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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.

2
votes
3answers
570 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
votes
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
781 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
16k 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
votes
1answer
237 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 ...
-1
votes
1answer
419 views

multidimensional multinomial density [closed]

I have data set X = {x_1, x_2, \ldots, x_N}, each x_i is a d-dimensional vector, where scalars are from some finite field (In practice they are categories, represented by integers from 1...C). If ...
1
vote
5answers
926 views

Estimating the number of clusters

For a collection of points in $\mathbb{R}^n$, is there a statistic that I can compute which will estimate the number of clusters with some level of confidence?
0
votes
5answers
1k views

Is there a tool for finding probability distributions given some samples?

I'm looking for a tool that does "probability distribution fitting" given a set of data points. Sort of like curve fitting, but tries to fit to standard density distributions. For example if I input ...
9
votes
4answers
765 views

What m minimizes E(|m-X|^3) for a random variable X?

Let X be a random variable. Then E(|m-X|^1) is minimized when (as a function of m) when m is the median of X, and E(|m-X|^2) is minimized when m is the mean of x. A couple weeks ago in a technical ...
35
votes
12answers
16k views

Why is it so cool to square numbers (in terms of finding the standard deviation)?

When we want to find the standard deviation of $\{1,2,2,3,5\}$ we do $$\sigma = \sqrt{ {1 \over 5-1} \left( (1-2.6)^2 + (2-2.6)^2 + (2-2.6)^2 + (3-2.6)^2 + (5 - 2.6)^2 \right) } \approx 1.52$$. Why ...
2
votes
2answers
743 views

What is the difference between the Power Law and Zipf's Law?

I am new to statistics. Could somebody tell me what is the difference between a Power Law and Zipf's Law. The latter could be just for texts but I cant see any difference in their essence.