Bayesian Analysis of the Data Worth of Pumping Tests Using Informative Prior Distributions

2020 ◽  
Author(s):  
Falk Heße ◽  
Lars Isachsen ◽  
Sebastian Müller ◽  
Attinger Sabine
Keyword(s):  
Correlation Length ◽  
Pumping Tests ◽  
Prior Distributions ◽  
Subsurface Characterization ◽  
Informative Prior ◽  
Background Data ◽  
Data Worth ◽  
Mean Variance ◽  
Informative Prior Distributions

<p><span>Characterizing the subsurface of our planet is an important task. Yet compared to many other fields, the characterization of the subsurface is always burdened by large uncertainties. These uncertainties are caused by the general lack of data and the large spatial variability of many subsurface properties. </span><span>Due to their </span><span>comparably </span><span>low costs, pumping test</span><span>s</span><span> are regularly applied for the characterization of groundwater aquifers. The </span><span>classic</span><span> approach is to </span><span>identify the parameters of some conceptual subsurface model</span> <span>by means of curve </span><span>fit</span><span>ting</span><span> some analytical expression </span><span>to the measured drawdown.</span> <span>One of the drawbacks of classic analyzation techniques of pumping tests is the assumption of the existence of a single representative parameter value for the whole aquifer. Consequently, they cannot account for spatial heterogeneities. To address this limitation, a number of studies have proposed extensions of both Thiem’s and Theis’ formula. Using these extensions, it is possible to estimate geostatistical parameters like the mean, variance and correlation length of a heterogeneous conductivity field from pumping tests.</span></p><p><span>W</span><span>hile these methods have demonstrated their ability to estimate </span><span>such</span><span> geostatistical parameters, their data worth has </span><span>rarely</span><span> been investigated within a Bayesian framework. This is particularly relevant since recent developments in the field of Bayesian inference facilitate the derivation of informative prior distributions for these parameters. </span><span>Here, informative means that the prior is</span> <span>based on currently available background data </span><span>and therefore may be able to substantially influence the posterior distribution</span><span>.</span> <span>If this is the case,</span><span> the actual data worth of pumping tests, as well as other subsurface characterization methods, may be lower than assumed.</span></p><p><span>To investigate this possibility, we implemented a series of numerical pumping tests in a synthetic model based on the Herten aquifer. Using informative prior distributions, we derived the posterior distributions over the </span><span>mean, variance and correlation length of </span><span>the synthetic</span><span> heterogeneous conductivity field. </span><span>Our results show that for mean and variance, we already get a substantially lowered data worth for pumping tests when using informative prior distributions, whereas the estimation of the correlation length remains mostly unaffected. These results suggest that with an increasing amount of background data, the data worth of pumping tests may fall </span><span>even lower, meaning that more informative techniques for subsurface characterization will be needed in the future.</span></p><p> </p><p> </p>

scholarly journals Updating Knowledge in The Estimation of The Genetics Parameters Multi-trait and Multi-Environment Bayesian Analysis in Rice (Oryza Sativa L.)

2021 ◽  
Author(s):  
Camila Ferreira Azevedo ◽  
Cynthia Barreto ◽  
Matheus Suela ◽  
Moysés Nascimento ◽  
Antônio Carlos Júnior ◽  
...  
Keyword(s):  
Bayesian Approach ◽  
Prior Distribution ◽  
Variance Components ◽  
Genetic Correlations ◽  
Bayesian Framework ◽  
Prior Distributions ◽  
Informative Prior ◽  
Informative Prior Distribution ◽  
Informative Prior Distributions ◽  
The Bayesian Approach

Abstract Among the multi-trait models used to jointly study several traits and environments, the Bayesian framework has been a preferable tool for using a more complex and biologically realistic model. In most cases, the non-informative prior distributions are adopted in studies using the Bayesian approach. Still, the Bayesian approach tends to present more accurate estimates when it uses informative prior distributions. The present study was developed to evaluate the efficiency and applicability of multi-trait multi-environment (MTME) models under a Bayesian framework utilizing a strategy for eliciting informative prior distribution using previous data from rice. The study involved data pertained to rice genotypes in three environments and five agricultural years (2010/2011 until 2014/2015) for the following traits: grain yield (GY), flowering in days (FLOR) and plant height (PH). Variance components and genetic and non-genetic parameters were estimated by the Bayesian method. In general, the informative prior distribution in Bayesian MTME models provided higher estimates of heritability and variance components, as well as minor lengths for the highest probability density interval (HPD), compared to their respective non-informative prior distribution analyses. The use of more informative prior distributions makes it possible to detect genetic correlations between traits, which cannot be achieved with the use of non-informative prior distributions. Therefore, this mechanism presented for updating knowledge to the elicitation of an informative prior distribution can be efficiently applied in rice genetic selection.

scholarly journals A Similarity-Weighted Informative Prior Distribution for Bayesian Multiple Regression Models

2021 ◽  
Vol 12 ◽  
Author(s):  
Christoph König
Keyword(s):  
Multiple Regression ◽  
Similarity Measure ◽  
Prior Distribution ◽  
Regression Models ◽  
Prior Distributions ◽  
Informative Prior ◽  
Informative Prior Distribution ◽  
Multiple Regression Models ◽  
Power Prior ◽  
Informative Prior Distributions

Specifying accurate informative prior distributions is a question of carefully selecting studies that comprise the body of comparable background knowledge. Psychological research, however, consists of studies that are being conducted under different circumstances, with different samples and varying instruments. Thus, results of previous studies are heterogeneous, and not all available results can and should contribute equally to an informative prior distribution. This implies a necessary weighting of background information based on the similarity of the previous studies to the focal study at hand. Current approaches to account for heterogeneity by weighting informative prior distributions, such as the power prior and the meta-analytic predictive prior are either not easily accessible or incomplete. To complicate matters further, in the context of Bayesian multiple regression models there are no methods available for quantifying the similarity of a given body of background knowledge to the focal study at hand. Consequently, the purpose of this study is threefold. We first present a novel method to combine the aforementioned sources of heterogeneity in the similarity measure ω. This method is based on a combination of a propensity-score approach to assess the similarity of samples with random- and mixed-effects meta-analytic models to quantify the heterogeneity in outcomes and study characteristics. Second, we show how to use the similarity measure ωas a weight for informative prior distributions for the substantial parameters (regression coefficients) in Bayesian multiple regression models. Third, we investigate the performance and the behavior of the similarity-weighted informative prior distribution in a comprehensive simulation study, where it is compared to the normalized power prior and the meta-analytic predictive prior. The similarity measure ω and the similarity-weighted informative prior distribution as the primary results of this study provide applied researchers with means to specify accurate informative prior distributions.

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