| Title:
|
Simple Monte Carlo integration with respect to Bernoulli convolutions (English) |
| Author:
|
Gómez, David M. |
| Author:
|
Dartnell, Pablo |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
6 |
| Year:
|
2012 |
| Pages:
|
617-626 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We apply a Markov chain Monte Carlo method to approximate the integral of a continuous function with respect to the asymmetric Bernoulli convolution and, in particular, with respect to a binomial measure. This method---inspired by a cognitive model of memory decay---is extremely easy to implement, because it samples only Bernoulli random variables and combines them in a simple way so as to obtain a sequence of empirical measures converging almost surely to the Bernoulli convolution. We give explicit bounds for the bias and the standard deviation for this approximation, and present numerical simulations showing that it outperforms a general Monte Carlo method using the same number of Bernoulli random samples. (English) |
| Keyword:
|
MCMC |
| Keyword:
|
Bernoulli convolution |
| Keyword:
|
binomial measure |
| Keyword:
|
Monte Carlo integration |
| Keyword:
|
empirical measures |
| MSC:
|
60G57 |
| MSC:
|
65C05 |
| MSC:
|
65D30 |
| idZBL:
|
Zbl 1274.65003 |
| idMR:
|
MR3010240 |
| DOI:
|
10.1007/s10492-012-0037-4 |
| . |
| Date available:
|
2012-11-10T20:44:04Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143006 |
| . |
| Reference:
|
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| Reference:
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| . |
