Bayesian model selection for complex dynamic systems

Mark, Christoph; Metzner, Claus; Lautscham, Lena; Strissel, Pamela L.; Strick, Reiner; Fabry, Ben

doi:10.1038/s41467-018-04241-5

Cited by 58 publications

(57 citation statements)

References 70 publications

(58 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also other definitions of the entropy could be investigated. It should also be mentioned that, when possible, the performance of the proposed indicators could be compared with complementary Bayesian model selection approaches [20,21].…”

Section: Discussionmentioning

confidence: 99%

On the Use of Entropy to Improve Model Selection Criteria

Murari

Peluso

Cianfrani

et al. 2019

Entropy

View full text Add to dashboard Cite

The most widely used forms of model selection criteria, the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC), are expressed in terms of synthetic indicators of the residual distribution: the variance and the mean-squared error of the residuals respectively. In many applications in science, the noise affecting the data can be expected to have a Gaussian distribution. Therefore, at the same level of variance and mean-squared error, models, whose residuals are more uniformly distributed, should be favoured. The degree of uniformity of the residuals can be quantified by the Shannon entropy. Including the Shannon entropy in the BIC and AIC expressions improves significantly these criteria. The better performances have been demonstrated empirically with a series of simulations for various classes of functions and for different levels and statistics of the noise. In presence of outliers, a better treatment of the errors, using the Geodesic Distance, has proved essential.

show abstract

Section: Discussionmentioning

confidence: 99%

On the Use of Entropy to Improve Model Selection Criteria

Murari

Peluso

Cianfrani

et al. 2019

Entropy

View full text Add to dashboard Cite

show abstract

“…In addition, a more general framework that aggregates all the displaced stations and all the effective time lags would be of great significance in improving the predictive power for extreme air pollution events. Since more stations and time lags mean more complexity which might add some fixed or random effects of the model and reduce the predictive power, a Bayesian updating scheme similar to looking one step back with spatial aggregation over multiple stations might help 15 .…”

Section: Discussionmentioning

confidence: 99%

“…However, we steer the wheel to another direction which focuses on the ARMA structure and spatial explanatory power. It’s worth to mention that Beck and Cohen put forward a two-compound superstatistical model to model multiple fragments characterized by the exponential inter-session time distribution, which has been widely used in complex systems for risk estimation 11 – 15 .…”

Section: Introductionmentioning

confidence: 99%

Forecasting extreme atmospheric events with a recurrence-interval-analysis-based autoregressive conditional duration model

Dai

Jiang

Zhou

2018

Sci Rep

View full text Add to dashboard Cite

With most city dwellers in China subjected to air pollution, forecasting extreme air pollution spells is of paramount significance in both scheduling outdoor activities and ameliorating air pollution. In this paper, we integrate the autoregressive conditional duration model (ACD) with the recurrence interval analysis (RIA) and also extend the ACD model to a spatially autoregressive conditional duration (SACD) model by adding a spatially reviewed term to quantitatively explain and predict extreme air pollution recurrence intervals. Using the hourly data of six pollutants and the air quality index (AQI) during 2013–2016 collected from 12 national air quality monitoring stations in Beijing as our test samples, we attest that the spatially reviewed recurrence intervals have some general explanatory power over the recurrence intervals in the neighbouring air quality monitoring stations. We also conduct a one-step forecast using the RIA-ACD(1,1) and RIA-SACD(1,1,1) models and find that 90% of the predicted recurrence intervals are smaller than 72 hours, which justifies the predictive power of the proposed models. When applied to more time lags and neighbouring stations, the models are found to yield results that are consistent with reality, which evinces the feasibility of predicting extreme air pollution events through a recurrence-interval-analysis-based autoregressive conditional duration model. Moreover, the addition of a spatial term has proved effective in enhancing the predictive power.

show abstract

“…Two approaches are used to infer time‐varying parameters and determine their uncertainty. The first is the Monte Carlo methods that approximate the distribution of parameters based on random sampling 12 . The second is variational Bayer techniques that approximate parameters using analytical distributions.…”

Section: Superstatisticsmentioning

confidence: 99%

Epidemic via superstatistics and random walk on a torus

Alzeley

2020

Comp and Math Methods

View full text Add to dashboard Cite

The mathematical study of diseases and their dissemination has, at most, been a subject for just over three centuries. Superstatistics is based on the idea of the superposition of at least two parameters. To date, this methodology has not been applied to epidemiology. In this article, we investigate the spread of epidemics of the susceptible‐infected‐removed (SIR) type using superstatistics and random walk on a torus. This article aims to bring together two areas which have recently become active areas of research. We model epidemics on a torus in terms of a “game” between the susceptible and the infected. We also compute the probabilities for all possible transitions between them. Furthermore, we investigate the behavior and structure of our setup model. Finally, we study the superstatistics of stochastic processes and apply their techniques to a well‐known model in the epidemic literature known as SIR. No other work, to the best of our knowledge, has studied SIR via superstatistics to date

show abstract

Bayesian model selection for complex dynamic systems

Cited by 58 publications

References 70 publications

On the Use of Entropy to Improve Model Selection Criteria

On the Use of Entropy to Improve Model Selection Criteria

Forecasting extreme atmospheric events with a recurrence-interval-analysis-based autoregressive conditional duration model

Epidemic via superstatistics and random walk on a torus

Contact Info

Product

Resources

About