Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [diffusion]

20 questions
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What is tantile regression?

My question follows on this discussion of medials and tantiles vs medians and quantiles from earlier this year: When would we use tantiles and the medial, rather than quantiles and the median? As described in the link, medials are a measure of…
Mike Hunter
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Theoretical link between the graph diffusion/heat kernel and spectral clustering

The graph diffusion kernel of a Graph is the exponential of its Laplacian $\exp(-\beta L)$ (or a similar expression depending on how you define the kernel). If you have labels on some vertices, you can get labels on the rest of the vertices by a…
highBandWidth
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Increase the number of samples when the PDF is invariant

Background: $$\frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2}$$ is given by Fick's second law, in which $D$ is the diffusion coefficient. The solution to this equation (given the initial condition) $C(x, t)$ is the probability…
meTchaikovsky
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Diffusion coefficient from double-normal probability density function

The spread of individuals of species is often described by so-called dispersal kernels. The main parameter of spread is then often the variance defined as the average squared movement distance of a specimen per time step (assuming all specimen start…
Johannes
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Probability distribution of the magnitude of a circular bivariate random variable?

I'm very new to this topic. I have a distribution similar to the picture below but with the center at zero. As I said, I'm very new to this, but if I understand correctly, if there was no hole in the middle, the probability distribution of the…
Maria
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Carré du champ operator is a quadratic variation

Let $X_t$ be a real valued Markov process (starting at $x$) with generator $L$. Let $\Gamma(f)$ denote Carré du champ operator i.e. $L(f^2) - 2f \cdot L (f)$. As far as I know under suitable regularity assumptions: $$ M_t^2 - \int_{0}^{t}…
marcusy
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What is the likelihood function of the starting time of diffusion?

I need to find the likelihood that a set of molecules was instantaneously released at time $t_0$, say $t_0=0$. Toy System Example: Let $N$ be the set of molecules released from a specific point in a 3D environment. The released molecules diffuse in…
nashynash
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How to apply the diffusion maps when the matrix is PSD but not positivity preserving?

In order to apply the diffusion maps in a matrix $C\in\mathbb R^{n\times n}$ , that matrix must obey some restrictions, C is symmetric: $C_{ij} = C_{ji}$, C is positivity preserving (PP): $\forall i, j$, $C_{ij}\ge0$, C is positive semi-definite…
daemon
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What is the distribution of the peak time of the first hitting time process

I need to find the distribution of the random variable $T_{peak}$ where $T_{peak}$ represents the peak time of the first hitting time process. Detailed Explanation of the System: There are $N^{Tx}$ amount of emitted molecules from a specific point…
fermat4214
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Stochastic Differential equation: CAPM

Let $R = (R_1, \dots , R_M)'$ denote a vector of excess returns of $M$ assets observed at $n$ time points, $0 < t_1 < t_2 < \cdots < t_n < T$, within a time span $T > 0$. We wish to explain the returns through a set of $J$ common tradeable factors,…
bardwell
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How to simulate anomalous diffusion of a 1D point like particle?

I want to simulate 3 types of diffusion processes: normal diffusion $[\langle x^2(t)\rangle \propto t ]$. subdiffusion $[\langle x^2(t)\rangle \propto t^\alpha ; \alpha<1 ]$ superdiffusion $[\langle x^2(t)\rangle \propto t^\alpha ; \alpha>1]$ I…
0x90
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Fit drift diffusion model with trial-type dependent input strength

I want to fit a drift diffusion model to a task which involves multiple decisions (n=400) between two different valuable choice options . I do understand how I would do that in general, also with the help of that great tutorial…
Laurie
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Diffusion tensor as a covariance matrix

TLDR: In nuclear magnetic resonance (NMR), to study molecular diffusion we assume that molecules displace in 3D space according to a trivariate gaussian distribution. The variables are then the displacements along the 3 directions and the "diffusion…
user241848
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Computing properties of non-uniform random walk/diffusion

I have a lot of numerical data which I'm looking to characterise as a (possibly continuous) random walk with variable (in space) step size, for example, along $x$ between $-1$ and $1$ with a step size of $1-x^2$. In particular I'm interested in the…
Sean D
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2 Dimensional Random Walk Simulation

I am trying to simulate random diffusion of particles using a random walk diffusion model. I have used probabilities of movement of particles in a 2D area, to be 1/4 in all 4 directions. The confusion that I am having is whether to assign the corner…
Rizwan Ali
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