scholarly journals Impacts of prior mis-specification on Bayesian fisheries stock assessment

2008 ◽  
Vol 59 (2) ◽  
pp. 145 ◽  
Author(s):  
Yong Chen ◽  
Chi-Lu Sun ◽  
Minoru Kanaiwa
Keyword(s):  
Distribution Function ◽  
Stock Assessment ◽  
Cauchy Distribution ◽  
Distribution Functions ◽  
Model Parameters ◽  
Large Uncertainty ◽  
Future Studies ◽  
Accuracy And Precision ◽  
Key Features ◽  
Sea Urchin Fishery

One of the key features of a Bayesian stock assessment is that the modeller needs to provide knowledge on model parameters. Priors summarise modellers’ understanding of model parameters and are often defined by a probability distribution function. Priors are often mis-specified with arbitrary and unrealistic accuracy and precision in perceiving the state of nature for the parameters as a result of our limited understanding of fisheries ecosystems. Commonly used probability functions such as normal distribution functions tend to be sensitive to prior mis-specification, resulting in large uncertainty and/or errors in Bayesian stock assessment. Fat-tailed functions such as the Cauchy distribution function have been found to be robust to prior mis-specification. Using the Maine sea urchin fishery as an example, we evaluated the impacts of mis-specification in defining the prior distributions on Bayesian stock assessment. The present study suggests that the quantification of priors with a Cauchy distribution tends to be robust to the prior mis-specification. Given our limited understanding of fisheries a function such as the Cauchy distribution function that is robust to prior mis-specification tends to be more desirable. Future studies should explore the use of other fat-tailed distribution functions for quantifying priors in fisheries stock assessment.

Impacts of outliers and mis-specification of priors on Bayesian fisheries-stock assessment

2000 ◽  
Vol 57 (11) ◽  
pp. 2293-2305 ◽  
Author(s):  
Y Chen ◽  
P A Breen ◽  
N L Andrew
Keyword(s):  
Normal Distribution ◽  
Stock Assessment ◽  
Management Strategies ◽  
Distribution Functions ◽  
Assessment Model ◽  
Fish Stock ◽  
Model Parameters ◽  
Prior Distributions ◽  
Likelihood Functions ◽  
Robust Likelihood

Bayesian inference is increasingly used in estimating model parameters for fish-stock assessment, because of its ability to incorporate uncertainty and prior knowledge and to provide information for risk analyses in evaluating alternative management strategies. Normal distributions are commonly used in formulating likelihood functions and informative prior distributions; these are sensitive to data outliers and mis-specification of prior distributions, both common problems in fisheries-stock assessment. Using a length-structured stock-assessment model for a New Zealand abalone fishery as an example, we evaluate the robustness of three likelihood functions and two prior-distribution functions, with respect to outliers and mis-specification of priors, in 48 different combinations. The two robust likelihood estimators performed slightly less well when no data outliers were present and much better when data outliers were present. Similarly, the Cauchy distribution was less sensitive to prior mis-specification than the normal distribution. We conclude that replacing the normal distribution with "fat-tailed" distributions for likelihoods and priors can improve Bayesian assessments when there are data outliers and mis-specification of priors, with relatively minor costs when there are none.

Estimation of thermal time model parameters for seed germination in 15 species: the importance of distribution function

2021 ◽  
pp. 1-8
Author(s):  
Dali Chen ◽  
Xianglai Chen ◽  
Jingjing Wang ◽  
Zuxin Zhang ◽  
Yan Wang ◽  
...  
Keyword(s):  
Distribution Function ◽  
Seed Germination ◽  
Normal Distribution ◽  
Distribution Functions ◽  
Thermal Time ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Time Model ◽  
Log Normal ◽  
Log Normal Distribution

Abstract Thermal time models have been widely applied to predict temperature requirements for seed germination. Generally, a log-normal distribution for thermal time [θT(g)] is used in such models at suboptimal temperatures to examine the variation in time to germination arising from variation in θT(g) within a seed population. Recently, additional distribution functions have been used in thermal time models to predict seed germination dynamics. However, the most suitable kind of the distribution function to use in thermal time models, especially at suboptimal temperatures, has not been determined. Five distributions (log-normal, Gumbel, logistic, Weibull and log-logistic) were used in thermal time models over a range of temperatures to fit the germination data for 15 species. The results showed that a more flexible model with the log-logistic distribution, rather than the log-normal distribution, provided the best explanation of θT(g) variation in 13 species at suboptimal temperatures. Thus, at least at suboptimal temperatures, the log-logistic distribution is an appropriate candidate among the five distributions used in this study. Therefore, the distribution of parameters [θT(g)] should be considered when using thermal time models to prevent large deviations; furthermore, an appropriate equation should be selected before using such a model to make predictions.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

scholarly journals An integrated tagging model to estimate mortality rates of Albemarle Sound – Roanoke River striped bass

2017 ◽  
Vol 74 (7) ◽  
pp. 1061-1076 ◽  
Author(s):  
Julianne E. Harris ◽  
Joseph E. Hightower
Keyword(s):  
Striped Bass ◽  
Stock Assessment ◽  
Mortality Rates ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Albemarle Sound ◽  
High Reward ◽  
Accuracy And Precision ◽  
Summer Mortality ◽  
Roanoke River

