Parameter estimation in modelling the dynamics of fish stock biomass: are currently used observation-error estimators reliable?

1998 ◽  
Vol 55 (3) ◽  
pp. 749-760 ◽  
Author(s):  
Y Chen ◽  
N Andrew
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Likelihood Method ◽  
Fish Stock ◽  
Error Estimator ◽  
Observation Error ◽  
Estimation Errors ◽  
Abundance Index ◽  
Error Estimators ◽  
Production Models

Production models are used in fisheries when only a time series of catch and abundance indices are available. Observation-error estimators are commonly used to fit the models to the data with a least squares type of objective function. An assumption associated with observation-error estimators is that errors occur only in the observed abundance index but not in the dynamics of stock and observed catch. This assumption is usually unrealistic. Because the least squares methods tend to be sensitive to error assumptions, results derived from these methods may be unreliable. In this study, we propose a robust observation-error estimator. We evaluate the performance of this method, together with the commonly used maximum likelihood method, under different error assumptions. When there was only observation error in the abundance index, maximum likelihood tended to perform better. However, with both observation and process errors, maximum likelihood yielded much larger estimation errors compared with the proposed method. This study suggests that the proposed method is robust to error assumptions. Because the magnitude and types of error cannot often be specified with confidence, the proposed method offers a potentially useful addition to methods used to fit production models to abundance index and catch data.

Fitting Surplus Production Models: Comparing Methods and Measuring Uncertainty

1993 ◽  
Vol 50 (12) ◽  
pp. 2597-2607 ◽  
Author(s):  
Tom Polacheck ◽  
Ray Hilborn ◽  
Andre E. Punt
Keyword(s):  
Maximum Sustainable Yield ◽  
Parameter Estimates ◽  
Error Estimator ◽  
Sustainable Yield ◽  
Observation Error ◽  
Error Estimators ◽  
Averaging Methods ◽  
Surplus Production ◽  
Production Models ◽  
Process Error

Three approaches are commonly used to fit surplus production models to observed data: effort-averaging methods; process-error estimators; and observation-error estimators. We compare these approaches using real and simulated data sets, and conclude that they yield substantially different interpretations of productivity. Effort-averaging methods assume the stock is in equilibrium relative to the recent effort; this assumption is rarely satisfied and usually leads to overestimation of potential yield and optimum effort. Effort-averaging methods will almost always produce what appears to be "reasonable" estimates of maximum sustainable yield and optimum effort, and the r2 statistic used to evaluate the goodness of fit can provide an unrealistic illusion of confidence about the parameter estimates obtained. Process-error estimators produce much less reliable estimates than observation-error estimators. The observation-error estimator provides the lowest estimates of maximum sustainable yield and optimum effort and is the least biased and the most precise (shown in Monte-Carlo trials). We suggest that observation-error estimators be used when fitting surplus production models, that effort-averaging methods be abandoned, and that process-error estimators should only be applied if simulation studies and practical experience suggest that they will be superior to observation-error estimators.

Extending production models to include process error in the population dynamics

2003 ◽  
Vol 60 (10) ◽  
pp. 1217-1228 ◽  
Author(s):  
Andre E Punt
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Population Dynamics ◽  
Total Error ◽  
Error Estimator ◽  
Observation Error ◽  
Production Models ◽  
Fitting Production ◽  
Process Error ◽  
Relative Errors

Four methods for fitting production models, including three that account for the effects of error in the population dynamics equation (process error) and when indexing the population (observation error), are evaluated by means of Monte Carlo simulation. An estimator that represents the distributions of biomass explicitly and integrates over the unknown process errors numerically (the NISS estimator) performs best of the four estimators considered, never being the worst estimator and often being the best in terms of the medians of the absolute values of the relative errors. The total-error approach outperforms the observation-error estimator conventionally used to fit dynamic production models, and the performance of a Kalman filter based estimator is particularly poor. Although the NISS estimator is the best-performing estimator considered, its estimates of quantities of management interest are severely biased and highly imprecise for some of the scenarios considered.

scholarly journals Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 62 ◽  
Author(s):  
Autcha Araveeporn
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Least Squares Method ◽  
Likelihood Function ◽  
Likelihood Method ◽  
Mean Square ◽  
Average Mean Square Error ◽  
Frequentist Method

