Tagged Questions

161 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 ...
175 views

Estimate the rank of a vector

Consider {0,1}-vectors $v$ with $n$ elements. For each $i\in[n]$ we are given $p_i = P(v_i = 1)$ and let us assume the $v_i$ are independent. We can therefore associate a probability to each of the ...
88 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 ...
80 views

Random weighted selection without replacement

I am using the following procedure to select $m$ different numbers $\{i_1,\ldots,i_m\}$ from the set $\Omega = \{1,\ldots,N\}$, with $m,N\in\mathbb{N}$ such that $m< N$. Selection procedure ...
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 ...
99 views

Generating random weak k-bounded reverse plane partitions

Fix a partition $\lambda$. A weak reverse plane partition of shape $\lambda$ is a filling $0\leq \pi_{ij}$ of $\lambda$ with $\pi_{ij}\leq \pi_{kl}$ whenever $i\leq k$ or $j\leq l$. Note that ...
139 views

Uniformly sampling from the set of all simplicial maps

Let $K$ and $L$ be finite simplicial complexes that remain fixed throughout. How does one efficiently sample (according to the uniform distribution) elements from the finite set of simplicial ...
160 views

Set of distributions that minimize KL divergence,

Assuming that $p,q$ are probability distributions defined on the same support $\{x_i\}_{0 \leq i \leq n}$, $\epsilon$ a small real number, and $D_{KL}$ the Kullback-Leibler divergence, is there a ...
114 views

On understanding Discrete-Valued Stochastic Processes( time series, panel data )

It seems to me that a significant proportion of work in probability theory, statistics and machine learning are on understanding continuous-valued, relatively weakly dependent, or linear dependent ...
194 views

Giving a general term of a recursive function, and upper bound for it

Let a constant $B \ge 1$, and let $l_1 = 0$, $b_1 = 0$ be the values of $l$ and $b$ (respectively) at time $t = 1$. Let $l_{t+1} = l_t + 1$ if $b_i < B$, and $l_{t+1} = l_t$ otherwise Let ...
195 views

An optimization problem, non complete bipartite graph and hungarian algorithm

I have two tables at my disposal, one work dataset and one reference dataset. Each dataset has got two columns, lets say these are fields A and B. I would like the rows in reference dataset with the ...
110 views

Median-of-k elements

Hello, Assume I am given a sequence of $n$ elements (by sequence I mean an ordered set). I want to randomly pick $k$ elements out of these $n$ elements, where $k$ is an odd number $\leq n$. Then out ...
473 views

Randomized algorithm?

The problem is as follows. Given a set $S$ of natural numbers of size $n$ where each $x_i \in S$ is from the set $[n^2]$. Elements of $S$ are not necessarily pairwise different, i.e., there can be ...
280 views

Terrain Generation: Infinite 2D space filled with Diffusion-limited aggregation clusters?

Disclaimer: I don't have a deep understanding of fractals or any higher math, I'm just personally interested in it, so please excuse me if I'm using wrong terms or if I'm being inaccurate. Making ...
353 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 ...
581 views

How I determine the probability that an unknown probability value is greater than others in a set?

I have a number of known beta distributions for different unknown probability values. Given the beta distributions, I want to determine the probability that each specific unknown probability values ...
523 views

Optimally directing switches for a random walk

If you are sometimes called upon directing a random walk in a directed graph, how should you direct it so as to maximize the probability it goes where you want? Formal statement More specifically, ...
226 views

Probability of Outcomes Algorithm

I have a probability problem, which I need to simulate in a reasonable amount of time. In it's simplified form, I have 30 unfair coins each with a different known probability. I then want to ask ...
1k views

Does an “efficient” random number generator exist?

Given some number $n$ and a seed number $s$<$n$, I want a random number generator (RNG) that will go through all integers `<$n$ before coming back to $s$. The resulting random number must be ...
265 views

Comparing normally distributed variables

Given two normally distributed variables x_1, x_2, is there a non-simulation method of calculating the probability that ...
80 views

The mathematics of Schellings segregation model

For those who don't know the model. You can read this pdf. I want to find what is the probability that 2 nodes are each others neighbors when the algorithm converges (i.e. when all nodes are happy). ...
181 views

understanding some derivation in random XORSAT problem

This question is concerned about the paper "The 3-XORSAT threshold" by O. Dubois, J.Mandler. Here is the link: http://dx.doi.org/10.1016/S1631-073X(02)02563-3 Basically one would like to know when is ...
451 views

When can a freely moving sphere escape from a 'cage' defined by a set of impassible coordinates?

To ask this question in a (hopefully) more direct way: Please imagine that I take a freely moving ball in 3-space and create a 'cage' around it by defining a set of impassible coordinates, $S_c$ ...