Evaluating uncertainty in harvest control law catches using Bayesian Markov chain Monte Carlo virtual population analysis with adaptive rejection sampling and including structural uncertainty

1999 ◽  
Vol 56 (2) ◽  
pp. 208-221 ◽  
Author(s):  
K R Patterson
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Reference Points ◽  
Clupea Harengus ◽  
Assessment Model ◽  
Critical Parameters ◽  
Control Law ◽  
Model Structure ◽  
Posterior Distributions

A new method is developed for calculating Bayes posterior distributions of future catches that conform to a specified harvest control law while incorporating uncertainty in biological reference points, natural mortality, and some aspects of model structure in addition to the usual stochastic noise. A Markov chain Monte Carlo approach is used to calculate Bayesian posterior distributions for critical parameters of a Norwegian spring-spawning herring (Clupea harengus) stock assessment using an assessment model that incorporates catch-at-age, survey, and tag release and recapture observations. Exceptionally, the approach allows prior uncertainty in model structure (e.g., whether survey observation errors should be treated as normal, lognormal, or gamma variates; whether Ricker or Beverton-Holt forms are used to model recruitment). This modelling approach is a useful tool that allows management advice to be provided that takes into account uncertainty in model structures and in some parameters that, by conventional methods, need to be specified as arbitrary "best" choices. The method is also used to quantify uncertainty in some biological reference points and to calculate a probability distribution for a future catch with respect to a specified harvest control law. This has the advantage of a consistent treatment of uncertainty throughout the process of stock modelling, reference point estimation, and concomitant catch forecasting.

scholarly journals Parallel Markov chain Monte Carlo for non-Gaussian posterior distributions

Stat ◽  
2015 ◽  
Vol 4 (1) ◽  
pp. 304-319 ◽  
Author(s):  
Alexey Miroshnikov ◽  
Zheng Wei ◽  
Erin Marie Conlon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Posterior Distributions ◽  
Non Gaussian

scholarly journals Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

2017 ◽  
Vol 14 (18) ◽  
pp. 4295-4314 ◽  
Author(s):  
Dan Lu ◽  
Daniel Ricciuto ◽  
Anthony Walker ◽  
Cosmin Safta ◽  
William Munger
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Likelihood Function ◽  
Terrestrial Ecosystem ◽  
Error Model ◽  
Model Parameters ◽  
Posterior Distributions ◽  
Ecosystem Models ◽  
Bayesian Calibration

Abstract. Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. The result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.

scholarly journals A sequential Bayesian approach for the estimation of the age–depth relationship of Dome Fuji ice core

2015 ◽  
Vol 2 (3) ◽  
pp. 939-968
Author(s):  
S. Nakano ◽  
K. Suzuki ◽  
K. Kawamura ◽  
F. Parrenin ◽  
T. Higuchi
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Sequential Monte Carlo ◽  
Ice Core ◽  
Posterior Distributions ◽  
Metropolis Method ◽  
Depth Relationship ◽  
Relationship Of ◽  
Thinning Process

Abstract. A technique for estimating the age–depth relationship in an ice core and evaluating its uncertainty is presented. The age–depth relationship is mainly determined by the accumulation of snow at the site of the ice core and the thinning process due to the horizontal stretching and vertical compression of ice layers. However, since neither the accumulation process nor the thinning process are fully understood, it is essential to incorporate observational information into a model that describes the accumulation and thinning processes. In the proposed technique, the age as a function of depth is estimated from age markers and δ18O data. The estimation is achieved using the particle Markov chain Monte Carlo (PMCMC) method, in which the sequential Monte Carlo (SMC) method is combined with the Markov chain Monte Carlo method. In this hybrid method, the posterior distributions for the parameters in the models for the accumulation and thinning processes are computed using the Metropolis method, in which the likelihood is obtained with the SMC method. Meanwhile, the posterior distribution for the age as a function of depth is obtained by collecting the samples generated by the SMC method with Metropolis iterations. The use of this PMCMC method enables us to estimate the age–depth relationship without assuming either linearity or Gaussianity. The performance of the proposed technique is demonstrated by applying it to ice core data from Dome Fuji in Antarctica.

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%.

Introduction to Simulation and MCMC Methods

2011 ◽  
pp. 182-217 ◽  
Author(s):  
Siddhartha Chib
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Marginal Likelihood ◽  
Mcmc Methods ◽  
Posterior Distributions ◽  
Extensive Discussion ◽  
Block Algorithm ◽  
Target Probability ◽  
Acceptance Condition

The purpose of this article is to provide an overview of Monte Carlo methods for generating variates from a target probability distribution that are based on Markov chains. These methods, called Markov chain Monte Carlo (MCMC) methods, are widely used to summarize complicated posterior distributions in Bayesian statistics and econometrics. This article begins with an intuitive explanation of the ideas and concepts that underlie popular algorithms such as the Metropolis-Hastings algorithm and multi-block algorithm. It provides the concept of a source or proposal density, which is used to supply a randomization step or an acceptance condition to determine if the candidate draw should be accepted. It is important to assess the performance of the sampling algorithm to determine the rate of mixing. Finally, this article offers an extensive discussion of marginal likelihood calculation using posterior simulator output.

scholarly journals Bayesian calibration of terrestrial ecosystem models: A study of advanced Markov chain Monte Carlo methods

