Bayesian stock assessment using a state–space implementation of the delay difference model

1999 ◽  
Vol 56 (1) ◽  
pp. 37-52 ◽  
Author(s):  
Renate Meyer ◽  
Russell B Millar
Keyword(s):  
State Space ◽  
Bayesian Approach ◽  
Stock Assessment ◽  
State Space Model ◽  
Random Errors ◽  
Difference Model ◽  
Spawning Stock ◽  
The Common ◽  
Biomass Dynamics ◽  
Delay Difference

This paper presents a Bayesian approach to fisheries stock assessment using the delay difference model to describe nonlinear population dynamics. Given a time series of annual catch and effort data, models in the Deriso-Schnute family predict exploitable biomass in the following year from biomass in the current and previous year and from past spawning stock. A state-space model is used, as it allows incorporation of random errors in both the biomass dynamics equations and the observations. Because the biomass dynamics are nonlinear, the common Kalman filter is generally not applicable for parameter estimation. However, it is demonstrated that the Bayesian approach can handle any form of nonlinear relationship in the state and observation equations as well as realistic distributional assumptions. Difficulties with posterior calculations are overcome by the Gibbs sampler in conjunction with the adaptive rejection Metropolis sampling algorithm.

Estimating multifleet catchability coefficients and natural mortality from fishery catch and effort data: comparison of Bayesian state–space and observation error models

2011 ◽  
Vol 68 (7) ◽  
pp. 1171-1181 ◽  
Author(s):  
Shijie Zhou ◽  
André E. Punt ◽  
Roy Deng ◽  
Janet Bishop
Keyword(s):  
State Space ◽  
Stock Assessment ◽  
Observation Error ◽  
Natural Mortality ◽  
Posterior Median ◽  
Median Estimate ◽  
Penaeus Semisulcatus ◽  
Process Error ◽  
Two Parameters ◽  
Delay Difference

Catchability and natural mortality are key quantities in fisheries stock assessment. However, it is difficult to estimate these two parameters simultaneously using only fishery catch and effort data. A Bayesian state–space modified delay–difference model is outlined that can estimate time series of catchability by fleet as well as natural mortality. This model, and three variants thereof, is fitted to data for grooved tiger prawns ( Penaeus semisulcatus ) in Australia’s Northern Prawn Fishery during the period of the year when there is little recruitment. A model that allows for both observation and process error and estimates natural mortality is best, in terms of model selection criteria as well as fit diagnostics. The posterior median estimate for catchability for the primary target fleet ranges from 6.15 × 10−4 to 1.09 × 10−4 during 1980–2007, while the posterior median estimate for catchability for a fleet with P. semisulcatus as its byproduct is about 20% of that for the primary fleet. Fishing efficiency increased at approximately 2% annually during 1980–2007, while the weekly natural mortality is estimated to be 0.053 week–1.

scholarly journals Modelling Complexity and Uncertainty in Fisheries Stock Assessment

2021 ◽  
Author(s):  
◽  
D'Arcy Webber
Keyword(s):  
New Zealand ◽  
State Space ◽  
Ross Sea ◽  
Stock Assessment ◽  
State Space Model ◽  
Computational Cost ◽  
Original Model ◽  
Agent Based Models ◽  
Agent Based ◽  
Space Model

