Transient dynamics of Pearson diffusions facilitates estimation of rate parameters

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985823%3A_____%2F20%3A00524893" target="_blank" >RIV/67985823:_____/20:00524893 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1016/j.cnsns.2019.105034" target="_blank" >https://doi.org/10.1016/j.cnsns.2019.105034</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cnsns.2019.105034" target="_blank" >10.1016/j.cnsns.2019.105034</a>

Result language

angličtina

Original language name

Transient dynamics of Pearson diffusions facilitates estimation of rate parameters

Original language description

Estimation of parameters in stochastic processes has been thoroughly investigated for decades and the asymptotic properties of the estimators are known. However, reaching the regime where the asymptotic properties are valid might require such a long time that the well based theoretical results have no practical value. One example of this situation is at the center of our interest. It concerns determination of the time constant in stochastic Langevin equations with additive or multiplicative white-noise terms. Often the number of observations to achieve the asymptotic conditions is beyond the physical limits. Here we show how to overcome the problem by external perturbation of the system. Furthermore, we show that the perturbation is not at the price of deterioration of the estimates of other parameters unless the observation interval is very short compared to the typical time constant of the system. Three processes from the class of Pearson diffusions are studied. They are frequently used in many applications, in particular, they are examples of leaky integrate-and-fire models, which describe the electrical properties of a neuronal membrane. These neuronal models are often used as examples of systems with excitable dynamics. The most commonly investigated process is the Ornstein-Uhlenbeck process, which has additive noise. Furthermore, the square-root process and the Jacobi process are examples of processes with multiplicative noise. The results are illustrated on computer experiments, which show a striking improvement of the estimates of the rate parameter. It has implications for experimental design, where the information about the parameters can be increased for the same amount and cost of data, which is particularly important when samples are expensive or difficult to obtain.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10103 - Statistics and probability

Project

<a href="/en/project/GA17-06943S" target="_blank" >GA17-06943S: Neural coding precision and its adaptation to the stimulus statistics</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Communications in Nonlinear Science and Numerical Simulation

ISSN

1007-5704

e-ISSN

—

Volume of the periodical

82

Issue of the periodical within the volume

Mar

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

15

Pages from-to

105034

UT code for WoS article

000499097900051

EID of the result in the Scopus database

2-s2.0-85073538492