This paper compares the frequentist method that consisted of the least-squares method and the maximum likelihood method for estimating an unknown parameter on the Random Coefficient Autoregressive (RCA) model. The frequentist methods depend on the likelihood function that draws a conclusion from observed data by emphasizing the frequency or proportion of the data namely least squares and maximum likelihood methods. The method of least squares is often used to estimate the parameter of the frequentist method. The minimum of the sum of squared residuals is found by setting the gradient to zero. The maximum likelihood method carries out the observed data to estimate the parameter of a probability distribution by maximizing a likelihood function under the statistical model, while this estimator is obtained by a differential parameter of the likelihood function. The efficiency of two methods is considered by average mean square error for simulation data, and mean square error for actual data. For simulation data, the data are generated at only the first-order models of the RCA model. The results have shown that the least-squares method performs better than the maximum likelihood. The average mean square error of the least-squares method shows the minimum values in all cases that indicated their performance. Finally, these methods are applied to the actual data. The series of monthly averages of the Stock Exchange of Thailand (SET) index and daily volume of the exchange rate of Baht/Dollar are considered to estimate and forecast based on the RCA model. The result shows that the least-squares method outperforms the maximum likelihood method.

Different inference approaches for the estimators of the sushila distribution

2021 ◽  
Vol 16 (4) ◽  
pp. 251-260
Author(s):  
Marcos Vinicius de Oliveira Peres ◽  
Ricardo Puziol de Oliveira ◽  
Edson Zangiacomi Martinez ◽  
Jorge Alberto Achcar
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Bayesian Method ◽  
Weighted Least Squares ◽  
Computational Cost ◽  
Estimation Method ◽  
Computation Time ◽  
Ordinary Least Squares ◽  
Likelihood Method ◽  
Estimation Methods

In this paper, we order to evaluate via Monte Carlo simulations the performance of sample properties of the estimates of the estimates for Sushila distribution, introduced by Shanker et al. (2013). We consider estimates obtained by six estimation methods, the known approaches of maximum likelihood, moments and Bayesian method, and other less traditional methods: L-moments, ordinary least-squares and weighted least-squares. As a comparison criterion, the biases and the roots of mean-squared errors were used through nine scenarios with samples ranging from 30 to 300 (every 30rd). In addition, we also considered a simulation and a real data application to illustrate the applicability of the proposed estimators as well as the computation time to get the estimates. In this case, the Bayesian method was also considered. The aim of the study was to find an estimation method to be considered as a better alternative or at least interchangeable with the traditional maximum likelihood method considering small or large sample sizes and with low computational cost.

RESILIENCE AND CRITICAL STOCK SIZE IN A STOCHASTIC RECRUITMENT MODEL

2001 ◽  
Vol 09 (01) ◽  
pp. 1-12 ◽  
Author(s):  
JOHAN GRASMAN ◽  
MARK J. HUISKES
Keyword(s):  
Maximum Likelihood ◽  
Stochastic Model ◽  
Stock Assessment ◽  
Life Stage ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Early Life Stage ◽  
Likelihood Method ◽  
Fish Stock ◽  
Stock Size

A stochastic model for fish recruitment is fitted to data after performing an age-structured stock assessment. The main aim is to investigate the relation between safe levels of spawning stock size and fish stock resilience. Resilience indicators, such as stock recovery time and the frequency that a stock is below a critical size, are computed by means of simulation using the fitted stochastic model. The stochastic element of the model describes the early life stage survival of the fish using a nonlinear stochastic Leslie type of matrix. From catch data and fishing mortality rates, the free parameters in the model are estimated by means of a maximum likelihood method. The performance of the maximum likelihood estimation method is tested by means of simulation. The method is applied to data of a halibut population (Hippoglossus stenolepis) in the Southeastern Bering Sea. It turns out that given the fluctuation in recruitment, data of at least 25 consecutive years are required.

scholarly journals Generalized Exponential Distribution - Estimation of parameters using modifications in methods of Ranked Set Sampling

2021 ◽  
Author(s):  
Vyomesh Prahlad Nandurbarkar ◽  
Ashok Shanubhogue
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Exponential Distribution ◽  
Random Sampling ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Likelihood Method ◽  
Generalized Exponential Distribution ◽  
Data Set ◽  
Extreme Ranked Set Sampling

Abstract In this study, we estimate the parameters of the Generalized Exponential Distribution using Moving Extreme Ranked Set Sampling (MERSS). Using the maximum likelihood estimation method, we derive the expressions. MERSS estimates are compared with estimates obtained by simple random sampling (SRS) using a real data set. We also study the other variations of the methods of Ranked Set Sampling like Quartile Ranked Set Sampling(QRSS), Median Ranked Set Sampling(MRSS) and Flexible Ranked Set Sampling(FLERSS) (a scheme based on QRSS and MRSS). For known shape parameter values, we present coefficients for linear combinations of order statistics for least squares estimates. Here, the expressions are derived through maximum likelihood, and the estimates are calculated numerically. Simulated results indicate that estimates generated using least-squares and the maximum likelihood method for Ranked Set Sampling (RSS) perform better than those generated using Simple Random Sampling (SRS). Asymptotically, MERSS outperforms SRS, QRSS, MRSS, and FLERSS.

