A general Bayesian framework for calibrating and evaluating stochastic models of annual multi-site hydrological data

2007 ◽  
Vol 340 (3-4) ◽  
pp. 129-148 ◽  
Author(s):  
Andrew J. Frost ◽  
Mark A. Thyer ◽  
R. Srikanthan ◽  
George Kuczera
2007 ◽  
Vol 19 (10) ◽  
pp. 2780-2796 ◽  
Author(s):  
Shun-ichi Amari

When there are a number of stochastic models in the form of probability distributions, one needs to integrate them. Mixtures of distributions are frequently used, but exponential mixtures also provide a good means of integration. This letter proposes a one-parameter family of integration, called α-integration, which includes all of these well-known integrations. These are generalizations of various averages of numbers such as arithmetic, geometric, and harmonic averages. There are psychophysical experiments that suggest that α-integrations are used in the brain. The α-divergence between two distributions is defined, which is a natural generalization of Kullback-Leibler divergence and Hellinger distance, and it is proved that α-integration is optimal in the sense of minimizing α-divergence. The theory is applied to generalize the mixture of experts and the product of experts to the α-mixture of experts. The α-predictive distribution is also stated in the Bayesian framework.


2017 ◽  
Vol 14 (136) ◽  
pp. 20170386 ◽  
Author(s):  
Hola K. Adrakey ◽  
George Streftaris ◽  
Nik J. Cunniffe ◽  
Tim R. Gottwald ◽  
Christopher A. Gilligan ◽  
...  

The control of highly infectious diseases of agricultural and plantation crops and livestock represents a key challenge in epidemiological and ecological modelling, with implemented control strategies often being controversial. Mathematical models, including the spatio-temporal stochastic models considered here, are playing an increasing role in the design of control as agencies seek to strengthen the evidence on which selected strategies are based. Here, we investigate a general approach to informing the choice of control strategies using spatio-temporal models within the Bayesian framework. We illustrate the approach for the case of strategies based on pre-emptive removal of individual hosts. For an exemplar model, using simulated data and historic data on an epidemic of Asiatic citrus canker in Florida, we assess a range of measures for prioritizing individuals for removal that take account of observations of an emerging epidemic. These measures are based on the potential infection hazard a host poses to susceptible individuals (hazard), the likelihood of infection of a host (risk) and a measure that combines both the hazard and risk (threat). We find that the threat measure typically leads to the most effective control strategies particularly for clustered epidemics when resources are scarce. The extension of the methods to a range of other settings is discussed. A key feature of the approach is the use of functional-model representations of the epidemic model to couple epidemic trajectories under different control strategies. This induces strong positive correlations between the epidemic outcomes under the respective controls, serving to reduce both the variance of the difference in outcomes and, consequently, the need for extensive simulation.


1955 ◽  
Vol 39 (6) ◽  
pp. 464-464
Author(s):  
John E. Anderson
Keyword(s):  

2019 ◽  
Vol 2 (5) ◽  
Author(s):  
Ji-hua Hu ◽  
Jia-xian Liang

Interstation travel speed is an important indicator of the running state of hybrid Bus Rapid Transit and passenger experience. Due to the influence of road traffic, traffic lights and other factors, the interstation travel speeds are often some kind of multi-peak and it is difficult to use a single distribution to model them. In this paper, a Gaussian mixture model charactizing the interstation travel speed of hybrid BRT under a Bayesian framework is established. The parameters of the model are inferred using the Reversible-Jump Markov Chain Monte Carlo approach (RJMCMC), including the number of model components and the weight, mean and variance of each component. Then the model is applied to Guangzhou BRT, a kind of hybrid BRT. From the results, it can be observed that the model can very effectively describe the heterogeneous speed data among different inter-stations, and provide richer information usually not available from the traditional models, and the model also produces an excellent fit to each multimodal speed distribution curve of the inter-stations. The causes of different speed distribution can be identified through investigating the Internet map of GBRT, they are big road traffic and long traffic lights respectively, which always contribute to a main road crossing. So, the BRT lane should be elevated through the main road to decrease the complexity of the running state.


Author(s):  
Colin P. R. McCarter ◽  
Stephen D. Sebestyen ◽  
Susan L. Eggert ◽  
Kristine M. Haynes ◽  
Randall K. Kolka ◽  
...  

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