Questions tagged [probability]
For computation questions involving computing probabilities or simulating probabilistic processes.
66
questions
1
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0
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27
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SageMath: How do I plot the sum of a deterministic variable and a random variable
Suppose I have the following function
$$f(x,y,z1,z2)=g(x-z1,y-z2)$$
where $g(x,y)$ is a deterministic function from the $X\times Y\to S$ and $z1,z2$ are random variables following a known probability ...
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-1
votes
1
answer
26
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How to generate p Sample of GGM of dimension m, for parameter : the weight, the means and the covariance?
after searching in the python numpy, scipy and sklearn module, there is no function who can generate p samples of a gmm (gaussian mixture model) for parameter means, covariances and the weight of each ...
- 1
0
votes
0
answers
33
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Algorithm for Probabilities in a "Random" Integers Runs test
Suppose you have a set of N random integers. ( aka bytes 0..255 )
You then consider each subsequent neighbor as "ascending" or "descending", counting the number of consecutive ...
1
vote
0
answers
38
views
Sampling points from space based on known density
I have a problem where I heavily need to restrict the number of points at which I sample a function based on the values of a different function.
I have two functions:
$f:{\mathbb{R}\times [0,\infty)\...
1
vote
0
answers
29
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Non-Linear Distributed Delayed Kalman Filter
I have a system $\vec{x}_{i + 1} = \vec{x}_i + W_i$ where $W = N(\vec{\mu}, \Sigma)$. For some matrix $H_i$, let $y_i = H_i$ and let $z_i = y_i + R$. Where $R$ is some random variable. We are given $...
- 23
0
votes
0
answers
55
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Finding optimal values from multiple parameter estimation runs
I've performed a parameter estimation repeat (i.e. 1000 parallel runs with the same
initial values of parameters). I am trying to estimate ~20 parameters using measurements from experiments.
After ...
- 411
1
vote
1
answer
85
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What are the Exact Rules for Significant Figures, Precision, and Uncertainty?
In the physical sciences (which are physics, chemistry, astronomy, materials science, etc.), we learned that the uncertainty is +/- the smallest unit (which is 1) of the last significant figure if the ...
6
votes
1
answer
730
views
Estimate the number of self-avoiding walks of length $n$
For the past couple of days, I have been thinking a lot and searching online for an algorithm capable of estimating the number of Self-Avoiding Walks (SAW) of length $n$ in $\mathbb{Z}^2$. There is a ...
- 63
3
votes
1
answer
297
views
Importance Sampling for multidimensional integrals and random numbers from multivariable pdf's
I am aiming to get a numerical value for a five-dimensional integral using Monte Carlo Integration. I am getting good results using the Mean Value Method, but I would like to try to use Importance ...
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-1
votes
1
answer
97
views
Generating Rvs for a given PDf in python
Two random variables $X$ and $Y$ are distributed according to
\begin{align}
f_{XY}(x,y)= \begin{cases}
x+y & 0\leq x \leq 1, 0\leq y \leq 1 \\
0 & otherwise
\end{cases}
\end{align}
I ...
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0
votes
0
answers
20
views
Probability Density Function of DNS velocity field [duplicate]
I am currently working on a DNS turbulent solver and I would like to compare my IHT simulations to papers. Those papers show the Probability Density Function of the velocity field:
I would like to ...
- 1
1
vote
1
answer
152
views
Define continuous, non-analytical pdfs in python
I am planning to do some basic algebra on continuous, non-analytical random variabels. I want to define their probability density functions as arrays x and f(x).
Yet, I was surprised to find out that ...
- 159
1
vote
0
answers
93
views
N-dimensional optimization of moments of distribution function
Let's say I have a bag of marbles. Each marble has several attributes (color, diameter, surface roughness, weight).
I know that there is a statistical relationship between various marble attributes ...