2017 ◽  
Author(s):  
Dan Lu ◽  
Daniel Ricciuto ◽  
Anthony Walker ◽  
Cosmin Safta ◽  
William Munger
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Differential Evolution ◽  
Terrestrial Ecosystem ◽  
Predictive Performance ◽  
Model Parameters ◽  
Posterior Distributions ◽  
Single Chain ◽  
Ecosystem Models

Abstract. Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this study, a Differential Evolution Adaptive Metropolis (DREAM) algorithm was used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The DREAM is a multi-chain method and uses differential evolution technique for chain movement, allowing it to be efficiently applied to high-dimensional problems, and can reliably estimate heavy-tailed and multimodal distributions that are difficult for single-chain schemes using a Gaussian proposal distribution. The results were evaluated against the popular Adaptive Metropolis (AM) scheme. DREAM indicated that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identified one mode. The calibration of DREAM resulted in a better model fit and predictive performance compared to the AM. DREAM provides means for a good exploration of the posterior distributions of model parameters. It reduces the risk of false convergence to a local optimum and potentially improves the predictive performance of the calibrated model.

Markov-chain Monte Carlo estimation of distributed Debye relaxations in spectral induced polarization

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. E159-E170 ◽  
Author(s):  
John Keery ◽  
Andrew Binley ◽  
Ahmed Elshenawy ◽  
Jeremy Clifford
Keyword(s):  
Porous Media ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Physical Properties ◽  
Relaxation Times ◽  
Synthetic Data ◽  
Induced Polarization ◽  
Posterior Distributions ◽  
Spectral Induced Polarization

There is growing interest in the link between electrical polarization and physical properties of geologic porous media. In particular, spectral characteristics may be controlled by the same pore geometric properties that influence fluid permeability of such media. Various models have been proposed to describe the spectral-induced-polarization (SIP) response of permeable rocks, and the links between these models and hydraulic properties have been explored, albeit empirically. Computation of the uncertainties in the parameters of such electrical models is essential for effective use of these relationships. The formulation of an electrical dispersion model in terms of a distribution of relaxation times and associated chargeabilities has been demonstrated to be an effective generalized approach; however, thus far, such an approach has only been considered in a deterministic framework. Here, we formulate a spectral model based on a distribution of polarizations. By using a simple polynomial descriptor of such a distribution, we are able to cast the model in a stochastic manner and solve it using a Markov-chain Monte Carlo (McMC) sampler, thus allowing the computation of model-parameter uncertainties. We apply the model to synthetic data and demonstrate that the stochastic method can provide posterior distributions of model parameters with narrow bounds around the true values when little or no noise is added to the synthetic data, with posterior distributions that broaden with increasing noise. We also apply our model to experimental measurements of six sandstone samples and compare physical properties of a number of samples of porous media with stochastic estimates of characteristic relaxation times. We demonstrate the utility of our method on electrical spectra with different response characteristics and show that a single metric of relaxation time for the SIP response is not sufficient to provide clear insight into the physical characteristics of a sample.

scholarly journals Performance of Hamiltonian Monte Carlo and No-U-Turn Sampler for estimating genetic parameters and breeding values

2019 ◽  
Vol 51 (1) ◽  
Author(s):  
Motohide Nishio ◽  
Aisaku Arakawa
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Gibbs Sampling ◽  
Genetic Parameters ◽  
Simulated Data ◽  
Animal Breeding ◽  
Posterior Distributions ◽  
Breeding Values ◽  
Hamiltonian Monte Carlo

Abstract Background Hamiltonian Monte Carlo is one of the algorithms of the Markov chain Monte Carlo method that uses Hamiltonian dynamics to propose samples that follow a target distribution. The method can avoid the random walk behavior to achieve a more effective and consistent exploration of the probability space and sensitivity to correlated parameters, which are shortcomings that plague many Markov chain Monte Carlo methods. However, the performance of Hamiltonian Monte Carlo is highly sensitive to two hyperparameters. The No-U-Turn Sampler, an extension of Hamiltonian Monte Carlo, was recently introduced to automate the tuning of these hyperparameters. Thus, this study compared the performances of Gibbs sampling, Hamiltonian Monte Carlo, and the No-U-Turn Sampler for estimating genetic parameters and breeding values as well as sampling qualities in both simulated and real pig data. For all datasets, we used a pedigree-based univariate linear mixed model. Results For all datasets, the No-U-Turn Sampler and Gibbs sampling performed comparably regarding the estimation of heritabilities and accuracies of breeding values. Compared with Gibbs sampling, the estimates of effective sample sizes for simulated and pig data with the No-U-Turn Sampler were 3.2 to 22.6 and 3.5 to 5.9 times larger, respectively. Autocorrelations decreased more quickly with the No-U-Turn Sampler than with Gibbs sampling. When true heritability was low in the simulated data, the skewness of the marginal posterior distributions with the No-U-Turn Sampler was smaller than that with Gibbs sampling. The performance of Hamiltonian Monte Carlo for sampling quality was inferior to that of No-U-Turn Sampler in the simulated data. Moreover, Hamiltonian Monte Carlo could not estimate genetic parameters because of difficulties with the hyperparameter settings with pig data. Conclusions The No-U-Turn Sampler is a promising sampling method for animal breeding because of its good sampling qualities: large effective sample sizes, low autocorrelations, and low skewness of marginal posterior distributions, particularly when heritability is low. Meanwhile, Hamiltonian Monte Carlo failed to converge with a simple univariate model for pig data. Thus, it might be difficult to use Hamiltonian Monte Carlo for usual complex models in animal breeding.

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