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...es Construction of dependent Dirichlet processes based on compound Poisson processes], Neural Information Processing Systems (NIPS), 2010. </ref> The concept is ...ir labeling. This assumption is invalid for modelling temporal and spatial processes in which the order of data points plays a critical role in creating meaning ...

...ea in a completely random fashion. It is synonymous with a ''homogeneous [[spatial Poisson process]]''.<ref name="Omaimon2010DataM">O. Maimon, L. Rokach, ''Da ...reas in most other statistical contexts it is referred to the concept of a spatial Poisson process.<ref name="Omaimon2010DataM"/> ...

...stics]], the '''rational quadratic [[covariance function]]''' is used in [[spatial statistics]], [[geostatistics]], [[machine learning]], image analysis, and ...st=Williams, Christopher K.I |first=Rasmussen, Carl Edward |title=Gaussian Processes for Machine Learning |publisher=MIT Press |year=2006 |location=United Kingd ...

...3">D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. I''. Probability and its Applications (New York). Springer, New York, ...P. Waagepetersen. ''Statistical inference and simulation for spatial point processes''. CRC Press, 2003.</ref> which are applied in various [[scientific]] and [ ...

...8">D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. {II''}. Probability and its Applications (New York). Springer, New Yo ...3">D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. I''. Probability and its Applications (New York). Springer, New York, ...

...3">D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. I''. Probability and its Applications (New York). Springer, New York, ...P. Waagepetersen. ''Statistical inference and simulation for spatial point processes''. CRC Press, 2003. [https://dx.doi.org/10.1201/9780203496930]</ref> which ...

The concept of a '''spatial weight''' is used in [[spatial analysis]] to describe neighbor relations between regions on a map.<ref nam | title=Spatial Processes: Models & Applications ...

...ommonly used to quantify topographic control on [[hydrology|hydrological]] processes.<ref name="Sorensenetal2006">{{cite journal |last=Sørensen|first=R. |last2= ...n]]s. The TWI has been used to study spatial scale effects on hydrological processes. The topographic wetness index (TWI) was developed by [[Keith Beven|Beven]] ...

...point process]]es and related fields such as [[stochastic geometry]] and [[spatial statistics]].<ref name="stoyan1995stochastic"/> ...point process]],<ref name="kingman1992poisson">J. F. C. Kingman. ''Poisson processes'', volume 3. Oxford university press, 1992.</ref> The Poisson point process ...

...s]]es, which are used in related fields such as [[stochastic geometry]], [[spatial statistics]] and [[continuum percolation theory]] and frequently serve as [ ...= D. | last2 = Vere-Jones| title = An Introduction to the Theory of Point Processes | url = https://archive.org/details/introductiontoth0000dale | url-access = ...

{{Short description|Statistics of spatial association}} ...d spdep.<ref>{{cite web | url=https://rdrr.io/rforge/spdep/ | title=Spdep: Spatial Dependence: Weighting Schemes, Statistics and Models version 0.6-15 from R- ...

...oung |last3=Taimre |first3=Thomas |date=2021 |title=The Elements of Hawkes Processes |url=https://link.springer.com/book/10.1007/978-3-030-84639-8 |language=en- ...date=1971 |title=Spectra of some self-exciting and mutually exciting point processes |url=https://doi.org/10.1093/biomet/58.1.83 |journal=Biometrika |volume=58 ...

...niversality class|universal limits]] describing the long time, large scale spatial fluctuations of the models in the [[Kardar–Parisi–Zhang equation#KPZ univer ...g|volume=38|number=33|pages=L549-L556|first1=Tomohiro|last1=Sasamoto|title=Spatial correlations of the 1D KPZ surface on a flat substrate|journal=Journal of P ...

...es <math>i,j,k</math> we already have full permutation symmetry, where the spatial indices and frequencies are permuted simultaneously according to ...d be [[Dispersionless equation|dispersionless]], and so we can permute the spatial indices without also permuting the frequency arguments. ...

...3">D. J. Daley and D. Vere-Jones. ''An introduction to the theory of point processes. Vol. I''. Probability and its Applications (New York). Springer, New York, ...> Factorial moment measures completely characterize a wide class of point processes, which means they can be used to uniquely identify a point process. ...

...er.hs.columbia.edu/courses/NMR_relaxation.pdf|title=Relaxation and Dynamic Processes|first=Arthur|last= Palmer|publisher=[[Columbia University]]|accessdate=2012 ...ks which have an nOe enhancement show up, demonstrating which spins are in spatial proximity in the [[molecule]] under study: only those will in fact have a s ...

...tatistical [[correlation]] between [[random variable]]s, contingent on the spatial or temporal distance between those variables.<ref>{{cite book ...]], and [[statistical mechanics]] differ only in the particular stochastic processes they are applied to. In [[quantum field theory]] there are [[Correlation f ...

...t so that it spans a time interval of length 1. The scaling factor for the spatial axis must be square root of the scaling factor for the time axis. The proce {{Stochastic processes}} ...

[[Category:Spatial processes]] ...

...math>. More precisely IPS are continuous-time [[Markov process|Markov jump processes]] describing the collective behavior of stochastically interacting componen IPS are usually defined via their [[Infinitesimal generator (stochastic processes)|Markov generator]] giving rise to a unique [[Markov process]] using Markov ...