https://github.com/maxbiostat/truncation_tests
Preliminary code to test truncation algorithms for infinite series and their applications in Statistics.
https://github.com/maxbiostat/truncation_tests
mathematics statistics summation truncation
Last synced: about 1 year ago
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Preliminary code to test truncation algorithms for infinite series and their applications in Statistics.
- Host: GitHub
- URL: https://github.com/maxbiostat/truncation_tests
- Owner: maxbiostat
- License: gpl-3.0
- Created: 2021-02-23T13:50:10.000Z (over 5 years ago)
- Default Branch: main
- Last Pushed: 2022-02-15T17:23:35.000Z (over 4 years ago)
- Last Synced: 2023-07-31T12:36:17.213Z (almost 3 years ago)
- Topics: mathematics, statistics, summation, truncation
- Language: R
- Homepage:
- Size: 801 KB
- Stars: 1
- Watchers: 2
- Forks: 0
- Open Issues: 4
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Test scripts for infinite series truncation algorithms
Accompanying code to the paper ["Adaptive truncation of infinite sums: applications to Statistics"](https://arxiv.org/abs/2202.06121) by [Luiz Max Carvalho](https://github.com/maxbiostat) and [Guido A. Moreira](https://github.com/GuidoAMoreira).
Note that the code provided here makes heavy use of our package [**sumR**](https://github.com/GuidoAMoreira/sumR) which is also on CRAN.
- The importance of selecting the right algorithm: as [this](https://github.com/maxbiostat/truncation_tests/blob/main/tests/adaptive_versus_threshold.r) script demonstrates, when L > 1/2 one really ought to use the error-bounding ("adaptive") algorithm or Batches with a suitably chosen `batch_size`.
- Ever wondered how many iterations you would need to correctly approximate the normalising constant of the [Conway-Maxwell Poisson](https://en.wikipedia.org/wiki/Conway%E2%80%93Maxwell%E2%80%93Poisson_distribution) distribution? [This](https://github.com/maxbiostat/truncation_tests/blob/main/COMP_normalisingConstant_table.r) script computes it for a few values, extending the results in Figure 5 of [Benson & Friel (2021)](https://projecteuclid.org/journals/bayesian-analysis/volume-16/issue-3/Bayesian-Inference-Model-Selection-and-Likelihood-Estimation-using-Fast-Rejection/10.1214/20-BA1230.full) .
- [This](https://github.com/maxbiostat/truncation_tests/blob/main/MMLE_Erlang_sumR.r) script implements the marginal maximum likelihood estimation (MMLE) example with a toy queuing model. The basic idea is that you have a Poisson number of calls with exponential duration, but you only observe the total call time (i.e. their sum). A simulation study is implemented [here](https://github.com/maxbiostat/truncation_tests/blob/main/MMLE_Erlang_sumR_simuStudy.r) and has a companion [script](https://github.com/maxbiostat/truncation_tests/blob/main/analyse_MMLE_Erlang.r) to analyse it.
- Tests where the true answer is known in closed form can be found in [this](https://github.com/maxbiostat/truncation_tests/tree/main/tests) folder. In particular, we provide tests for the [factorial moments](https://en.wikipedia.org/wiki/Factorial_moment) of a Poisson random variable ([script](https://github.com/maxbiostat/truncation_tests/blob/main/tests/Poisson_factorial_moments.r)) and the marginal probability in a size-independent (binomial) observation error model with a negative binomial count-generating distribution ([script](https://github.com/maxbiostat/truncation_tests/blob/main/tests/Negative_binomial_obsError.r)).