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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.

3
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4answers
3k views

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
votes
2answers
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 ...
0
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2answers
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 ...
2
votes
5answers
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/...
3
votes
4answers
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
7answers
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
1answer
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: ...
12
votes
7answers
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
3answers
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
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2answers
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_{...
4
votes
2answers
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 ...
13
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7answers
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}^...
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votes
3answers
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
2answers
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 ...
1
vote
1answer
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?
7
votes
3answers
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
1answer
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 ...
2
votes
3answers
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(&...
2
votes
1answer
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
2answers
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
2answers
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 $m$ ...
3
votes
2answers
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 ...
4
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0answers
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 ...
3
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5answers
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 ...
-1
votes
6answers
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 ...
7
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2answers
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 ...
2
votes
1answer
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 ...
0
votes
1answer
685 views

Introduction to Structural Equation Modeling

Can you suggest an introduction to structural equation modeling for math majors and mathematicians?
4
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5answers
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 $Corr(e_n,m_n)=p$. ...
-1
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6answers
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?
2
votes
2answers
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 ...
12
votes
4answers
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
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2answers
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?
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4answers
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 $C$) ...
17
votes
2answers
2k views

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 ...
8
votes
3answers
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?
3
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2answers
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 ...
2
votes
4answers
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,...
1
vote
2answers
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 ...
0
votes
2answers
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 ...
2
votes
3answers
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 ...
11
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5answers
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?
1
vote
1answer
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 ...
2
votes
4answers
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 ...
5
votes
2answers
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 ...
3
votes
3answers
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}{...
1
vote
1answer
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 ...
2
votes
1answer
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 ...
7
votes
6answers
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 ...
0
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1answer
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 ...