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0
votes
1answer
35 views

Probability of reconstructing a word using c substrings from a random sample

Consider a voice recording split into it's phonemes as our sample $S=(s_1,...,s_k) \in \Omega = P^k$. The number of phonemes is $|P| = 40$. Then I have a word $w = (w_1,...,w_n) \in P^n$. I want to ...
4
votes
1answer
52 views

Efficient and stable computation of inverse CDF

What is the most efficient and numerically stable algorithm for computing the inverse CDF $F^{-1}(y)$ of a probability function, assuming that both the PDF $f(x)$ and the CDF $F(x)$ are known ...
7
votes
2answers
182 views

Learning parameters of noise and filter coefficients from data where data and noise both have Gaussian distributions

Assume $X$ and $N$ are two sets of vectors (observations) from two different normal distributions, where $X$ represents clean data and $N$ represents noise; and $A$ a projection matrix of a filter. ...
1
vote
0answers
36 views

Probabilistic model to approach problem that is usually dealt with linear programming

I have the following problem. Let's say we have $x_{jk}$ it is an expression value of gene $j$ in a sample $k$. It is the average of expression levels across the cell types $s_{ij}$, weighted by ...
0
votes
0answers
12 views

Assigning new values based on original guesstimates and ranking / ordering?

Lets say we have two things as input, $N$ scalars (measurements) that we know are erroneous to some degree (i.e. the correct values are somewhat similar). In addition, we also have a roughly more ...
3
votes
1answer
646 views

How do I generate maxwell-boltzmann variates using a uniform distribution random number generator?

I am doing a molecular dynamics simulation. I need to assign initial velocities to the atoms. I want to assign the initial velocities which follow the maxwell-boltzmann distribution. How do I ...
1
vote
0answers
72 views

Simple MCMC Algorithm in Matlab

I would be really glad to get some specific advise on how to implement a simple MCMC algorithm (in Matlab, if possible). I'm not yet too familiar with optimization methods. My problem goes as follows: ...
0
votes
0answers
85 views

Cyclic Coordinate Descent Optimization for Bayes Logistic Regression (Code Problem?)

I am trying to reproduce the CLG algorithm for the Laplace prior given in Genkin et al to find the MAP estimates for a logistic regression model. I am using Python (Anaconda 2.2) with Numpy to ...
2
votes
1answer
84 views

Metropolis Monte Carlo integration of Area with unknown normalization

I probably miss something very basic. I don't see how to use Metropolis–Hastings algorithm for computation of integrals, if I don't know the volume of accessible phase space (i.e. proper normalization ...
2
votes
1answer
129 views

solving for unknown inside an expectation

I have a an equation that need to find its root. The function is the following $f(\theta) \equiv E[R(\theta;\eta)]=0$ for some unknown $\theta$ which is deterministic, while the expectation is taken ...
2
votes
2answers
134 views

Python: What is a good way to generate a 1D particle field with a gaussian distribution?

If I have N particles how do I assign their x values so that the end result is Gaussian distribution. i.e. particles near the ends are more spread out than particles near the center.
2
votes
2answers
130 views

Extracting time scales information from empirical cumulative distribution function

I have a stochastic process (a Markov chain actually) that has two absorbing states. I am using a difference equation to calculate the first passage time to either of the absorbing states. There are ...
1
vote
1answer
244 views

Coding complex equations into C++

I have here equations from a paper by E. Bradlow. They're for counting the events in a Weibull-distributed data set. $$\begin{align} \Pr(N(t)=n) &= \sum_{j=n}^\infty{\frac{(-1)^{j+n}(\lambda ...
1
vote
2answers
6k views

How to plot probability density function in MATLAB?

I'm trying to get a frequency plot, or PDF (probability density function) plot for my biometrics project in MATLAB. I have two vectors genuine_scores and ...
2
votes
2answers
579 views

visualization of 3D probability flow

I have a master equation for $P(N_A^+,N_B^+,N_C^+,t)$, with $N_A^+,N_B^+,N_C^+$ all discrete. The numerical integration is done by this Matlab program using Euler's method. Despite the crude Euler's ...
2
votes
0answers
23 views

Approximate convolution of independent Beta variates?

Is there a way to approximate the convolution of Beta variables? Specifically, I am trying to find an approximation to $g(x_0)$: $$g(x_0) = \int \delta(x_0-\sum_{i=1}^{n} a_i x_i) \prod_{i=1}^{n} ...
2
votes
3answers
107 views

Hash in set probability?

First off I would like to mention that I am absolutely terrible at statistics... so bear with me please. The question: a sha1 hash is a hexadecimal string of 40 characters, the largest number being: ...
10
votes
2answers
2k views

How do I plot the surface of a 4D plot?

I am trying to plot the wave function for a particle in a 3D box. This requires me to plot 4 variables: x, y, z axes and the probability density function. The probability density function is: ...
2
votes
1answer
113 views

Multiple independent random number streams

Having multiple streams of pseudo-random numbers known to be independent and with a uniform distribution I want to do Monte Carlo simulations in parallel. In other words, one thread will have a ...
5
votes
3answers
705 views

How to sample numerically from an arbitrary smooth distribution?

I'm given a smooth probability density function via its values on a reasonable fine grid. I assume that cubic spline interpolation (or cubic spline interpolation of the logarithm of the density) will ...
2
votes
1answer
172 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 ...
3
votes
2answers
495 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
79 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
78 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
446 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
213 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
2answers
4k views

Define custom probability density function in Python

Is there a way, using some established Python package (e.g. SciPy) to define my own probability density function (without any prior data, just $f(x) = a x + b$), so I can then make calculations with ...
5
votes
1answer
1k views

How can I generate half-normal variates in MATLAB?

I can find the random('normal', 0, 1, 10000,1) command in MATLAB but it generates half-normal variates. I would like to generate random half-normal variates. The ...
9
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, ...