Hi all!
In my problem, an element is a set of numeric and categorical values. I have sampling models to generate these values, i.e. to generate an element. These models are based on continuous (for numeric values) and discrete (for categorical values) probability distributions. Periodically, I update the parameters of these models based on the best elements I have found.
When the models converge, the sampled elements are very similar to those already evaluated. How can I detect convergence of these distributions, and what strategy can be used to aggregate over all distributions to have a single indicator of convergence?
Thank you in advance!
Cheers,
Marcelo
I think, it is still unknown or open problem, for in how many iteration the approximate function could converge to the nearly exact solution. However, you may need some bound for termination and may check your algorithm for where (with hw many iterations) you can get good approximation. For details, you may follow Article A convergence analysis of iterative methods for the solution...
https://pdfs.semanticscholar.org/9918/cc3e2d5938d6ffc1b8a741f3f7916fd5a1fa.pdf
https://arxiv.org/pdf/1510.06148.pdf
There's no single solution for this issue. One simple answer is to increase the number of replications.
I am not sure to understand exactly the question but when performing Monte carlo silulation this can be done by considering the average, m, and the standard deviation, s, of the simulated sample. They do converge toward constant values when the the number N of simulations increases. Observing them when N increases gives an idea of te speed of the convergence.
Another way is to estimate the 90% confidence interval of the calculation by considering the coefficient e =1.64.s/sqr(N). Then the true average value has 90% to be in the interval [m-e, m+e]. This interval goes to 0 when N goes to infinity.
Best regards
The idea underlying the answer of Jean-Pierre Signoret can be extended by using the techniques of either "jackknifing" or "bootstrapping". That is, you use the overall data-set (via "resampling") to provide an estimate of the variance of a complicated function of the data-set (such as estimates of the parameters of a distribution).
Outlines of these approaches can be found at :
https://en.wikipedia.org/wiki/Jackknife_resampling
https://en.wikipedia.org/wiki/Bootstrapping_(statistics)
https://en.wikipedia.org/wiki/Resampling_(statistics)
You can estimate the number of required samples based on Bayesian probability and the amount of deviation in the mean of results. Check out the criterion used in the following article:
Article Seismic evaluation of ordinary RC buildings retrofitted with...
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Inorganic Materials
- Ceramics
- Glass