Bayesian data analysis for agricultural experiments

2010 ◽  
Vol 90 (5) ◽  
pp. 575-603 ◽  
Author(s):  
X. Che ◽  
S. Xu
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Data Analysis ◽  
Markov Chain Monte Carlo ◽  
Linear Model ◽  
Generalized Linear Model ◽  
Bayesian Method ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Mcmc Algorithm

Data collected in agricultural experiments can be analyzed in many different ways using different models. The most commonly used models are the linear model and the generalized linear model. The maximum likelihood method is often used for data analysis. However, this method may not be able to handle complicated models, especially multiple level hierarchical models. The Bayesian method partitions complicated models into simple components, each of which may be formulated analytically. Therefore, the Bayesian method is capable of handling very complicated models. The Bayesian method itself may not be more complicated than the maximum likelihood method, but the analysis is time consuming, because numerical integration involved in Bayesian analysis is almost exclusively accomplished based on Monte Carlo simulations, the so called Markov Chain Monte Carlo (MCMC) algorithm. Although the MCMC algorithm is intuitive and straightforward to statisticians, it may not be that simple to agricultural scientists, whose main purpose is to implement the method and interpret the results. In this review, we provide the general concept of Bayesian analysis and the MCMC algorithm in a way that can be understood by non-statisticians. We also demonstrate the implementation of the MCMC algorithm using professional software packages such as the MCMC procedure in SAS software. Three datasets from agricultural experiments were analyzed to demonstrate the MCMC algorithm.Key words: Bayesian method, Generalized linear model, Markov Chain Monte Carlo, SAS, WinBUGS

Markov Chain Monte Carlo

2015 ◽  
Author(s):  
N. Thompson Hobbs ◽  
Mevin B. Hooten
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Analysis ◽  
Posterior Distribution ◽  
Mcmc Algorithm ◽  
Bayesian Analyses ◽  
Seminal Paper ◽  
Formal Treatment ◽  
High Level

This chapter explains how to implement Bayesian analyses using the Markov chain Monte Carlo (MCMC) algorithm, a set of methods for Bayesian analysis made popular by the seminal paper of Gelfand and Smith (1990). It begins with an explanation of MCMC with a heuristic, high-level treatment of the algorithm, describing its operation in simple terms with a minimum of formalism. In this first part, the chapter explains the algorithm so that all readers can gain an intuitive understanding of how to find the posterior distribution by sampling from it. Next, the chapter offers a somewhat more formal treatment of how MCMC is implemented mathematically. Finally, this chapter discusses implementation of Bayesian models via two routes—by using software and by writing one's own algorithm.

A two-step inversion approach for seismic-reservoir characterization and a comparison with a single-loop Markov-chain Monte Carlo algorithm

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. R227-R244 ◽  
Author(s):  
Mattia Aleardi ◽  
Fabio Ciabarri ◽  
Timur Gukov
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Reservoir Characterization ◽  
Gaussian Mixture ◽  
Petrophysical Properties ◽  
Mcmc Algorithm ◽  
Prior Model ◽  
Single Loop ◽  
Seismic Reservoir

