Automatic calculation of the sensitivity of Bayesian fisheries models to informative priors

2005 ◽  
Vol 62 (5) ◽  
pp. 1028-1036 ◽  
Author(s):  
Russell B Millar ◽  
Wayne S Stewart
Keyword(s):  
Exponential Family ◽  
Stock Assessment ◽  
Reproductive Rate ◽  
Model Parameters ◽  
Minor Addition ◽  
Ricker Model ◽  
Log Normal ◽  
A Minor ◽  
Us West ◽  
Derivatives Of

The derivatives of Bayes estimators, with respect to changes in hyper-parameters of the prior density, are posterior covariances. Hence, these derivatives can be readily estimated from a posterior sample and the calculation is shown to be especially straightforward for parameters having a marginal prior that is of exponential family form. Three examples are given. The first fits a Ricker curve to stock–recruit data and, for several important management parameters, examines the sensitivity of the Bayes estimates to the informative log-normal priors placed on the maximum annual reproductive rate and density-dependent compensation parameters. Using the WinBUGS software, it is demonstrated that these derivatives can easily be estimated by a minor addition to the program code. The utility of the estimated sensitivities is examined by refitting the Ricker model using a range of different priors. The second example revisits a hierarchical model that was used to perform a meta-stock assessment on several US West Coast rockfish (Sebastes spp.) stocks, and examines the sensitivity of the Bayes estimate of bulk catchability to the hyper-prior. The final example looks at an example from the literature and uses summary statistics provided therein to determine the sensitivity of model parameters to their prior means.

scholarly journals Avocado-Derived Biomass: Chemical Composition and Antioxidant Potential

Proceedings ◽  
2020 ◽  
Vol 70 (1) ◽  
pp. 100
Author(s):  
Minerva C. García-Vargas ◽  
María del Mar Contreras ◽  
Irene Gómez-Cruz ◽  
Juan Miguel Romero-García ◽  
Eulogio Castro
Keyword(s):  
Chemical Composition ◽  
Phenolic Content ◽  
Antioxidant Properties ◽  
Total Phenolic ◽  
Nutritional Properties ◽  
Aqueous Fraction ◽  
Extraction Solvent ◽  
Main Components ◽  
A Minor ◽  
Derivatives Of

Avocado has become fashionable due to its great organoleptic and nutritional properties. It is consumed as a fresh product and it is also processed to obtain salad oil and guacamole. In all cases, the only usable portion is the pulp. Therefore, to be a more sustainable and profitable agribusiness, it is important to recognize which compounds from the peel and the stone waste can be converted into valuable bio-products. Therefore, their chemical composition was determined according to the National Renewable Energy Laboratory, the total phenolic content by the Folin-Ciocalteu method and the antioxidant properties by the FRAP and TEAC assays. The main components of the peel and stone were acid-insoluble lignin (35.0% and 15.3%, respectively), polymeric sugars (23.6% and 43.9%, respectively), and the aqueous extractives (15.5% and 16.9%, respectively). Both biomasses contain lipids and protein, but a minor proportion (<6%). The valorization of lignin and sugars is of interest given the high content; stones are a rich source of glucose (93.2% of the polymeric fraction), which could be used to obtain biofuels or derivatives of interest. The extractive fraction of the peel contained the highest number of phenolic compounds (4.7 g/100 g biomass), mainly concentrated in the aqueous fraction (i.e., 87%) compared to the ethanol one, which was subsequently extracted. It correlated with major antioxidant activity and, therefore, the peel can be applied to obtain antioxidants and water can be used as an environmentally friendly extraction solvent.

Implications of Using Dual Number Derivatives With a Numerical Solution

2013 ◽  
Author(s):  
Suryanarayana R. Pakalapati ◽  
Hayri Sezer ◽  
Ismail B. Celik
Keyword(s):  
Automatic Differentiation ◽  
Numerical Solutions ◽  
Computer Code ◽  
Model Parameters ◽  
Model Parameter ◽  
Systematic Assessment ◽  
Dual Number ◽  
Advection Diffusion Equation ◽  
Model Equations ◽  
Derivatives Of

Dual number arithmetic is a well-known strategy for automatic differentiation of computer codes which gives exact derivatives, to the machine accuracy, of the computed quantities with respect to any of the involved variables. A common application of this concept in Computational Fluid Dynamics, or numerical modeling in general, is to assess the sensitivity of mathematical models to the model parameters. However, dual number arithmetic, in theory, finds the derivatives of the actual mathematical expressions evaluated by the computer code. Thus the sensitivity to a model parameter found by dual number automatic differentiation is essentially that of the combination of the actual mathematical equations, the numerical scheme and the grid used to solve the equations not just that of the model equations alone as implied by some studies. This aspect of the sensitivity analysis of numerical simulations using dual number auto derivation is explored in the current study. A simple one-dimensional advection diffusion equation is discretized using different schemes of finite volume method and the resulting systems of equations are solved numerically. Derivatives of the numerical solutions with respect to parameters are evaluated automatically using dual number automatic differentiation. In addition the derivatives are also estimated using finite differencing for comparison. The analytical solution was also found for the original PDE and derivatives of this solution are also computed analytically. It is shown that a mathematical model could potentially show different sensitivity to a model parameter depending on the numerical method employed to solve the equations and the grid resolution used. This distinction is important since such inter-dependence needs to be carefully addressed to avoid confusion when reporting the sensitivity of predictions to a model parameter using a computer code. A systematic assessment of numerical uncertainty in the sensitivities computed using automatic differentiation is presented.

