An analytical description of the time-integrated Brownian bridge
| Autor: | Jan M. Baetens, Steffie Van Nieuland, Hans De Meyer, Bernard De Baets |
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| Rok vydání: | 2015 |
| Předmět: |
0106 biological sciences
010604 marine biology & hydrobiology Applied Mathematics Probability density function Brownian excursion Brownian bridge 010603 evolutionary biology 01 natural sciences Numerical integration Normal distribution Moment (mathematics) Computational Mathematics Data point Econometrics Statistical physics Marginal distribution Mathematics |
| Zdroj: | Computational and Applied Mathematics. 36:627-645 |
| ISSN: | 1807-0302 0101-8205 |
| DOI: | 10.1007/s40314-015-0250-3 |
| Popis: | In animal movement research, the probability density function (PDF) of the time-integrated Brownian bridge (TIBB) is used to delineate important regions on the basis of tracking data. Here, it is assumed that an animal performs a Brownian bridge between the data points. As such, the location at any moment in time of an individual performing a Brownian bridge is described by a normal distribution. The (time-independent) marginal probability density at a given point, i.e., the value of the PDF of the TIBB at that point, is obtained by averaging these normal distributions over time. To the best of our knowledge, the PDF of the TIBB is thus far always computed through the use of numerical integration methods. Here, we demonstrate that it is nevertheless possible to derive its analytical expression. Although the two-dimensional setting is the most interesting one for animal movement studies, also the one- and, in general, the n-dimensional setting are considered. |
| Databáze: | OpenAIRE |
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