# Questions tagged [probability]

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### 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 ...
39 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 ...
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 ...
81 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 ...
90 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 ...
236 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 ...
235 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 ...
24 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-...
200 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 ...
27 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 ...
19 views

### I have a trouble determining appropriate transition matrix

M.Sc students of the Department of statistics, FUTA are expected to do course work for a year and write their thesis the following year before graduating. A student has a probability of 0.25 of ...
58 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 ...
98 views

### difference between PLSA and LDA

What is the difference between Probabilistic Latent Semantic Analysis(pLSA) and Latent Dirichlet Allocation (LDA)?
86 views

110 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 ...
63 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 ...
295 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 ...
393 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 ...
194 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 ...
537 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 ...
225 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. ...
43 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 ...
20 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 ...
9k 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 ...
169 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: ...
245 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 ...
162 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 ...
150 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 ...
746 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.
337 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 ...
1k views

130 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: ...
10k 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: ...