We developed an integrated tagging model to estimate mortality rates and run sizes of Albemarle Sound – Roanoke River striped bass (Morone saxatilis), including (i) a multistate component for telemetered fish with a high reward external tag; (ii) tag return components for fish with a low reward external or PIT tag; and (iii) catch-at-age data. Total annual instantaneous mortality was 1.08 for resident (458–899 mm total length, TL) and 0.45 for anadromous (≥900 mm TL) individuals. Annual instantaneous natural mortality was higher for resident (0.70) than for anadromous (0.21) fish due to high summer mortality in Albemarle Sound. Natural mortality for residents was substantially higher than currently assumed for stock assessment. Monthly fishing mortality from multiple sectors (including catch-and-release) corresponded to seasonal periods of legal harvest. Run size estimates were 499 000–715 000. Results and simulation suggest increasing sample size for the multistate component increases accuracy and precision of annual estimates and low reward tags are valuable for estimating monthly fishing mortality rates among sectors. Our results suggest that integrated tagging models can produce seasonal and annual mortality estimates needed for stock assessment and management.

scholarly journals Improving probabilistic flood forecasting through a data assimilation scheme based on genetic programming

2012 ◽  
Vol 12 (12) ◽  
pp. 3719-3732 ◽  
Author(s):  
L. Mediero ◽  
L. Garrote ◽  
A. Chavez-Jimenez
Keyword(s):  
Data Assimilation ◽  
Genetic Programming ◽  
Real Time ◽  
High Performance ◽  
Forecast Model ◽  
Flood Forecasting ◽  
Distribution Functions ◽  
Model Parameters ◽  
Hydrological Process ◽  
Model Based

Abstract. Opportunities offered by high performance computing provide a significant degree of promise in the enhancement of the performance of real-time flood forecasting systems. In this paper, a real-time framework for probabilistic flood forecasting through data assimilation is presented. The distributed rainfall-runoff real-time interactive basin simulator (RIBS) model is selected to simulate the hydrological process in the basin. Although the RIBS model is deterministic, it is run in a probabilistic way through the results of calibration developed in a previous work performed by the authors that identifies the probability distribution functions that best characterise the most relevant model parameters. Adaptive techniques improve the result of flood forecasts because the model can be adapted to observations in real time as new information is available. The new adaptive forecast model based on genetic programming as a data assimilation technique is compared with the previously developed flood forecast model based on the calibration results. Both models are probabilistic as they generate an ensemble of hydrographs, taking the different uncertainties inherent in any forecast process into account. The Manzanares River basin was selected as a case study, with the process being computationally intensive as it requires simulation of many replicas of the ensemble in real time.

scholarly journals Population changes in rattail species on the Chatham Rise

2021 ◽  
Author(s):  
◽  
Kathleen Large
Keyword(s):  
Maximum Likelihood ◽  
Stock Assessment ◽  
Production Model ◽  
Likelihood Method ◽  
Model Parameters ◽  
Important Species ◽  
Surplus Production ◽  
Surplus Production Model ◽  
Abundance Indices ◽  
The Impact

<p>The aim of this project was to conduct a stock assessment to determine the population dynamic characteristics of rattail species taken as bycatch in the hoki, hake and ling fishery on the Chatham Rise. No quantitative assessment of the current size of rattail populations , and how these may have changed over time, has been carried out before. There is interest in the need to quantify the impact of commercial fishing on the rattail populations, as rattails (Macrouridae family) are considered to be an ecologically important species complex in the deep ocean, and there may be the potential for the development of a commercial fishery based on their value as processed fishmeal. The minimum data required for a stock assessment are an abundance index and a catch history. Abundance indices are available for over 20 species of rattail produced from scientific surveys conducted annually on the Chatham Rise since 1992. Catch histories for individual rattail species in the same area are not available. A method was developed to reconstruct commercial catches of rattails from commercial effort data and survey catch and effort data. A surplus production model was fitted to the reconstructed catch data and survey abundance indices, using maximum likelihood and Bayesian methods to estimate model parameters and uncertainty. A surplus production model has two components: an observation model for abundance indices and a process model for population dynamics. Maximum likelihood estimation was applied to a model that specified errors for the observations only, and this produced estimates that had wide confidence intervals. A Bayesian approach was then taken to fit a statespace version of the model that incorporates errors associated with the observation and process models. While the Bayesian method produced more plausible parameter estimates (in comparison to the maximum likelihood method) and parameter uncertainty was reduced, our analysis indicated the posterior estimates were highly sensitive to the specification of different priors. There may be several reasons for these results, including: the small number of observations, lack of contrast in the data and mis-specification of the model. Meaningful estimates of the absolute size of rattail populations are not possible with these results, where estimates can vary by orders of magnitude depending on prior specification. This implies that more work needs to be done to develop more effective methods that can be used to help inform decisions regarding the management of these fish populations. Improving data collection, investigating informative priors and extending/respecifying the model are considered worthwhile avenues of future work to improve stock assessments of rattails.</p>

scholarly journals Estimating a Distribution Function at the Boundary

2020 ◽  
Vol 49 (1) ◽  
pp. 1-23
Author(s):  
Shunpu Zhang ◽  
Zhong Li ◽  
Zhiying Zhang
Keyword(s):  
Distribution Function ◽  
Kernel Estimation ◽  
Kernel Estimator ◽  
Distribution Functions ◽  
Practical Application ◽  
Real World Applications ◽  
Distribution Kernel ◽  
Estimation Of Distribution ◽  
Simulation Results ◽  
Boundary Correction

Estimation of distribution functions has many real-world applications. We study kernel estimation of a distribution function when the density function has compact support. We show that, for densities taking value zero at the endpoints of the support, the kernel distribution estimator does not need boundary correction. Otherwise, boundary correction is necessary. In this paper, we propose a boundary distribution kernel estimator which is free of boundary problem and provides non-negative and non-decreasing distribution estimates between zero and one. Extensive simulation results show that boundary distribution kernel estimator provides better distribution estimates than the existing boundary correction methods. For practical application of the proposed methods, a data-dependent method for choosing the bandwidth is also proposed.

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