<p>Stock assessment models are used to determine the population size of fish stocks. Although stock assessment models are complex, they still make simplifying assumptions. Generally, they treat each species separately, include little, if any, spatial structure, and may not adequately quantify uncertainty. These assumptions can introduce bias and can lead to incorrect inferences. This thesis is about more realistic models and their inference. This realism may be incorporated by explicitly modelling complex processes, or by admitting our uncertainty and modelling it correctly.  We develop an agent-based model that can describe fish populations as a collection of individuals which differ in their growth, maturation, migration, and mortality. The aim of this model is to better capture the richness in natural processes that determine fish abundance and subsequent population response to anthropogenic removals. However, this detail comes at considerable computational cost. A single model run can take many hours, making inference using standard methods impractical. We apply this model to New Zealand snapper (Pagurus auratus) in northern New Zealand.  Next, we developed an age-structured state-space model. We suggest that this sophisticated model has the potential to better represent uncertainty in stock assessment. However, it pushes the boundaries of the current practical limits of computing and we admit that its practical application remains limited until the MCMC mixing issues that we encountered can be resolved.   The processes that underpin agent-based models are complex and we may need to seek new sources of data to inform these types of models. To make a start here we derive a state-space model to estimate the path taken by individual fish from the day they are tagged to the day of their recapture. The model uses environmental information collected using pop-up satellite archival tags. We use tag recorded depth and oceanographic temperature to estimate the location at any given time. We apply this model to Antarctic toothfish (Dissostichus mawsoni) in the Ross Sea.  Finally, to reduce the computational burden of agent-based models we use Bayesian emulation. This approach replaces the simulation model with an approximating algorithm called an emulator. The emulator is calibrated using relatively few runs of the original model. A good emulator provides a close approximation to the original model and has significant speed gains. Thus, inferences become tractable.  We have made the first steps towards developing a tractable approach to fisheries modelling in complex settings through the creation of realistic models, and their emulation. With further development, Bayesian emulation could result in the increased ability to consider and evaluate innovative methods in fisheries modelling. Future avenues for application and exploration range from spatial and multi species models, to ecosystem-based models and beyond.</p>

BUGS in Bayesian stock assessments

1999 ◽  
Vol 56 (6) ◽  
pp. 1078-1087 ◽  
Author(s):  
Renate Meyer ◽  
Russell B Millar
Keyword(s):  
State Space ◽  
Stock Assessment ◽  
State Space Model ◽  
Production Model ◽  
Posterior Density ◽  
Convergence Diagnostics ◽  
Surplus Production Model ◽  
Nonlinear State Space Models ◽  
Age Structured ◽  
Joint Posterior Density

This paper illustrates the ease with which Bayesian nonlinear state-space models can now be used for practical fisheries stock assessment. Sampling from the joint posterior density is accomplished using Gibbs sampling via BUGS, a freely available software package. By taking advantage of the model representation as a directed acyclic graph, BUGS automates the hitherto tedious calculation of the full conditional posterior distributions. Moreover, the output from BUGS can be read directly into the software CODA for convergence diagnostics and statistical summary. We illustrate the BUGS implementation of a nonlinear nonnormal state-space model using a Schaefer surplus production model as a basic example. This approach extends to other assessment methodologies, including delay difference and age-structured models.

scholarly journals A latent low-dimensional common input drives a pool of motor neurons: a probabilistic latent state-space model

2017 ◽  
Vol 118 (4) ◽  
pp. 2238-2250 ◽  
Author(s):  
Daniel F. Feeney ◽  
François G. Meyer ◽  
Nicholas Noone ◽  
Roger M. Enoka
Keyword(s):  
State Space ◽  
Motor Neurons ◽  
Input Signal ◽  
State Space Model ◽  
Motor Units ◽  
Common Input ◽  
State Space Approach ◽  
Space Model ◽  
Discharge Activity ◽  
The Common

Motor neurons appear to be activated with a common input signal that modulates the discharge activity of all neurons in the motor nucleus. It has proven difficult for neurophysiologists to quantify the variability in a common input signal, but characterization of such a signal may improve our understanding of how the activation signal varies across motor tasks. Contemporary methods of quantifying the common input to motor neurons rely on compiling discrete action potentials into continuous time series, assuming the motor pool acts as a linear filter, and requiring signals to be of sufficient duration for frequency analysis. We introduce a space-state model in which the discharge activity of motor neurons is modeled as inhomogeneous Poisson processes and propose a method to quantify an abstract latent trajectory that represents the common input received by motor neurons. The approach also approximates the variation in synaptic noise in the common input signal. The model is validated with four data sets: a simulation of 120 motor units, a pair of integrate-and-fire neurons with a Renshaw cell providing inhibitory feedback, the discharge activity of 10 integrate-and-fire neurons, and the discharge times of concurrently active motor units during an isometric voluntary contraction. The simulations revealed that a latent state-space model is able to quantify the trajectory and variability of the common input signal across all four conditions. When compared with the cumulative spike train method of characterizing common input, the state-space approach was more sensitive to the details of the common input current and was less influenced by the duration of the signal. The state-space approach appears to be capable of detecting rather modest changes in common input signals across conditions. NEW & NOTEWORTHY We propose a state-space model that explicitly delineates a common input signal sent to motor neurons and the physiological noise inherent in synaptic signal transmission. This is the first application of a deterministic state-space model to represent the discharge characteristics of motor units during voluntary contractions.

