# 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.

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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 ...

**13**

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**2**answers

611 views

### 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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votes

**2**answers

304 views

### 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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votes

**5**answers

3k views

### 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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votes

**4**answers

14k views

### 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
...

**4**

votes

**7**answers

876 views

### 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 ...

**3**

votes

**1**answer

457 views

### 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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votes

**7**answers

15k views

### 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 ...

**4**

votes

**3**answers

2k views

### 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/...

**9**

votes

**2**answers

541 views

### Integrating a simple exponential over the space of matrices that define a metric

I want to interpret an $n\times n$ matrix $D$ as a set of pairwise distances, and assume that $D$ obeys metric properties. Namely, $D_{ii} = 0$, $D_{ij} \geq 0$, $D_{ij} = D_{ji}$ and $D_{ij} \leq D_{...

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votes

**2**answers

5k views

### Difference between Beta Process and Dirichlet process

I'm trying to understand the definition of a Beta process, as given in the paper:
www.ece.duke.edu/~lcarin/Paisley_BP-FA_ICML.pdf
The problem is that from the definition it follows that every ...

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**7**answers

4k views

### Uniformly Sampling from Convex Polytopes

How to choose a point uniformly from a convex polytope $P \subset [0,1]^n$ defined by some inequalities, $Ax < b$? (Here $A$ is an $m \times n$ matrix, $x \in \mathbb{R}^n$, and $b \in \mathbb{R}^...

**5**

votes

**3**answers

3k views

### 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 ...

**1**

vote

**2**answers

964 views

### 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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vote

**1**answer

290 views

### 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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2k views

### 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 ...

**1**

vote

**1**answer

256 views

### 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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votes

**3**answers

514 views

### 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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votes

**1**answer

279 views

### 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 $y$ ...

**3**

votes

**2**answers

2k views

### Population Spearman Rank Correlation Coefficient

I am doing some research on the Spearman Rank Correlation Coefficient; all the references I can find refer essentially to a sample statistic. That is, given a sample of the jointly distributed $(x_i,...

**2**

votes

**2**answers

485 views

### A variant of the hypergeometric distribution - in the literature?

I have been working on a problem in combinatorics that makes use of the following discrete distribution.
Let $a_{1}, a_{2},..., a_{N}$ be any binary sequence of of length $N$ with $n$ ones and $m$ ...

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votes

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485 views

### Monte Carlo simulations

I was wondering what were the models of statistical physics that are still considered difficult/slow to simulate (exactly, or approximately) with the current technology of Monte Carlo approaches. I ...

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votes

**0**answers

426 views

### A Local CLT with large variance

For n an even integer, $0 \leq i \leq$ ${n} \choose{j}$, $1 \leq j \leq n$ let $X_{i,j}$ be a
random variable taking values $\frac{n}{2}-j,0,j - \frac{n}{2}$ with equal probability. Let $S_{n}$ be ...

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votes

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1k views

### Martingales and Betting Strategies

Does anyone know of a good introduction to the theory of martingales and betting strategies from the point of view of statistics and/or probability theory? I'm looking for something basic, with lots ...

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votes

**6**answers

463 views

### Chances to win an election

Let's say that tomorrow national president election is held. A poll asks 1100 persons which of the two candidates, A or B, will he or she will vote. 750 say will vote A, and 250 say will vote B. What ...

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votes

**2**answers

587 views

### What's the standard name for sets of a given size with maximal probability (or a given probability and minimal size)?

The definition I'm going to give isn't quite the concept I really want, but it's a good approximation. I don't want to make the definition too technical and specific because if there's a standard name ...

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votes

**1**answer

344 views

### Parity, Balls and Boxes

Start with a distribution $\mu$ on [n], and drop m balls into these n+1 slots independently and according to the distribution &mu. That is, we have iid random variables x 1 through x m ...

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votes

**1**answer

685 views

### Introduction to Structural Equation Modeling

Can you suggest an introduction to structural equation modeling for math majors and mathematicians?

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votes

**5**answers

2k views

### Computing correlation between time series with missing data.

Suppose you have two simple Ar[1] series of the form $y_n=y_{n-1}+e_n$ and $x_n=x_{n-1}+m_n$, where $e_n$ and $m_n$ are normal white noise processes with no auto-correlation and $Corr(e_n,m_n)=p$. ...

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votes

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2k views

### Regression problem/detect outliers

I am doing a linear regression problem. It is a multivariate one and I do not know how to detect outliers because it is multivariate and the scatter graph will not help. Any suggestions?

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votes

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237 views

### determining a fair betting scheme

Preface: I think this is interesting (and hopefully at least one other mathematician will agree!), but it's entirely possible that y'all will consider this too low-brow for MO. There isn't a ...

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1k views

### How long for a simple random walk to exceed $\sqrt{T}$?

Let $R_n$ be a simple random walk with $R_0 = 0$, and let $T$ be the smallest index such that $k\sqrt{T} < |R_T|$ for some positive $k$.
What is an expression for the probability distribution of $...

**4**

votes

**2**answers

1k views

### 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?

**2**

votes

**4**answers

635 views

### 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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votes

**3**answers

9k views

### 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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votes

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4k views

### 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 ...

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votes

**4**answers

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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vote

**2**answers

492 views

### 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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votes

**2**answers

424 views

### 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 ...

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votes

**3**answers

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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1k views

### 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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vote

**1**answer

780 views

### 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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votes

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15k views

### 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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3k views

### 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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votes

**3**answers

1k views

### 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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vote

**1**answer

622 views

### 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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votes

**1**answer

794 views

### 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 ...

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votes

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600 views

### Data Mining— How do You Know Whether The Pattern You Extract is Valid?

I've been asking myself this question all the time. Let's say you are given a large set of time series data. Your task is to find out patterns that are meaningful or that you can use for future trend ...

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votes

**1**answer

235 views

### Correlation measure between signals of different dimensions?

I have several temporal signals of different dimensions, for example the motion of a point throughout time which would be of dimension 3, and the value of a temperature sensor, of dimension 1.
I ...