Explicit solutions for a probabilistic moraine preservation model
| Autor: | PAUL MUZIKAR |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Journal of Glaciology, Vol 62, Pp 1181-1185 (2016) |
| Druh dokumentu: | article |
| ISSN: | 0022-1430 1727-5652 |
| DOI: | 10.1017/jog.2016.109 |
| Popis: | If a series of glacial advances occurs over the same pathway, the moraines that are now present may constitute an incomplete record of the total history. This is because a given advance can destroy the moraine left by a previous one, if the previous advance was less extensive. Gibbons, Megeath and Pierce (GMP) formulated an elegant stochastic model for this process; the key quantity in their analysis is $\bi P(n\vert N)$ , the probability that n moraines are preserved after N glacial advances. In their paper, GMP derive a recursion formula satisfied by $\bi P(n\vert N)$ , and use this formula to compute values of P for a range of values of n and N. In the present paper, we derive an explicit general answer for $\bi P(n\vert N)$ , and show explicit, exact results for the mean value and standard deviation of n. We use these results to develop more insight into the consequences of the GMP model; for example, to a good approximation, 〈n〉 increases as ln(N). We explain how a Bayesian approach can be used to analyze $\bi P(N\vert n)$ , the probability that there were N advances, given that we now observe n moraines. |
| Databáze: | Directory of Open Access Journals |
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