A state-space spatial survey-based stock assessment (SSURBA) model to inform spatial variation in relative stock trends

2020 ◽  
Vol 77 (10) ◽  
pp. 1638-1658
Author(s):  
Rajeev Kumar ◽  
Noel G. Cadigan ◽  
Nan Zheng ◽  
Divya A. Varkey ◽  
M. Joanne Morgan
Keyword(s):  
State Space ◽  
Stock Assessment ◽  
State Space Model ◽  
Logistic Function ◽  
Fish Growth ◽  
Assessment Model ◽  
Fish Length ◽  
Stock Size ◽  
Age Cohort ◽  
Size At Age

An age-structured, spatial survey-based assessment model (SSURBA) is developed and applied to the Grand Banks stock (NAFO Divisions 3LNO) of American plaice (Hippoglossoides platessoides) in Newfoundland and Labrador. The state-space model is fit to annual spatial (i.e., three divisions) stock size-at-age research vessel (RV) survey indices that are assumed to be proportional to abundance. We model index catchability (q) as a logistic function of fish length, which varies with age, cohort, and the time of the survey; therefore, the model facilitates the estimation of q values that change spatially and temporally following changes in fish growth and survey gears. The SSURBA model produces division-level estimates of fishing mortality rates (F), stock productivity, and stock size relative to the logistic catchability assumption with q = 1 for fully selected ages. The spatial model allows us to include additional survey information compared with the space-aggregated assessment model (all of 3LNO) that is currently used to assess stock status. The model can provide estimates of relative catch, which we compare with reported catch trends to partially validate the model.

scholarly journals Modelling Complexity and Uncertainty in Fisheries Stock Assessment

2021 ◽  
Author(s):  
◽  
D'Arcy Webber
Keyword(s):  
New Zealand ◽  
State Space ◽  
Ross Sea ◽  
Stock Assessment ◽  
State Space Model ◽  
Computational Cost ◽  
Original Model ◽  
Agent Based Models ◽  
Agent Based ◽  
Space Model

<p>Stock assessment models are used to determine the population size of fish stocks. Although stock assessment models are complex, they still make simplifying assumptions. Generally, they treat each species separately, include little, if any, spatial structure, and may not adequately quantify uncertainty. These assumptions can introduce bias and can lead to incorrect inferences. This thesis is about more realistic models and their inference. This realism may be incorporated by explicitly modelling complex processes, or by admitting our uncertainty and modelling it correctly.  We develop an agent-based model that can describe fish populations as a collection of individuals which differ in their growth, maturation, migration, and mortality. The aim of this model is to better capture the richness in natural processes that determine fish abundance and subsequent population response to anthropogenic removals. However, this detail comes at considerable computational cost. A single model run can take many hours, making inference using standard methods impractical. We apply this model to New Zealand snapper (Pagurus auratus) in northern New Zealand.  Next, we developed an age-structured state-space model. We suggest that this sophisticated model has the potential to better represent uncertainty in stock assessment. However, it pushes the boundaries of the current practical limits of computing and we admit that its practical application remains limited until the MCMC mixing issues that we encountered can be resolved.   The processes that underpin agent-based models are complex and we may need to seek new sources of data to inform these types of models. To make a start here we derive a state-space model to estimate the path taken by individual fish from the day they are tagged to the day of their recapture. The model uses environmental information collected using pop-up satellite archival tags. We use tag recorded depth and oceanographic temperature to estimate the location at any given time. We apply this model to Antarctic toothfish (Dissostichus mawsoni) in the Ross Sea.  Finally, to reduce the computational burden of agent-based models we use Bayesian emulation. This approach replaces the simulation model with an approximating algorithm called an emulator. The emulator is calibrated using relatively few runs of the original model. A good emulator provides a close approximation to the original model and has significant speed gains. Thus, inferences become tractable.  We have made the first steps towards developing a tractable approach to fisheries modelling in complex settings through the creation of realistic models, and their emulation. With further development, Bayesian emulation could result in the increased ability to consider and evaluate innovative methods in fisheries modelling. Future avenues for application and exploration range from spatial and multi species models, to ecosystem-based models and beyond.</p>

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