# Tagged Questions

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### 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 ...
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### Does the principle of indifference apply to the Borel-Kolmogorov paradox?

Consider Jaynes' 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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### Similarity theory: Testing whether dimensions are separable or integral

Note: I'm not referring to linear separability. I've found the interesting comment in Edelman, Shahbazi: "Renewing the respect for similarity" that for integral dimensions, Euclidean distance is ...
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### Approximating a binomial distribution with a mixture normal

This is purely a theoretical question (I legitimately can't think of a real application), but if you wanted to approximate a binomial distributed variable with a two-component mixture normal, is there ...
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### Non significant Pearson correlations included in hierarchical regression?

I would like to perform hierarchical regression in which all variables are based on previous research/theory. But when I perform Pearson correlations, I found that some variables did not correlate to ...
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### Is there a statistical application that requires strong consistency?

I was wondering if someone knows or if there exists an application in statistics in which strong consistency of an estimator is required instead of weak consistency. That is, strong consistency is ...
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### Does the presence of an outlier increase the probability that another outlier will also be present on the same observation?

**Edit: (10/26/13) More clear (hopefully) mini-rewrites added at the bottom** I'm asking this from a theoretical/general standpoint - not one that applies to a specific use case. I was thinking ...
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### Building models with unequal intervals between time series observations

I'm trying to get into econometric/trading modeling and the universe of variables out there is immense. There are practically continuously updated variables (currency exchange rates, interest rates, ...
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### Theoretical expected value and variance

Let $X$ be a random variable having expected value $\mu$ and variance $\sigma^2$. Find the Expected Value and Variance of $Y = \frac{X−\mu}{\sigma}$. I would like to show some progress I've made so ...
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### Modelling with multiple-valued variables

I am about to start out analysis of a microbiological data set (ETEC: enterotoxic echerichia coli in children with diarrhea). The variables refer to the ETEC, not to the children. Some of the ...
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### 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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### How do we understand the relationship between independent probabilities and real-world independence?

From what I have come to understand, the events A and B are considered independent for purposes of probability theory when $$p(A \cap B) = p(A) \cdot p(B)$$ Now, supposing I flip two coins. I ...
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### Frequency of data: is quarterly data better than half-year data? Why?

Hi have a dataset which I constructed using quarterly observations (from bank accounts). I could have also used half-year or yearly data, but I chose quarterly because I thought that higher frequency ...
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### 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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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### 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 ...
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 ...