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.

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

scholarly journals Pushing the Limits of AMS Radiocarbon Dating with Improved Bayesian Data Analysis

Radiocarbon ◽  
2007 ◽  
Vol 49 (3) ◽  
pp. 1261-1272 ◽  
Author(s):  
V Palonen ◽  
P Tikkanen
Keyword(s):  
Mass Spectrometry ◽  
Data Analysis ◽  
Measurement Error ◽  
Accelerator Mass Spectrometry ◽  
Radiocarbon Dating ◽  
Analysis Model ◽  
Very Old ◽  
Ams Radiocarbon Dating ◽  
Car Model ◽  
Bayesian Data Analysis

We present an improved version of the continuous autoregressive (CAR) model, a Bayesian data analysis model for accelerator mass spectrometry (AMS). Measurement error is taken to be Poisson-distributed, improving the analysis for samples with only a few counts. This, in turn, enables pushing the limit of radiocarbon measurements to lower concentrations. On the computational side, machine drift is described with a vector of parameters, and hence the user can examine the probable shape of the trend. The model is compared to the conventional mean-based (MB) method, with simulated measurements representing a typical run of a modern AMS machine and a run with very old samples. In both comparisons, CAR has better precision, gives much more stable uncertainties, and is slightly more accurate. Finally, some results are given from Helsinki AMS measurements of background sample materials, with natural diamonds among them.

Exact Markov Chain Monte Carlo Algorithms and Their Applications in Probabilistic Data Analysis and Inference

2009 ◽  
pp. 161-183
Author(s):  
Dominic Savio Lee
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Data Analysis ◽  
Markov Chain Monte Carlo ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Probabilistic Data ◽  
Perfect Sampling ◽  
Monte Carlo Algorithms ◽  
Sampling Algorithms

This chapter describes algorithms that use Markov chains for generating exact sample values from complex distributions, and discusses their use in probabilistic data analysis and inference. Its purpose is to disseminate these ideas more widely so that their use will become more widespread, thereby improving Monte Carlo simulation results and stimulating greater research interest in the algorithms themselves. The chapter begins by introducing Markov chain Monte Carlo (MCMC), which stems from the idea that sample values from a desired distribution f can be obtained from the stationary states of an ergodic Markov chain whose stationary distribution is f. To get sample values that have distribution f exactly, it is necessary to detect when the Markov chain has reached its stationary distribution. Under certain conditions, this can be achieved by means of coupled Markov chains—these conditions and the resulting exact MCMC or perfect sampling algorithms and their applications are described.

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