We have evaluated a two-step Bayesian algorithm for seismic-reservoir characterization, which, thanks to some simplifying assumptions, is computationally very efficient. The applicability and reliability of this method are assessed by comparison with a more sophisticated and computer-intensive Markov-chain Monte Carlo (MCMC) algorithm, which in a single loop directly estimates petrophysical properties and lithofluid facies from prestack data. The two-step method first combines a linear rock-physics model (RPM) with the analytical solution of a linearized amplitude versus angle (AVA) inversion, to directly estimate the petrophysical properties, and related uncertainties, from prestack data under the assumptions of a Gaussian prior model and weak elastic contrasts at the reflecting interface. In particular, we use an empirical, linear RPM, properly calibrated for the investigated area, to reparameterize the linear time-continuous P-wave reflectivity equation in terms of petrophysical contrasts instead of elastic constants. In the second step, a downward 1D Markov-chain prior model is used to infer the lithofluid classes from the outcomes of the first step. The single-loop (SL) MCMC algorithm uses a convolutional forward modeling based on the exact Zoeppritz equations, and it adopts a nonlinear RPM. Moreover, it assumes a more realistic Gaussian mixture distribution for the petrophysical properties. Both approaches are applied on an onshore 3D seismic data set for the characterization of a gas-bearing, clastic reservoir. Notwithstanding the differences in the forward-model parameterization, in the considered RPM, and in the assumed a priori probability density functions, the two methods yield maximum a posteriori solutions that are consistent with well-log data, although the Gaussian mixture assumption adopted by the SL method slightly improves the description of the multimodal behavior of the petrophysical parameters. However, in the considered reservoir, the main difference between the two approaches remains the very different computational times, the SL method being much more computationally intensive than the two-step approach.

scholarly journals Parameters Identification for Inverse Option Problems Using Markov Chain Monte Carlo Methods

2019 ◽  
Author(s):  
Yasushi Ota ◽  
Yu Jiang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Inference ◽  
Financial Markets ◽  
Sampling Strategy ◽  
Measured Data ◽  
Mcmc Algorithm ◽  
Unknown Parameters ◽  
Posterior Probability Density

This paper investigates the inverse option problems (IOP) in the extended Black--Scholes model arising in financial markets. We identify the volatility and the drift coefficient from the measured data in financial markets using a Bayesian inference approach, which is presented as an IOP solution. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC) algorithm, which exploits the posterior state space. The efficient sampling strategy of the MCMC algorithm enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown trend and volatility coefficients from the measured data.

A two-stage Markov chain Monte Carlo method for seismic inversion and uncertainty quantification

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R1003-R1020 ◽  
Author(s):  
Georgia K. Stuart ◽  
Susan E. Minkoff ◽  
Felipe Pereira
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Uncertainty Quantification ◽  
Bayesian Methods ◽  
Posterior Distributions ◽  
Mcmc Algorithm ◽  
Two Stage ◽  
Fine Grid ◽  
Highest Posterior Density

Bayesian methods for full-waveform inversion allow quantification of uncertainty in the solution, including determination of interval estimates and posterior distributions of the model unknowns. Markov chain Monte Carlo (MCMC) methods produce posterior distributions subject to fewer assumptions, such as normality, than deterministic Bayesian methods. However, MCMC is computationally a very expensive process that requires repeated solution of the wave equation for different velocity samples. Ultimately, a large proportion of these samples (often 40%–90%) is rejected. We have evaluated a two-stage MCMC algorithm that uses a coarse-grid filter to quickly reject unacceptable velocity proposals, thereby reducing the computational expense of solving the velocity inversion problem and quantifying uncertainty. Our filter stage uses operator upscaling, which provides near-perfect speedup in parallel with essentially no communication between processes and produces data that are highly correlated with those obtained from the full fine-grid solution. Four numerical experiments demonstrate the efficiency and accuracy of the method. The two-stage MCMC algorithm produce the same results (i.e., posterior distributions and uncertainty information, such as medians and highest posterior density intervals) as the Metropolis-Hastings MCMC. Thus, no information needed for uncertainty quantification is compromised when replacing the one-stage MCMC with the more computationally efficient two-stage MCMC. In four representative experiments, the two-stage method reduces the time spent on rejected models by one-third to one-half, which is important because most of models tried during the course of the MCMC algorithm are rejected. Furthermore, the two-stage MCMC algorithm substantially reduced the overall time-per-trial by as much as 40%, while increasing the acceptance rate from 9% to 90%.

