other, how can i prove that $E[(X-Y)^2] = 0$?
7
votes
3answers
492 views
Can you say that statistics and probability is like induction and deduction?
I've read through this thread, and it looks to me like it can be said that:
statistics = induction ?
probability = deduction ?
But I am wondering if there might be some more details on the ...
4
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2answers
228 views
What are good resources/criteria for judging human bias in data collection?
I've just been given a stack of polling data to analyse. Some of the questions are obviously leading or present subtle incentives (for the poller or polled) for specific answers. Of other questions ...
2
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2answers
178 views
What types of data analysis do not count as statistics?
When does data analysis cease to be statistics ?
Are the following examples all applications of statistics ?: computer vision, face recognition, compressed sensing, lossy data compression, signal ...
-3
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2answers
241 views
Lies, Damn Lies and Statistics [closed]
Is there something about statistics that lends itself to this sort of saying, or is it just that people will say anything to support their case, and this includes citing irrelevant or incomplete ...
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8answers
2k views
What is Bayes' theorem all about?
What are the main ideas, that is, concepts related to Bayes' theorem?
I am not asking for any derivations of complex mathematical notation.
19
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7answers
710 views
How do you convey the beauty of the Central Limit Theorem to a non-statistician?
My father is a math enthusiast, but not interested in statistics much. It would be neat to try to illustrate some of the wonderful bits of statistics, and the CLT is a prime candidate. How would you ...
6
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1answer
364 views
What are some good frameworks for method selection?
I have been looking into theoretical frameworks for method selection (note: not model selection) and have found very little systematic, mathematically-motivated work. By 'method selection', I mean a ...
