scholarly journals Bayesian Modelling of the effects of nitrogen doses on the morphological characteristics of braquiaria grass

2018 ◽  
Vol 12 (4) ◽  
pp. 245 ◽  
Author(s):  
Luiz Henrique Marra da Silva Ribeiro ◽  
Matheus De Souza Costa ◽  
Luiz Alberto Beijo ◽  
Alberto Frank Lázaro Aguirre ◽  
Tatiane Gomes de Araújo ◽  
...  
Keyword(s):  
Bayesian Approach ◽  
Regression Models ◽  
A Priori ◽  
Morphological Characteristics ◽  
Linear Regression Models ◽  
Interval Model ◽  
Distribution Ranges ◽  
Posteriori Distribution ◽  
A Posteriori Distribution ◽  
The Bayesian Approach

The Bayesian approach in regression models has shown good results in parameter estimations, where it can increase accuracy and precision. The objective of the current study was to analyze the application of Bayesian statistics to the modeling yield for leaf dry matter (LM) and stem (SM), in kg ha-1, leaf ratio (LR), crude protein content for leaves (CPL) and stem (CPS) (%) of Brachiaria grass as a function of varying N doses (0; 100; 200 and 300 kg ha-1 yr-1). Simple and two degree polynomial linear regression models were analyzed. Information for a priori distributions was obtained from the literature. A posteriori distribution was generated using a Monte Carlo method via Markov chains. Parameters significance was assyed with HPD (Highest Posteriori Density) with a 95% interval. Model selections was performed using DIC (Deviance Information Criterion); and adjustment quality estimated with means and 95% HPD for Bayesian R2 distribution ranges. The models selected for the variables LM, SM and CPS were linear, while for LR and CPL, they were second level polynomial. The lowest doses that maximize response variables were: LM: 274 ha-1yr-1, SM: 280 ha-1yr-1, LR: 113 ha-1yr-1, CPL: 265 ha-1yr-1, CPS: 289 ha-1yr-1. The Bayesian approach allowed the inclusion of literatureverified a priori information, and the identification of evidence optimization range intervals.

scholarly journals Bayesian approach to uncertainty evaluation: is it always working?

2019 ◽  
Author(s):  
Alessandro Ferrero ◽  
Simona Salicone ◽  
Harsha Vardhana Jetti
Keyword(s):  
Bayesian Approach ◽  
A Priori ◽  
Measurement Data ◽  
Probabilistic Methods ◽  
Uncertainty Evaluation ◽  
A Priori Knowledge ◽  
Main Question ◽  
Priori Information ◽  
The Bayesian Approach ◽  
Priori Knowledge

Since the GUM has been published, measurement uncertainty has been defined in terms of the standard deviation of the probability distribution of the values that can be reasonably attributed to the measurand, and it has been evaluated using statistical or probabilistic methods. A debate has always been alive, among the metrologists, on whether a frequentist approach or a Bayesian approach should be followed to evaluate uncertainty. The Bayesian approach, based on some available a-priori knowledge about the measurand seems to prevail, nowadays. This paper starts from the consideration that the Bayesian approach is based on the well-known Bayes theorem that, as all mathematical theorems, is valid only to the extent the assumptions made to prove it are valid. The main question, when following the Bayesian approach, is hence whether these assumptions are satisfied in the practical cases, especially when the a-priori information is combined with the information coming from the measurement data to refine uncertainty evaluation. This paper will take into account some case studies to analyze when the Bayesian approach can be usefully and reliably employed by discussing the amount and pertinence of the available a-priori knowledge.

scholarly journals Ruminal pH and N-NH3 behavior: a Bayesian approach

2016 ◽  
Vol 37 (1) ◽  
pp. 311
Author(s):  
Osvaldo Martins Souza ◽  
Elias Nunes Martins ◽  
Robson Marcelo Rossi ◽  
Carlos Antonio Lopes de Oliveira ◽  
Sílvia Cristina de Aguiar ◽  
...  
Keyword(s):  
Bayesian Approach ◽  
Regression Models ◽  
Correlated Data ◽  
Linear Functions ◽  
A Posteriori ◽  
Ruminal Ph ◽  
Estimated Parameters ◽  
A Posteriori Estimates ◽  
Least Squares Estimates ◽  
The Bayesian Approach