Railway ballast damage detection by Markov chain Monte Carlo-based Bayesian method

2017 ◽  
Vol 17 (3) ◽  
pp. 706-724 ◽  
Author(s):  
Heung F Lam ◽  
Jia H Yang ◽  
Qin Hu ◽  
Ching T Ng
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Damage Detection ◽  
Bayesian Method ◽  
Model Updating ◽  
Railway Ballast ◽  
Vibration Data ◽  
Important Region ◽  
Stiffness Distribution

This article reports the development of a Bayesian method for assessing the damage status of railway ballast under a concrete sleeper based on vibration data of the in situ sleeper. One of the important contributions of the proposed method is to describe the variation of stiffness distribution of ballast using Lagrange polynomial, for which the order of the polynomial is decided by the Bayesian approach. The probability of various orders of polynomial conditional on a given set of measured vibration data is calculated. The order of polynomial with the highest probability is selected as the most plausible order and used for updating the ballast stiffness distribution. Due to the uncertain nature of railway ballast, the corresponding model updating problem is usually unidentifiable. To ensure the applicability of the proposed method even in unidentifiable cases, a computational efficient Markov chain Monte Carlo–based Bayesian method was employed in the proposed method for generating a set of samples in the important region of parameter space to approximate the posterior (updated) probability density function of ballast stiffness. The proposed ballast damage detection method was verified with roving hammer test data from a segment of full-scale ballasted track. The experimental verification results positively show the potential of the proposed method in ballast damage detection.

scholarly journals Using car4ams, the Bayesian AMS Data Analysis Code

Radiocarbon ◽  
2010 ◽  
Vol 52 (3) ◽  
pp. 948-952 ◽  
Author(s):  
V Palonen ◽  
P Tikkanen ◽  
J Keinonen
Keyword(s):  
Mass Spectrometry ◽  
Monte Carlo ◽  
Markov Chain ◽  
Data Analysis ◽  
Markov Chain Monte Carlo ◽  
Accelerator Mass Spectrometry ◽  
Autoregressive Model ◽  
Car Model ◽  
R Program ◽  
Main Disadvantage

The Bayesian CAR (continuous autoregressive) model for accelerator mass spectrometry (AMS) data analysis delivers uncertainties with less scatter and bias. Better detection and estimation of the instrumental error of the AMS machine are also achieved. Presently, the main disadvantage is the several-hour duration of the analysis. The Markov chain Monte Carlo (MCMC) program for CAR model analysis, car4ams, has been made freely available under the GPL license. Included in the package is an R program that analyzes the car4ams output and summarizes the results in graphical and spreadsheet formats. We describe the main properties of the CAR analysis and the use of the 2 parts of the program package for radiocarbon AMS data analysis.

The estimated parameter of logistic regression model by Markov Chain Monte Carlo method with multicollinearity

2020 ◽  
Vol 36 (4) ◽  
pp. 1253-1259
Author(s):  
Autcha Araveeporn ◽  
Yuwadee Klomwises
Keyword(s):  
Monte Carlo ◽  
Logistic Regression ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Maximum Likelihood ◽  
Regression Model ◽  
Ridge Regression ◽  
Logistic Regression Model ◽  
Classical Method ◽  
Likelihood Method

Markov Chain Monte Carlo (MCMC) method has been a popular method for getting information about probability distribution for estimating posterior distribution by Gibbs sampling. So far, the standard methods such as maximum likelihood and logistic ridge regression methods have represented to compare with MCMC. The maximum likelihood method is the classical method to estimate the parameter on the logistic regression model by differential the loglikelihood function on the estimator. The logistic ridge regression depends on the choice of ridge parameter by using crossvalidation for computing estimator on penalty function. This paper provides maximum likelihood, logistic ridge regression, and MCMC to estimate parameter on logit function and transforms into a probability. The logistic regression model predicts the probability to observe a phenomenon. The prediction accuracy evaluates in terms of the percentage with correct predictions of a binary event. A simulation study conducts a binary response variable by using 2, 4, and 6 explanatory variables, which are generated from multivariate normal distribution on the positive and negative correlation coefficient or called multicollinearity problem. The criterion of these methods is to compare by a maximum of predictive accuracy. The outcomes find that MCMC satisfies all situations.

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