The Nu Expression for Probabilistic Data Integration

Polyakova, E. I.; Journel, André G.

doi:10.1007/s11004-007-9117-5

Cited by 28 publications

(10 citation statements)

References 9 publications

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“…This is made difficult because the weights describe at the same time both concepts of confidence and redundancy. Polyakova and Journel [2007] suggest two methods to determine them: the first one is to calibrate the weights using available data, and the second one is to determine them using proxy cases. In our example, the first method gave similar weights to the ones found with a complete sensitivity analysis including a full knowledge of the true reference field.…”

Section: Discussionmentioning

confidence: 99%

“…By construction, Bordley's formula has a certain number of important mathematical properties [see Clemen and Winkler , 2007, for a discussion], but nevertheless it is only an approximation allowing to combine several probabilities of the same event to occur (estimated from different sources of information) when the complete probability model including all the sources of information, and all the data interaction, is lacking. is closely related to the tau and nu models [ Journel , 2002; Krishnan , 2005; Polyakova and Journel , 2007]. In the same spirit, Tarantola [2005] defines the conjunction of probability densities as the simplest way to aggregate probabilities in that manner: …”

Section: Simulation By Probability Aggregationmentioning

confidence: 99%

“…So far, both weights w 1 and w 2 have been kept identical and equal to 1. This is justified when the confidence related to each source of information as well as the data interaction are unknown [ Polyakova and Journel , 2007]. Nevertheless, using allows setting these parameters to modify the influence of each source of information.…”

Section: Realistic Examplementioning

confidence: 99%

See 2 more Smart Citations

Integrating collocated auxiliary parameters in geostatistical simulations using joint probability distributions and probability aggregation

Mariethoz

Renard

Froidevaux³

2009

Water Resources Research

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[1] We propose a new cosimulation algorithm for simulating a primary attribute using one or several secondary attributes known exhaustively on the domain. This problem is frequently encountered in surface and groundwater hydrology when a variable of interest is measured only at a discrete number of locations and when the secondary variable is mapped by indirect techniques such as geophysics or remote sensing. In the proposed approach, the correlation between the two variables is modeled by a joint probability distribution function. A technique to construct such relation using underlying variables and physical laws is proposed when field data are insufficient. The simulation algorithm proceeds sequentially. At each location of the domain, two conditional probability distribution functions (cpdf) are inferred. The cpdf of the main attribute is inferred in a classical way from the neighboring data and a model of spatial variability. The second cpdf is inferred directly from the joint probability distribution function of the two attributes and the value of the secondary attribute at the location to be simulated. The two distribution functions are combined by probability aggregation to obtain the local cpdf from which a value for the primary attribute is randomly drawn. Various examples using synthetic and remote sensing data demonstrate that the method is more accurate than the classical collocated cosimulation technique when a complex relation relates the two attributes.Citation: Mariethoz, G., P. Renard, and R. Froidevaux (2009), Integrating collocated auxiliary parameters in geostatistical simulations using joint probability distributions and probability aggregation, Water Resour. Res., 45, W08421,

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Section: Discussionmentioning

confidence: 99%

Section: Simulation By Probability Aggregationmentioning

confidence: 99%

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Integrating collocated auxiliary parameters in geostatistical simulations using joint probability distributions and probability aggregation

Mariethoz

Renard

Froidevaux³

2009

Water Resources Research

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“…We use MANN with interaction noise to solve this problem. Just as MCRF, Tau (τ) model [18] and Nu (υ) expression [19] …”

Section: Methodsmentioning

confidence: 99%

Multiple Artificial Neural Networks with Interaction Noise for Estimation of Spatial Categorical Variables

Huang

Wang

2016

Algorithms

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This paper presents a multiple artificial neural networks (MANN) method with interaction noise for estimating the occurrence probabilities of different classes at any site in space. The MANN consists of several independent artificial neural networks, the number of which is determined by the neighbors around the target location. In the proposed algorithm, the conditional or pre-posterior (multi-point) probabilities are viewed as output nodes, which can be estimated by weighted combinations of input nodes: two-point transition probabilities. The occurrence probability of a certain class at a certain location can be easily computed by the product of output probabilities using Bayes' theorem. Spatial interaction or redundancy information can be measured in the form of interaction noises. Prediction results show that the method of MANN with interaction noise has a higher classification accuracy than the traditional Markov chain random fields (MCRF) model and can successfully preserve small-scale features.

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“…Journel (2002) proposed the permanence of ratio model based on the conditional independence of the secondary information. The data sources are not entirely conditionally independent; thus, the Tau model (Journel 2002) and other weighted combination models (Hong 2010;Polyakova and Journel 2007) account for this redundancy and improve the predictive capabilities of the models.…”

Section: Multiplicative Aggregation For Training Imagesmentioning

confidence: 99%

A Multiple Training Image Approach for Spatial Modeling of Geologic Domains

Silva

Deutsch

2014

Math Geosci

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Characterization of complex geological features and patterns remains one of the most challenging tasks in geostatistics. Multiple point statistics (MPS) simulation offers an alternative to accomplish this aim by going beyond classical two-point statistics. Reproduction of features in the final realizations is achieved by borrowing high-order spatial statistics from a training image. Most MPS algorithms use one training image at a time chosen by the geomodeler. This paper proposes the use of multiple training images simultaneously for spatial modeling through a scheme of data integration for conditional probabilities known as a linear opinion pool. The training images (TIs) are based on the available information and not on conceptual geological models; one image comes from modeling the categories by a deterministic approach and another comes from the application of conventional sequential indicator simulation. The first is too continuous and the second too random. The mixing of TIs requires weights for each of them. A methodology for calibrating the weights based on the available drillholes is proposed. A measure of multipoint entropy along the drillholes is matched by the combination of the two TIs. The proposed methodology reproduces geologic features from both TIs with the correct amount of continuity and variability. There is no need for a conceptual training image from another modeling technique; the data-driven TIs permit a robust inference of spatial structure from reasonably spaced drillhole data.

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The Nu Expression for Probabilistic Data Integration

Cited by 28 publications

References 9 publications

Integrating collocated auxiliary parameters in geostatistical simulations using joint probability distributions and probability aggregation

Integrating collocated auxiliary parameters in geostatistical simulations using joint probability distributions and probability aggregation

Multiple Artificial Neural Networks with Interaction Noise for Estimation of Spatial Categorical Variables

A Multiple Training Image Approach for Spatial Modeling of Geologic Domains

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