In this work, we present the Bayesian approach as an alternative to frequentist analysis regarding correlated data of pH and N-NH3 in the Holstein cow rumen. It was observed that for pH and N-NH3 data, a posteriori estimates of coefficients of the regression models were significant, which was not observed for least-squares estimates. Thus, the Bayesian approach allowed inferences that were directly linked to the sampling of parameters of interest and statistical comparisons of non-linear functions of the estimated parameters.

scholarly journals Information Collecting and Dissemination in the Network of Taxpayers: Bayesian Approach

2021 ◽  
Vol 14 ◽  
pp. 236-256
Author(s):  
Suriya Sh. Kumacheva ◽  
◽  
Galina A. Tomilina ◽  
Keyword(s):  
Bayesian Approach ◽  
A Priori ◽  
Repeated Game ◽  
Social Connections ◽  
Tax Revenue ◽  
A Posteriori ◽  
A Posteriori Estimate ◽  
In The Beginning ◽  
Information Collecting ◽  
The Bayesian Approach

The current research is based on the assumption that the result of tax inspections is not only collection of taxes and fines. The information about audited taxpayers is also collected and helps to renew a priori knowledge of each agent's evasion propensity and obtain new a posteriori estimate of this propensity. In the beginning of the following tax period the fiscal authority can correct auditing strategy using updated information on every taxpayer. Each inspection is considered as a repeated game, in which the choice of agents to audit is associated with their revealed tendency to evade. Taxpayers also renew the information on the number of inspected neighbors using their social connections, represented by networks of various con gurations, and estimate the probability of auditing before the next tax period. Thus, the application of the Bayesian approach to the process of collecting and disseminating information in the network of taxpayers allows to optimize the audit scheme, reducing unnecessary expenses of tax authority and eventually increasing net tax revenue. To illustrate the application of the approach described above to the indicated problem, numerical simulation and scenario analysis were carried out.

USING FULL PROBABILITY MODELS TO COMPUTE PROBABILITIES OF ACTUAL INTEREST TO DECISION MAKERS

2001 ◽  
Vol 17 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Frank E. Harrell ◽  
Ya-Chen Tina Shih
Keyword(s):  
Bayesian Approach ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Likelihood Function ◽  
Scientific Evidence ◽  
A Priori ◽  
Relevant Information ◽  
Decision Makers ◽  
Probability Models ◽  
The Bayesian Approach

The objective of this paper is to illustrate the advantages of the Bayesian approach in quantifying, presenting, and reporting scientific evidence and in assisting decision making. Three basic components in the Bayesian framework are the prior distribution, likelihood function, and posterior distribution. The prior distribution describes analysts' belief a priori; the likelihood function captures how data modify the prior knowledge; and the posterior distribution synthesizes both prior and likelihood information. The Bayesian approach treats the parameters of interest as random variables, uses the entire posterior distribution to quantify the evidence, and reports evidence in a “probabilistic” manner. Two clinical examples are used to demonstrate the value of the Bayesian approach to decision makers. Using either an uninformative or a skeptical prior distribution, these examples show that the Bayesian methods allow calculations of probabilities that are usually of more interest to decision makers, e.g., the probability that treatment A is similar to treatment B, the probability that treatment A is at least 5% better than treatment B, and the probability that treatment A is not within the “similarity region” of treatment B, etc. In addition, the Bayesian approach can deal with multiple endpoints more easily than the classic approach. For example, if decision makers wish to examine mortality and cost jointly, the Bayesian method can report the probability that a treatment achieves at least 2% mortality reduction and less than $20,000 increase in costs. In conclusion, probabilities computed from the Bayesian approach provide more relevant information to decision makers and are easier to interpret.

Spiking band‐limited traces with a relative‐entropy algorithm

Geophysics ◽  
1991 ◽  
Vol 56 (7) ◽  
pp. 1003-1014 ◽  
Author(s):  
F. J. Jacobs ◽  
P. A. G. van der Geest
Keyword(s):  
Relative Entropy ◽  
Fourier Coefficients ◽  
A Priori ◽  
Map Estimation ◽  
A Posteriori ◽  
Novel Method ◽  
Band Limited ◽  
Posteriori Distribution ◽  
A Priori Distribution ◽  
A Posteriori Distribution