- 173
0
votes
2
answers
248
views
Different questions about "Inverse Physics problems"
I am in a context of forecasts in astrophysics. Don't be too rude if questions seem to you stupid or naive but rather indulgent, I am just looking for better undertsand all these numerical methods of ...
user14831
5
votes
1
answer
339
views
Non-negative least squares with very small numbers
(I have asked this question on StackOverflow previously but it has been pointed to me that CSSE or MSE could be more appropriate)
I have to solve a constrained optimization problem of the following ...
- 51
1
vote
0
answers
36
views
Combining many probabilities, modifying, seeking general formula
CONTEXT
I need to combine the probability of occurrence of many thousands of events for millions of individuals (trees) in an agent-based/individual-based simulation model developed in NetLogo (agent-...
- 11
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votes
2
answers
541
views
How to solve system of equations with almost-zero determinant?
I have a system of equations that I am trying to solve. In matrix form, it's written as
$$x(I - S) = b.$$
I am solving for $x$, where $I$ is the identity matrix and $S$ is a matrix where each column ...
- 119
1
vote
0
answers
71
views
How to simulate a PDF using data samples like this?
I know two methods to simulate a PDF from random data samples using MATLAB :
1) Using a histogram where I use this command
histogram(data,'Normalization','pdf'), it gives PDF like bins.
2) Another ...
- 151
0
votes
1
answer
70
views
Change of random variables and check by plot
Question
As a test, I transform a uniform distribution over the unit square.
But when I check the transformed distribution with Monte Carlo, it is wrong.
What went wrong?
Thanks.
Problem
Random ...
- 163
2
votes
0
answers
123
views
difference between PLSA and LDA
What is the difference between Probabilistic Latent Semantic Analysis(pLSA) and Latent Dirichlet Allocation (LDA)?
- 21
2
votes
1
answer
107
views
How to add extra constraints to a linear system for probabilities？
Background：
I have an equation which looks like as follows:
$W \times P = R$
$$\left[\begin{array} &{1}&{0}&{0}&-\frac{w_{1}}{w_{o1}} &\dots &{0} &-\frac{w_{1}}{w_{0} } \...
- 123
2
votes
1
answer
362
views
Numerical integration of Fokker-Planck equation allowing for negative drift?
The Fokker-Planck equation (a.k.a Kolmogorov forward equation or Smoluchowski equation) describes the evolution of a probability density function and numerical integration of the FPE should conserve ...
- 123
1
vote
0
answers
56
views
Uniformly sample a point per polytope
I want to uniformly sample a point within each of $10^5$ convex polytopes in each iteration of a solver.
The polytopes in one iteration are completely different from the polytopes in another iteration....
- 163
3
votes
1
answer
124
views
GPGPU/FPGA programming for Combinatorial Analysis
Recently, I have taken an interest in performing combinatorial analysis for the game of 21 (blackjack) and attempted to use my AMD APU to try and thread the program via the 4 cores on the chip. ...
- 31
2
votes
1
answer
339
views
Finding probability vectors from an implicit equation
I have $q$ $n$-dimensional vectors $\vec y_i$ and a matrix $\hat B$ of shape $n\times m$. I'm looking for $q$ $m$-dimensional vectors $\vec x_i$ such that:
$\vec y_i=\hat B \vec x_i$
each vector $\...
- 23
3
votes
0
answers
53
views
Book Suggestion for Approximating Integrals using Random Partitions
Suppose I want to approximate the integral $\int_0^1 x^2\,dx$ using Riemann Sums or Darboux sums over random partitions of the interval $[0,1]$, Like in the image below:
Here, A "random" partition of ...
- 131
5
votes
1
answer
170
views
Kernel-based differentiation
Consider a $\mathcal{C}^1$ function $V:\Omega\rightarrow\mathbb{R}$ where $\Omega\subset\mathbb{R}^n$. If a random vector $X$ has a parametric density $p_\theta(\textbf{x})$ that's smooth in its ...
