Questions tagged [probability]

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2
votes
1answer
229 views

Chinese Restaurant Process… Why?

I recently started to study non-parametric clustering methods and I come across to CRP. After reading all the material I found on the web there is one thing which is not completely clear to me: which ...
5
votes
2answers
625 views

Efficient computation of Markov chain transition probability matrix

Consider a continuous Markov chain $X=(X_t)$ on a finite state space and let $Q$ be the (given) transition rate matrix. This matrix is very sparse, with non-zero values on 3 diagonals only (so from ...
0
votes
1answer
101 views

sum of random variables, probability 101

Consider $n$ integer-valued and independent random variables $e_1, e_2, \dots, e_n$ with known distribution functions $m_1, m_2, \dots, m_n$. Let's denote with $E^{1..n}$ the random variable given by ...
2
votes
0answers
84 views

function over conditional probability

I need to create a scoring model out of estimated conditional probability functions for two events, A and B. Let 0.5 be the threshold value. Ideally, the probability is in the interval $[0,0.5)$ for A ...
5
votes
3answers
871 views

Computing the PDF of a quadratic function of two random variables

Given the function $\mathcal{M} = g + Ah + Bh^2$ where $A$ and $B$ are constants and $g$ and $h$ are random variables with their distributions $f_G(g)$ and $f_H(h)$ known, is it possible to compute ...
4
votes
1answer
371 views

Convert ODE into discrete probabilistic model

how can I turn an ODE equation into a discrete probabilistic model? I take for example the Verhulst equation for the growth of a population. $$\frac{dP}{dt} = rP(1-P/K)$$ I was thinking to simulate ...
10
votes
3answers
1k views

Drawing samples from a finite mixture of normal distributions?

After some Bayesian update steps, I am left with a posterior distribution of the form of a mixture of normal distributions,$$\Pr(\theta| \text{data} ) = \sum_{i=1}^k w_i N(\mu_i, \sigma^2).$$ That is, ...

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