3
votes
1answer
162 views

An efficient method to find the MLE of the combination of two point processes

I have a point process defined in two parts as follows. Consider first the main process which we call $A$ which is homogeneous Poisson process with conditional intensity $$\lambda(t) = \mu$$ For ...
1
vote
0answers
19 views

Minimal rectangular confidence regions

For a given multivariate pdf $f$ (mainly the gaussian one) I'm looking to compute a minimal rectangular confidence region for a given level $\alpha$. For example, I would like to solve problems of the ...
2
votes
2answers
89 views

Sampling from maximally skewed stable distribution

I am reading a paper which refers to a maximally skewed stable distribution $F(x;1,-1,\pi/2,0)$ . Is there an efficient way to sample from this distribution? If $X$ has distribution ...
2
votes
0answers
58 views

Smallest distribution of points with genuinely different clusterings

An hierarchical clustering algorithm for (finite) sets of points in a given metric space is essentially determined by its linkage criterion, which defines the distance between arbitrary (finite) sets ...
3
votes
1answer
168 views

How to perform Importance Sampling with Prior Information

Let us define a random variable $X$ with density function $p(x)$. We wish to calculate $\mathbb{E}[f(X)] = \int f(x)p(x)dx$. We can compute the expectation by Monte Carlo simulations as ...
0
votes
1answer
102 views

What is the Bahadur-Anderson Algorithm?

What is the Bahadur-Anderson Algorithm, and which book could one read to learn it?
0
votes
2answers
258 views

Creating composite rank [closed]

Problem: Suppose that $K$ different students are ranked based on $N$ different parameters (such as Physics marks, English marks, Biology marks, IQ etc). The rank under each parameter can be repetitive ...
0
votes
2answers
363 views

Is there a method to find (fit) a function with four (4) independent variables?

I have a system with 4 sensors (say $s_1..s_4$) which I want to combine into a single signal. I have logged the 4 outputs as well as a "control" sensor ($s_c$) which has the desired ouput signal. ...
6
votes
2answers
345 views

finding the $n$ closest pairs between $2n$ points

Given $2n$ points $x_1, x_2 \ldots x_{2n}$ and a distance $d_{i,j}$ defined between them, how can I best find the set $P$ of mutually exclusive pairs $(i,j)$ such that the sum of their distances $$ ...
1
vote
3answers
763 views

Concrete examples concerning standard deviations and mean absolute deviations

Once again stackexchange is not responding to one of my questions (so far no comments, no answers, two up-votes). Hence this "crossposting": Is there a simple (or not simple?) algorithm that will ...
4
votes
2answers
3k views

Numerically most robust way to compute sum of products (standard deviation) in floating-point?

I stumbled across a paper by Welford (1962), where he proclaims a method that should compute the standard deviation numerically more robust than the naive algorithms ...
4
votes
3answers
354 views

Probability estimates for “beans & boxes”

From a discussion with some friends, this apparently easy problem has come out; I decided to post it here, because I believe that the answer is non-trivial and the maths beneath interesting. Partial ...
3
votes
4answers
767 views

Question about this ratio in Metropolis-Hastings MCMC algorithm

I have a stupid question about the Metropolis-Hastings sampling algorithm. If I got this right, for every variable $X$ in turn, which currently has value $x_{old}$, you generate a new sample ...
1
vote
2answers
161 views

Finding a representative of a branch in hierarchical clustering

I have constructed a hierarchical clustering of data using some proximity function. Now I would like to calculate a representative value of any given node of this clustering, such that it reflects the ...