Curve Fitting of Heterodyne Data

1985 ◽  
Vol 39 (3) ◽  
pp. 480-484 ◽  
Author(s):  
B. R. Reddy
Keyword(s):  
Experimental Data ◽  
Maximum Likelihood ◽  
Least Squares ◽  
Curve Fitting ◽  
Maximum Likelihood Method ◽  
Heterodyne Detection ◽  
Likelihood Method ◽  
Fitting Procedure ◽  
Least Squares Curve Fitting

The least-squares curve fitting procedure of experimental data is described for heterodyne detection. Two independent methods, the Maximum Likelihood method of Fisher and SIMPLEX, have been tried. The relative merits and limitations are discussed in detail.

scholarly journals Validation and Comparison of Different Statistical Models for the Prediction of Water Main Pipe Breaks in a Municipal Network in Québec, Canada

2016 ◽  
Vol 29 (1) ◽  
pp. 11-24 ◽  
Author(s):  
Sophie Duchesne ◽  
Babacar Toumbou ◽  
Jean-Pierre Villeneuve
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Maximum Likelihood Method ◽  
Least Squares Method ◽  
Likelihood Method ◽  
Water Main ◽  
Pipe Replacement ◽  
The Impact ◽  
Over Time ◽  
Observation Period

In this study, three models for the simulation of the number of breaks in a water main network are presented and compared: linear regression, the Weibull-Exponential-Exponential (WEE), and the Weibull-Exponential-Exponential-Exponential (WEEE) models. These models were calibrated using a database of recorded breaks in a real water main network of a municipality in the province of Québec, for the observation period 1976 to 1996, with the least squares and the maximum likelihood methods. The ability of these models to predict breaks over time was then evaluated by comparing the predicted number of breaks for the years 1997 to 2007 with the observed breaks in the network over the same time period. Results show that if the period of observation is short (around 20 years), calibration of the WEE and WEEE models with the maximum likelihood method leads to estimates that are closer to the observations than when these models are calibrated with the least squares method. When the observation period is longer (around 30 years), the predictions obtained with the models calibrated using the maximum likelihood or the least squares methods are similar. However, the use of the maximum likelihood method for calibration is only possible when data for the occurrence of each break for each pipe of the network are available (a pipe being a homogeneous network segment between two adjacent street junctions). If this is not the case, a trend line will be sufficient to predict the number of breaks over time, though this type of curve does not allow to account for pipe replacement scenarios. If the only information available is the total number of breaks on the network each year, then the impact of replacement scenarios could be simulated with the WEE and WEEE models calibrated using the least squares method.

scholarly journals Indoor Ultra-Wide Band Network Adjustment using Maximum Likelihood Estimation

2014 ◽  
Vol II-1 ◽  
pp. 31-35 ◽  
Author(s):  
Z. Koppanyi ◽  
C. K. Toth
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Least Squares ◽  
Sampling Rate ◽  
Functional Model ◽  
Likelihood Estimation ◽  
Wide Band ◽  
Likelihood Method ◽  
Ultra Wide Band ◽  
Ongoing Research

This study is the part of our ongoing research on using ultra-wide band (UWB) technology for navigation at the Ohio State University. Our tests have indicated that the UWB two-way time-of-flight ranges under indoor circumstances follow a Gaussian mixture distribution that may be caused by the incompleteness of the functional model. In this case, to adjust the UWB network from the observed ranges, the maximum likelihood estimation (MLE) may provide a better solution for the node coordinates than the widely-used least squares approach. The prerequisite of the maximum likelihood method is to know the probability density functions. The 30 Hz sampling rate of the UWB sensors enables to estimate these functions between each node from the samples in static positioning mode. In order to prove the MLE hypothesis, an UWB network has been established in a multi-path density environment for test data acquisition. The least squares and maximum likelihood coordinate solutions are determined and compared, and the results indicate that better accuracy can be achieved with maximum likelihood estimation.

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