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>

Grenadiers of the World Oceans: Biology, Stock Assessment, and Fisheries

2008 ◽  
Keyword(s):  
Deep Water ◽  
Stock Assessment ◽  
Data Availability ◽  
Biological Knowledge ◽  
Human Consumption ◽  
British Isles ◽  
The North ◽  
Mid Atlantic Ridge ◽  
Pros And Cons ◽  
A Minor

<em>Abstract</em>.—The biology and fisheries of macrourid species in the NE Atlantic are reviewed. Of about 30 species that occur within that area, the roundnose grenadier <em>Coryphaenoides rupestris </em>is one of the main target species of deep-water fisheries. Roughhead grenadier <em>Macrourus berglax </em>is a minor bycatch of other deep-water fisheries and an occasional target of some small fisheries. Other macrourid species are not commercially exploited because they are too small and/or in too deep waters, but some are also taken as accidental bycatch. There are three main fisheries for roundnose grenadier: north and west of the British Isles, Skagerrak, and Mid-Atlantic Ridge. The Skagerrak fishery is mainly for fish meal while the others are for human consumption. Due to data availability, a range of assessment methods has been trialled primarily for stocks to the north and west of the British Isles. Although uncertain, these assessments provide evidence that the stock has been severely depleted. Fisheries were largely unregulated until the early 2000s, but following repeated International Council for the Exploration of the Sea (ICES) advice, total allowable catches were introduced in 2003 together with effort and capacity regulations. Roundnose grenadier is the most studied species. It lives more than 50 years, compared to 30 years or more for roughhead grenadier. The limited knowledge of other species suggests a contrasting picture of maximum age ranging from 10 to 40 years. Taking into account the limited biological knowledge for these species, the pros and cons of the current management regime are discussed.

Processing properties of polypropylene with a minor addition of silicone oil

2010 ◽  
Vol 50 (7) ◽  
pp. 1340-1349 ◽  
Author(s):  
Wei Zhang ◽  
Sarang Deodhar ◽  
Donggang Yao
Keyword(s):  
Silicone Oil ◽  
Minor Addition ◽  
A Minor ◽  
Processing Properties

scholarly journals Variational Inference over Nonstationary Data Streams for Exponential Family Models

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1942
Author(s):  
Andrés R. Masegosa ◽  
Darío Ramos-López ◽  
Antonio Salmerón ◽  
Helge Langseth ◽  
Thomas D. Nielsen
Keyword(s):  
Bayesian Inference ◽  
Variational Methods ◽  
Latent Variables ◽  
Exponential Family ◽  
Concept Drift ◽  
Variational Inference ◽  
Model Parameters ◽  
Time Step ◽  
Data Set ◽  
Family Models

In many modern data analysis problems, the available data is not static but, instead, comes in a streaming fashion. Performing Bayesian inference on a data stream is challenging for several reasons. First, it requires continuous model updating and the ability to handle a posterior distribution conditioned on an unbounded data set. Secondly, the underlying data distribution may drift from one time step to another, and the classic i.i.d. (independent and identically distributed), or data exchangeability assumption does not hold anymore. In this paper, we present an approximate Bayesian inference approach using variational methods that addresses these issues for conjugate exponential family models with latent variables. Our proposal makes use of a novel scheme based on hierarchical priors to explicitly model temporal changes of the model parameters. We show how this approach induces an exponential forgetting mechanism with adaptive forgetting rates. The method is able to capture the smoothness of the concept drift, ranging from no drift to abrupt drift. The proposed variational inference scheme maintains the computational efficiency of variational methods over conjugate models, which is critical in streaming settings. The approach is validated on four different domains (energy, finance, geolocation, and text) using four real-world data sets.

The Refinement of the Nanoporous Copper by Adding Third Elements

2014 ◽  
Vol 783-786 ◽  
pp. 1986-1989
Author(s):  
Zhen Hua Dan ◽  
Feng Xiang Qin ◽  
Nobuyoshi Hara
Keyword(s):  
Lower Surface ◽  
Pore Sizes ◽  
Surface Diffusivity ◽  
Minor Addition ◽  
Cu Alloys ◽  
Nanoporous Copper ◽  
Order Of Magnitude ◽  
A Minor ◽  
Trace Formation ◽  
Nanoporous Structures

Fine nanoporous copper was fabricated from the amorphous Ti-Cu alloys with a minor addition of silver in 10 mM HF solutions. The pore sizes decreased from 100 nm to 12 nm with the increase of the Ag contents in comparison of Ti60Cu40 ribbons free of Ag. With increasing of the dealloying time, the sizes of the nanopores and ligaments increased for the nanostrucutres on Ti60Cu38Ag2 ribbons since the segregation of the Ag phase which triggered the galvanic dissolution of the adjacent Cu matrix in form of micro-couplings to further coarsen the nanoporous Cu. On the contrary, the trace formation of the Ag phase on the Ti60Cu39Ag1 ribbons had a weak ability to motivate the galvanic dissolution, indicating by the constant pore sizes and slight decrease in the ligament sizes with the increase in the dealloying time. The refinement of the nanoporous structures was ascribed to the drastic decrease in the surface diffusivity. The decrease in the surface diffusivity due to the involvement of Ag with a lower surface diffusivity in comparison of Cu was more than one order of magnitude. The involvement of Ag adatoms restricted the diffusion of Cu adatoms in the interface regions in the inward and outward directions.

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.

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