Modeling Sampling Distributions of Test Statistics with Autograd
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918125196279808 |
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| author | Kadhim, Ali Al Prosper, Harrison B. |
| author_facet | Kadhim, Ali Al Prosper, Harrison B. |
| contents | Simulation-based inference methods that feature correct conditional coverage of confidence sets based on observations that have been compressed to a scalar test statistic require accurate modeling of either the p-value function or the cumulative distribution function (cdf) of the test statistic. If the model of the cdf, which is typically a deep neural network, is a function of the test statistic then the derivative of the neural network with respect to the test statistic furnishes an approximation of the sampling distribution of the test statistic. We explore whether this approach to modeling conditional 1-dimensional sampling distributions is a viable alternative to the probability density-ratio method, also known as the likelihood-ratio trick. Relatively simple, yet effective, neural network models are used whose predictive uncertainty is quantified through a variety of methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02488 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modeling Sampling Distributions of Test Statistics with Autograd Kadhim, Ali Al Prosper, Harrison B. Machine Learning High Energy Physics - Experiment Computation Simulation-based inference methods that feature correct conditional coverage of confidence sets based on observations that have been compressed to a scalar test statistic require accurate modeling of either the p-value function or the cumulative distribution function (cdf) of the test statistic. If the model of the cdf, which is typically a deep neural network, is a function of the test statistic then the derivative of the neural network with respect to the test statistic furnishes an approximation of the sampling distribution of the test statistic. We explore whether this approach to modeling conditional 1-dimensional sampling distributions is a viable alternative to the probability density-ratio method, also known as the likelihood-ratio trick. Relatively simple, yet effective, neural network models are used whose predictive uncertainty is quantified through a variety of methods. |
| title | Modeling Sampling Distributions of Test Statistics with Autograd |
| topic | Machine Learning High Energy Physics - Experiment Computation |
| url | https://arxiv.org/abs/2405.02488 |