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The process is named after the statistician David Cox, who first published the model in 1955. [ 1 ] Cox processes are used to generate simulations of spike trains (the sequence of action potentials generated by a neuron ), [ 2 ] and also in financial mathematics where they produce a "useful framework for modeling prices of financial instruments ...
Plot with random data showing heteroscedasticity: The variance of the y-values of the dots increases with increasing values of x. In statistics, a sequence of random variables is homoscedastic (/ ˌ h oʊ m oʊ s k ə ˈ d æ s t ɪ k /) if all its random variables have the same finite variance; this is also known as homogeneity of variance ...
However, direct output from computer simulations of the atmosphere needs calibration before it can be meaningfully compared with observations of weather variables. This calibration process is often known as model output statistics (MOS). The simplest form of such calibration is to correct biases, using a bias correction calculated from past ...
The term random function is also used to refer to a stochastic or random process, [25] [26] because a stochastic process can also be interpreted as a random element in a function space. [27] [28] The terms stochastic process and random process are used interchangeably, often with no specific mathematical space for the set that indexes the ...
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
Complete spatial randomness (CSR) describes a point process whereby point events occur within a given study area in a completely random fashion. It is synonymous with a homogeneous spatial Poisson process. [1] Such a process is modeled using only one parameter , i.e. the density of points within the defined area. The term complete spatial ...
Hawkes process; Homogeneous processes: processes where the domain has some symmetry and the finite-dimensional probability distributions also have that symmetry. Special cases include stationary processes, also called time-homogeneous. Karhunen–Loève theorem; Lévy process; Local time (mathematics) Loop-erased random walk
In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in nature and hence is used to model many real-life stochastic systems.