Fourier methods for model selection

Jiménez-Gamero, M. D.; Batsidis, Apostolos; Alba-Fernández, V.

doi:10.1007/s10463-014-0491-8

Cited by 16 publications

(6 citation statements)

References 26 publications

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“…Second, the overall computational complexity of an inference procedure that uses the Fourier transform method and samples M candidate parameters is O (MN log N ). Performing the entire analysis in the Fourier domain requires only a single Fourier transform to determine the empirical 022409-4 This approach has been explored for use in goodness-of-fit testing and model selection [51,52], but only rarely for parameter inference [53]. However, we anticipate that the computational advantages may outweigh the incompatibility with Bayesian inference, similarly to the recent interest in using nonparametric Kolmogorov and Wasserstein distances for parameter inference [54][55][56].…”

Section: Resultsmentioning

confidence: 99%

Special function methods for bursty models of transcription

Gorin

Pachter

2020

Phys. Rev. E

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We explore a Markov model used in the analysis of gene expression, involving the bursty production of pre-mRNA, its conversion to mature mRNA, and its consequent degradation. We demonstrate that the integration used to compute the solution of the stochastic system can be approximated by the evaluation of special functions. Furthermore, the form of the special function solution generalizes to a broader class of burst distributions. In light of the broader goal of biophysical parameter inference from transcriptomics data, we apply the method to simulated data, demonstrating effective control of precision and runtime. Finally, we propose and validate a non-Bayesian approach for parameter estimation based on the characteristic function of the target joint distribution of pre-mRNA and mRNA.

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Section: Resultsmentioning

confidence: 99%

Special function methods for bursty models of transcription

Gorin

Pachter

2020

Phys. Rev. E

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“…Secondly, the overall computational complexity of an inference procedure that uses the Fourier transform method and samples M candidate parameters is O(MN log N ). Performing the entire analysis in the Fourier domain requires only a single Fourier transform to determine the empirical characteristic function, reducing the computational complexity to O(N log N + MN ), equivalent to O(MN ) in the practical limit of large M. This approach is has been explored for use in goodness-of-fit testing and model selection [37,38], but only rarely for parameter inference [39]. However, we anticipate that the computational advantages may outweigh the incompatibility with Bayesian inference, similarly to the recent interest in using nonparametric Kolmogorov and Wasserstein distances for parameter inference [40][41][42].…”

Section: Resultsmentioning

confidence: 99%

Special Function Methods for Bursty Models of Transcription

Gorin,

Pachter

2020

Preprint

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We explore a Markov model used in the analysis of gene expression, involving the bursty production of pre-mRNA, its conversion to mature mRNA, and its consequent degradation. We demonstrate that the integration used to compute the solution of the stochastic system can be approximated by the evaluation of special functions. Furthermore, the form of the special function solution generalizes to a broader class of burst distributions. In light of the broader goal of biophysical parameter inference from transcriptomics data, we apply the method to simulated data, demonstrating effective control of precision and runtime. Finally, we suggest a non-Bayesian approach to reducing the computational complexity of parameter inference to linear order in state space size and number of candidate parameters.

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“…Among them, it can be highlighted that the family of phi-divergences introduced by Csiszár in 1963 (see [10] (p. 1787)) has been extensively used in testing statistical hypotheses involving multinomial distributions. Examples in goodness-of-fit tests, homogeneity of two multinomial distributions and in model selection can be found in [11][12][13], among many others.…”

Section: Proposal To Test the Similarity Of Two Confusion Matricesmentioning

confidence: 99%

Analysis of Thematic Similarity Using Confusion Matrices

Balboa

Alba-Fernández

López

et al. 2018

IJGI

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Abstract:The confusion matrix is the standard way to report on the thematic accuracy of geographic data (spatial databases, topographic maps, thematic maps, classified images, remote sensing products, etc.). Two widely adopted indices for the assessment of thematic quality are derived from the confusion matrix. They are overall accuracy (OA) and the Kappa coefficient (k), which have received some criticism from some authors. Both can be used to test the similarity of two independent classifications by means of a simple statistical hypothesis test, which is the usual practice. Nevertheless, this is not recommended, because different combinations of cell values in the matrix can obtain the same value of OA or k, due to the aggregation of data needed to compute these indices. Thus, not rejecting a test for equality between two index values does not necessarily mean that the two matrices are similar. Therefore, we present a new statistical tool to evaluate the similarity between two confusion matrices. It takes into account that the number of sample units correctly and incorrectly classified can be modeled by means of a multinomial distribution. Thus, it uses the individual cell values in the matrices and not aggregated information, such as the OA or k values. For this purpose, it is considered a test function based on the discrete squared Hellinger distance, which is a measure of similarity between probability distributions. Given that the asymptotic approximation of the null distribution of the test statistic is rather poor for small and moderate sample sizes, we used a bootstrap estimator. To explore how the p-value evolves, we applied the proposed method over several predefined matrices which are perturbed in a specified range. Finally, a complete numerical example of the comparison of two matrices is presented.

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Fourier methods for model selection

Cited by 16 publications

References 26 publications

Special function methods for bursty models of transcription

Special function methods for bursty models of transcription

Special Function Methods for Bursty Models of Transcription

Analysis of Thematic Similarity Using Confusion Matrices

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