The theory tag has no wiki summary.
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21 views
Partials of PDF with no closed form solution
I need to estimate partial derivatives for all N parameters denoted $\theta_{N}$ of a probability density function(PDF) $\mathcal{f}$.
This PDF $\mathcal{f}$ has no closed form solution and is ...
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1answer
80 views
How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?
I've been doing a machine learning competition where they use RMSLE (Root Mean Squared Logarithmic Error) to evaluate the performance predicting the sale price of a category of equipment. The problem ...
3
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1answer
62 views
Question regarding Bonferroni correction
Prove the following version of the Bonferroni inequality-
$$P\left(\bigcap_{i=1}^kA_i\right)\ge1-\sum_{i=1}^kP(A_i^c)$$
When creating simultaneous confidence interval, what are $A_i$ and $A_i^c$?
...
2
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1answer
54 views
What is the name of the theory (if there is one) that states lottery winners are more likely to tell others about their lottery entry?
I've previously read about a theory that I remember (correctly or not) being called the "Winning Lottery Theory" which is essentially the following:
An individual hears about disproportionately ...
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0answers
31 views
Confusion related to inverse problems in statistics
I am getting started with inverse problems in statistics. However, I didn't something related to it.
I was reading this paper http://math.uni-heidelberg.de/studinfo/reiss/CavalierInvProb.pdf.
It ...
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4answers
376 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 ...
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0answers
93 views
The formula for covariance in terms of joint cdf
I want to show that
$$\newcommand{\cov}{\operatorname{cov}}\newcommand{\d}{\mathrm{d}}\cov(x,y) = \iint (F_{X,Y}(x,y) - F_X(x)F_Y(y))\,\d x\,\d y$$
However, I have no idea how to start. I know that
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1answer
105 views
Random forest like procedure for regression or other statistical models
I'm wondering if there exist methods similar to one used in random forest algorithm - I mean taking simultaneously bootstrap sample and random subset of features, then building statistisal model. Have ...
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44 views
Comparing two different leagues of similar but not equal distributions around a standard deviation of error of a prediction from a rating system
This query ties a lot of my interests in rating sports teams together, because as I’ve mentioned before I do a version of the Kenneth Massey method (as per his 1997 thesis ...
2
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0answers
22 views
Generalization error for classification with a nonconvex loss function
I've been working my way through Vapnik's 1998 Statistical Learning Theory book and one thing that I'm still unsure of is if his risk bounds hold for nonconvex loss functions -- i.e., when we can't be ...
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3answers
1k 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 ...
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5answers
1k 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 ...
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2answers
65 views
Algebra for data confidence
Very often, we use data which are derived from some measurements. These measurements usually have a confidence measure associated which tells how reliable or confident we are about the measure. For ...
0
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1answer
233 views
For linear regression, what's the distribution of error term from Classical and Bayesian point of views?
I know that linear regression is based on the assumption that the errors are normally distributed (from both bayesian and classical views). I'm just trying to verify this assumption based on the final ...
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5answers
904 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 though I have never taken a course on measure theory or probability ...
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2answers
85 views
Independence in a sum relationship
I have a model of total reaction time T, which is a composite of a selection time S and a discrimination time D. So a person first finds something, this takes the tS. Then he discriminates and reports ...
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1answer
148 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 ...
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0answers
92 views
Is possible use HoG features to train a Neural Network?
I was wondering if it is possible use HoG features to train a Neural Network, I know that in the original paper by Dalal and Triggs they used the data generated to train a SVM.
If not is possible or ...
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3answers
209 views
Is it true that in high dimensions, data is easier to separate linearly?
I have often seen the statement that linear separability is more easily achieved in high dimensions, but I don't see why. Is it an empirical fact? An heuristic? Plain nonsense?
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1answer
125 views
Does the principle of indifference apply to the Borel-Kolmogorov paradox?
Consider Jayne's solution to the Bertrand paradox using the principle of indifference. Why doesn't a similar argument apply to the Borel-Kolmogorov paradox?
Is there something wrong with arguing that ...
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1answer
327 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 ...
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2answers
445 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 ...
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1answer
258 views
Problems with a simulation study of the repeated experiments explanation of a 95% Confidence interval - where am I going wrong?
I'm trying to write an R script to simulate the repeated experiments interpretation of a 95% confidence interval. I've found that it overestimates the proportion of times in which the true population ...
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0answers
49 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
65 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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1answer
126 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. ...
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2answers
352 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, ...
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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 ...
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3answers
1k 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?
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8answers
4k 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.
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2answers
679 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 ...
14
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3answers
990 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 ...
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4answers
869 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 ...
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2answers
382 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 ...
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2answers
314 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 ...
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1answer
698 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:
...
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506 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
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1answer
1k 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 $E[(X-Y)^2] = 0$?
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2answers
311 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 ...
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7answers
1k 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 ...
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2answers
478 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 ...
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3answers
926 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 ...
8
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1answer
397 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 ...
4
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2answers
249 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
212 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 ...
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1answer
270 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 ...
