# Questions tagged [st.statistics]

Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

1,206 questions
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### How can I tell if y is a function of x in a random sample?

I have some data and believe that a given metric is a function of another metric. I have the values of both metrics and many different sets of these values. Can I tell if one is a function of the ...
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### Archaeogenetics

This question is meant to be applied to recover historic information from genetic data. The following model, is (probably) the simplest possible which takes recombinations into account. First, let ...
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### Building a multi-variable regression model [closed]

I have a large set of data points which have 18 dimensions to them. I know that these data points must follow a strict polynomial formula with no possible variance. Given that I have enough data (I ...
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### Linear Regression Confidence Interval

I am fitting a linear regression line to my data and computing the confidence interval for some predicted $y$ (independent variable) (http://people.stfx.ca/bliengme/ExcelTips/...
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### unbiased estimate of the variance of a weighted mean

I am trying to track down a formula (and derivation) for an unbiased estimate of the variance of a weighted mean. Wikipedia provides such a formula: http://en.wikipedia.org/wiki/Weighted_mean ...
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### Reference for elementary and “cool” statistics or financial math

I signed up for a Math Mentorship Program (for high school students) this term, but one of the students assigned to me is more interested in Statistics and Finance - something that would help him to ...
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### Do all correlation coefficients induce a pseudometric?

The Kendall tau distance was originally defined as a correlation coefficient. It seems clear to me that every metric function $d$ that is bounded by $b$, induces a correlation coefficient. That is: ...
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### Why isn't Likelihood a Probability Density Function?

I've been trying to get my head around why a likelihood isn't a probability density function. My understanding says that for an event $X$ and a model parameter $m$: $P(X|m)$ is a probability density ...
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### ANOVA analysis with no homogeneity of variances

I have conducted a within-subject user study. Each user works with 3 user interfaces and reads a couple of tweets in each UI and we record how many milliseconds they spend on reading each tweet/...
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### measure of quality of curve fit

I am interested in a measure for the quality of fit to a curve which would distinguish the two cases shown in the following image (without addressing the fact that incidentally the right one has more ...
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### Can you explain a step in an expectation maximization algorithm in a Nature article?

I am currently going through the following article: http://www.nature.com/nbt/journal/v26/n8/full/nbt1406.html In this article, how did they arrive at the values in the Estimation step (Figure 1 Step ...
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### Is there a text on estimation theory online?

Where can I find graduate level, thorough, parameter estimation/ estimation theory material on the web?
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### randomness in nature [closed]

What is the explanation of the apparent randomness of high-level phenomena in nature? For example the distribution of females vs. males in a population (I am referring to randomness in terms of the ...
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### for a natural exponential family, A is the cumulant function of h?

Reading "Monte Carlo Statistical Methods" by Robert and Casella, they mention that if $f(x) = h(x) \exp(\langle \theta, x \rangle - A(\theta))$ defines a family of distributions for $X$, parametrized ...
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### How does the Dirichlet process work?

Hi, i'm looking to get into nonparametric bayesian techniques but I'm having problem understanding what's going on in the definition of the Dirichlet process or how it works. So what does P ~ DP(&...
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### construct random variable with a fixed level of Spearman Coefficient to another

In my quest to understand all things Spearman, consider the following problem: Given random variable $x$ with known variance, $\sigma^2$, and $p \in [-1,1]$, one can construct a random variable $y$ ...
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### Algebraic Statistics textbook

Hey A friend and I are thinking of having an algebraic statistics seminar next semester. Does anyone know of a good book to try learn it out of?
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### Which fortuneteller is better

We have a probability game, where we have $N$ number of events, each of which outcome can be $A,B$ or $C$. We do/will NOT know real probabilities afterwards: only the discrete outcome ($A, B$ or $C$) ...
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### Calculating the “Most Helpful” review

How would you calculate the order of a list of reviews sorted by "Most Helpful" to "Least Helpful"? Here's an example inspired by product reviews on Amazon: Say a product has 8 total reviews and ...
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### What's an efficient way to calculate covariance for a large data set?

What is the best algorithm for computing covariance that would be accurate for a large number of values like 100,000 or more?
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### Finding correlation in large data, non-numeric sets

Suppose I collect a lot of data from a group of persons, like their height their weight color of eyes (chosen from eg the four categories blue/brown/black/other) sex day of the week the measurement ...
336 views

### Where can i find 'getting started' resources for statistical prediction

I wanted to learn prediction, forecasting etc. I also have time series data on millions of online videos. I would like to test out prediction algorithms etc on this data set, for eg. Linear Prediction,...
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### Is the min function ever an unbiased estimator for the mean?

Given n iid variables X1 to Xn with an unknown probability distribution, the sample average is an unbiased estimator for the mean of the distribution. Is there some non-trivial probability ...
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### How to present overlap of related sets [closed]

I have extracted URL links from a number of webpages and many of the webpages contain the same set of links (or subsets) as other webpages. I have ~1000 webpages and ~10 links per webpage. What is an ...
569 views

### When do binomial distributions occur?

A binomial distribution is the distribution of the number of successes of n independent, identical Bernoulli trials. What happens when the trials are dependent and the Bernoulli trials are not ...
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### What is hidden in Hidden Markov Models? [closed]

Why the word "hidden" present in hidden markov model? What exactly is hidden. Whatever is hidden in HMM isn't it hidden in normal Markov Models?
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### Parameter orthogonality (zeros in Fisher info matrix) in logistic regression and MLE

In the simplest logistic regression we model the (logit) probability of a 0/1 valued outcome as a (linear) function of some given 0/1 valued predictor (dummy) variables encoding membership in certain ...
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### Is it alright for STD error bars to be below zero?

I have some statistical data from which I want to graph the means and use the standard deviations as error bars. However this produces a graph with some of the error bars passing below zero. A ...
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### Something like mathoverflow in other sciences [closed]

Are the sites similar to mathoverflow in other sciences related to mathematics? statistics, computer science, physics, economics, etc? Let me explain what I mean by "similar": those are sites devoted ...
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### Error analysis of implicit functions

I'm trying to do propagation of error using the linearized variance method (assuming independent variables, thus no need for the covariance terms): \sigma^2_f = \sum^n_{k=0} \left(\frac{\partial f}{...
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### Quantifying Aggregate Vector Strength/Vector Arithmatic

Say I have 5 vectors and I measure the similarity of each one to a fixed reference vector using cosine similarity. But now what I want to do is understand the aggregate or collective strength of these ...
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### Question about orthogonal matching pursuit

Let y be a n-vector, X a n-by-p matrix of full rank (p < n) and b a p-vector, so that y = Xb + e, for some noise vector e. I am not sure how to show reduction of error in orthogonal matching ...