A novel method for the inversion of band‐limited seismic traces to full bandwidth reflectivity traces, is based on a probabilistic spiky model of the reflectivity trace, in which position indicators and amplitudes of the spikes occur as random variables, and relies on relative entropy inference from information theory. First, an a priori model for general reflectivity traces in the prospect is derived from nearby wells. Second, the a priori distribution is updated into an a posteriori distribution for the specific trace being studied by the addition of the Fourier data of the seismic trace within a passband. Uncertainty about the Fourier coefficients can be accounted for by specification of a noise variance, which implicitly is infinite outside the passband. The update with relative entropy inference is justified because of its relationship with Bayesian inference. Application of maximum a posteriori (MAP) estimation to the a posteriori distribution results in the most likely spiky reflectivity trace of full bandwidth. A numerical algorithm for obtaining the MAP estimates of spike positions and spike amplitudes is derived from the concept of continuation and is described in detail. The algorithm avoids searching among all possible patterns of spike positions.

2-D Bayesian deconvolution

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 2008-2018 ◽  
Author(s):  
Marc Lavielle
Keyword(s):  
Objective Function ◽  
Seismic Data ◽  
Layer Structure ◽  
A Priori ◽  
A Priori Information ◽  
The Earth ◽  
Markov Random ◽  
Posteriori Distribution ◽  
A Posteriori Distribution ◽  
Priori Information

Inverse problems can be solved in different ways. One way is to define natural criteria of good recovery and build an objective function to be minimized. If, instead, we prefer a Bayesian approach, inversion can be formulated as an estimation problem where a priori information is introduced and the a posteriori distribution of the unobserved variables is maximized. When this distribution is a Gibbs distribution, these two methods are equivalent. Furthermore, global optimization of the objective function can be performed with a Monte Carlo technique, in spite of the presence of numerous local minima. Application to multitrace deconvolution is proposed. In traditional 1-D deconvolution, a set of uni‐dimensional processes models the seismic data, while a Markov random field is used for 2-D deconvolution. In fact, the introduction of a neighborhood system permits one to model the layer structure that exists in the earth and to obtain solutions that present lateral coherency. Moreover, optimization of an appropriated objective function by simulated annealing allows one to control the fit with the input data as well as the spatial distribution of the reflectors. Extension to 3-D deconvolution is straightforward.

scholarly journals Predictive and mechanistic multivariate linear regression models for reaction development

2018 ◽  
Vol 9 (9) ◽  
pp. 2398-2412 ◽  
Author(s):  
Celine B. Santiago ◽  
Jing-Yao Guo ◽  
Matthew S. Sigman
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Molecular Descriptors ◽  
A Priori ◽  
Quantitative Description ◽  
Multivariate Linear Regression ◽  
Linear Regression Models ◽  
Physical Organic

The utilization of physical organic molecular descriptors for the quantitative description of reaction outcomes in multivariate linear regression models is demonstrated as an effective tool for a priori prediction and mechanistic interrogation.

scholarly journals Inverted Weibull Regression Models and Their Applications

Stats ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 269-290
Author(s):  
Sarah R. Al-Dawsari ◽  
Khalaf S. Sultan
Keyword(s):  
Regression Model ◽  
Bayesian Approach ◽  
Regression Models ◽  
Mean Squared Error ◽  
Information Criterion ◽  
Bayesian Regression ◽  
Loss Functions ◽  
Performance Criteria ◽  
Weibull Regression ◽  
The Bayesian Approach

In this paper, we propose the classical and Bayesian regression models for use in conjunction with the inverted Weibull (IW) distribution; there are the inverted Weibull Regression model (IW-Reg) and inverted Weibull Bayesian regression model (IW-BReg). In the proposed models, we suggest the logarithm and identity link functions, while in the Bayesian approach, we use a gamma prior and two loss functions, namely zero-one and modified general entropy (MGE) loss functions. To deal with the outliers in the proposed models, we apply Huber and Tukey’s bisquare (biweight) functions. In addition, we use the iteratively reweighted least squares (IRLS) algorithm to estimate Bayesian regression coefficients. Further, we compare IW-Reg and IW-BReg using some performance criteria, such as Akaike’s information criterion (AIC), deviance (D), and mean squared error (MSE). Finally, we apply the some real datasets collected from Saudi Arabia with the corresponding explanatory variables to the theoretical findings. The Bayesian approach shows better performance compare to the classical approach in terms of the considered performance criteria.

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