- 211
2
votes
1
answer
54
views
Verifying that ODE integration generates Theoretical Stationary distribution
I am trying to simulate an ODE, like $ \dot{x} = \xi(x) $ that should have a stationary distribution (a la Stat Mech). Assuming that my ODE algorithm generates time samples of my system state $ x $ ...
user23933
2
votes
0
answers
47
views
Deterministic method to compute "Process noise covariance matrix, Q" for a Kalman filter when parameter variations of the model is known apriori
I am implementing a Kalman filter (for a linear ODE system for now).
My model represents a physical device that has 6 "parameters", i.e. those values of the device do not evolve over time (within a ...
0
votes
1
answer
103
views
What is the expected value of area of intersection of a circle and a rectangle
$r$: cicle C1's radius
$w$,$h$: rectangle R1's edges: $x=w$, $y=h$, $x=0$, $y=0$
$(w>2r, h>2r)$
$S(x,y)$: area of ...
0
votes
2
answers
5k
views
How to generate Poisson-distributed random numbers quickly and accurately?
I have attempted to create Poisson-distributed random numbers, seeing that it is not so easy as the simple multiplicative algorithm works accurately only if the mean is less than 500. Using logarithms ...
- 151
1
vote
1
answer
145
views
How is KDE used in stochastic tomography
I am currently writing my masters thesis and my topic also touches on Stochastic Tomography for volume reconstruction presented in this
paper. Now i understand most of the process described, but i ...
- 113
3
votes
0
answers
143
views
Closed form PDF/CDF using Orthogonal Polynomial Expansion (gPC)
Consider a random variable which is given by an orthogonal polynomial expansion in one parameter (or polynomial chaos expansion PCE), i.e. ,
$$ f(\alpha) = \sum\limits_{n=0}^{\infty} \hat{f} (n) \psi ...
- 245
1
vote
0
answers
118
views
Numerically compute PDF given a function
Consider $[0,1]$ with the Lebesgue measure $m$ and $f:[0,1]\to \mathbb{R}$, and $x$ a uniformly distributed random variable in $[0,1]$. Then, $f(x)$ itself define a new random variable.
We can then ...
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2
votes
1
answer
73
views
Using physical parameter as a Gaussian random variable in a simple Poisson problem
I want to vary the input parameter of a physical dynamic mechanics problem, as a Gaussian Random variable and view the resulting Probability Density Function (PDF). I used the Finite Element Method to ...
- 347
2
votes
1
answer
426
views
Optimize custom probability distribution in Python [closed]
Consider random variables $X$ and $Y$, their distributions are given. $Z = f_a(X, Y)$ where $f(\cdot, \cdot)$ is a deterministic, not random function $f_a: \mathbb{R}^2 \to \mathbb{R}$ depending on a ...
- 121
2
votes
0
answers
474
views
Numerical methods for calculating the inverse CDF when closed form approximation not available
I need to calculate the inverse CDF for a probability distribution, however there is no closed form approximation available in the literature.
The distribution I am working with is the Normal Inverse ...
- 121
2
votes
1
answer
200
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 ...
- 121
5
votes
1
answer
759
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 ...
- 183
7
votes
2
answers
239
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. ...
- 195
1
vote
0
answers
45
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 ...
- 111
0
votes
0
answers
21
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 ...
- 113
6
votes
1
answer
11k
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 ...
- 203
1
vote
0
answers
192
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:
...
- 11
2
votes
1
answer
292
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 ...
- 907
4
votes
1
answer
173
views
solving for unknown inside an expectation
I need to find roots for the following function:
$$f(\theta) \equiv E[R(\theta;\eta)]=0$$
for some unknown $\theta$ which is deterministic, while the expectation is taken over a normally ...
- 235
3
votes
1
answer
157
views
Computing expectations
I want to compute the following conditional expectation
$E_{t}[\phi(A_{t+1}, \eta_{t+1})| A_t]$
where $\log A_{t}=\rho \log A_{t-1} + e_{t}$ and $e_{t}$ is IID $N~(0,\sigma_e)$ and $\eta_{t}$ is ...
- 235
2
votes
2
answers
905
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
2
answers
377
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 ...
- 279
1
vote
1
answer
1k
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 t^c)^...
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