Sensitivity-Informed Bayesian Inference for Home PLC Network Models with Unknown Parameters

Ching, David S.; Safta, Cosmin; Reichardt, Thomas A.

doi:10.3390/en14092402

Cited by 4 publications

(2 citation statements)

References 47 publications

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“…Firm conclusions on the selection of the best SA method could not be reached in the majority of the studies pertaining to SA, which is understandable, because there are numerous ways to define which is the best one [46]. Sobol SA is very popular (see, e.g., [47][48][49][50][51][52][53][54]); on the contrary, less unified types of SA are less widespread [55][56][57][58][59][60][61][62][63][64]. In general, a global SA, which analyzes the influence of the variability of inputs throughout their distribution range and can describe the influence of interactions between input variables on the output, can be recommended.…”

Section: Introductionmentioning

confidence: 99%

Global Sensitivity Analysis Based on Entropy: From Differential Entropy to Alternative Measures

Kala¹

2021

Entropy

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Differential entropy can be negative, while discrete entropy is always non-negative. This article shows that negative entropy is a significant flaw when entropy is used as a sensitivity measure in global sensitivity analysis. Global sensitivity analysis based on differential entropy cannot have negative entropy, just as Sobol sensitivity analysis does not have negative variance. Entropy is similar to variance but does not have the same properties. An alternative sensitivity measure based on the approximation of the differential entropy using dome-shaped functionals with non-negative values is proposed in the article. Case studies have shown that new sensitivity measures lead to a rational structure of sensitivity indices with a significantly lower proportion of higher-order sensitivity indices compared to other types of distributional sensitivity analysis. In terms of the concept of sensitivity analysis, a decrease in variance to zero means a transition from the differential to discrete entropy. The form of this transition is an open question, which can be studied using other scientific disciplines. The search for new functionals for distributional sensitivity analysis is not closed, and other suitable sensitivity measures may be found.

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Section: Introductionmentioning

confidence: 99%

Global Sensitivity Analysis Based on Entropy: From Differential Entropy to Alternative Measures

Kala¹

2021

Entropy

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“…At each iteration of TMCMC, the likelihood function can be independently evaluated across all samples, leading to naturally parallelizable sampling strategies as opposed to standard MCMC methods that evaluate the likelihood sequentially. The ability to sample from complex target PDFs in parallel has promoted TM-CMC, and its modified versions, for use in estimating model parameters in many areas of application [19,20,21,22,23,24,25,26,27].…”

Section: Introductionmentioning

confidence: 99%

Generalized Transitional Markov Chain Monte Carlo Sampling Technique for Bayesian Inversion

Han¹,

Catanach²,

Chen³

et al. 2021

Preprint

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In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo sampling strategies are the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density functions (PDFs). However, these algorithms been shown to be inefficient when sampling from posterior distributions that are high-dimensional or exhibit multi-modality and/or strong parameter correlations. In such contexts, the sequential Monte Carlo technique of transitional Markov chain Monte Carlo (TMCMC) provides a more efficient alternative. Despite the recent applicability for Bayesian updating and model selection across a variety of disciplines, TMCMC may require a prohibitive number of tempering stages when the prior PDF is significantly different from the target posterior. Furthermore, the need to start with an initial set of samples from the prior distribution may present a challenge when dealing with implicit priors, e.g. based on feasible regions. Finally, TMCMC can not be used for inverse problems with improper prior PDFs that represent lack of prior knowledge on all or a subset of parameters. In this investigation, a generalization of TM-CMC that alleviates such challenges and limitations is proposed, resulting in a tempering sampling strategy of enhanced robustness and computational efficiency. Convergence analysis of the proposed sequential Monte Carlo algorithm is presented, proving that the distance between the intermediate distributions and the target posterior distribution monotonically decreases as the algorithm proceeds. The enhanced efficiency associated with the pro-

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Input Impedance Characterization of a Power Factor Corrected Rectifier for Harmonic Power Flow Studies

Schwartz,

Tabarez,

Barnes

et al. 2023

2023 North American Power Symposium (NAPS)

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Sensitivity-Informed Bayesian Inference for Home PLC Network Models with Unknown Parameters

Cited by 4 publications

References 47 publications

Global Sensitivity Analysis Based on Entropy: From Differential Entropy to Alternative Measures

Global Sensitivity Analysis Based on Entropy: From Differential Entropy to Alternative Measures

Generalized Transitional Markov Chain Monte Carlo Sampling Technique for Bayesian Inversion

Input Impedance Characterization of a Power Factor Corrected Rectifier for Harmonic Power Flow Studies

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