Alternative sampling and estimation methods for multispecies trawl surveys

Thesis (Ph.D.) University of Alaska Fairbanks, 2004Multispecies demersal trawl surveys are used in the United States and internationally to estimate the relative abundance of commercial and non-commercial fish species. Their usefulness for estimating species' abundance is often limited by the variance associated with estimates. This study implemented and evaluated alternative sampling and estimation methods, with the goal to incorporate additional sources of information for increased precision of individual species' estimates from multispecies trawl surveys. First, habitat characteristics and past spatial distributions of four flatfish species' density were incorporated into a multispecies trawl survey design conducted in Kalsin and Middle Bays, Kodiak Island, Alaska. Stratification by depth and percent sand produced estimates of relative abundance with lower CV s than those from unstratified sampling. Additional decreases in relative precision were generally not achieved by estimating the relative abundance of multiple species from regions of species-specific suboptimal habitat. Second, a poststratification technique was used to incorporate species-specific habitat characteristics and previous distributions of species' density into the estimation of species' abundance from the Kalsin and Middle Bays' trawl survey. Poststratification by habitat gave estimates with lower variance and/or less design-bias than an unstratified estimator for all species in all years. Poststratification by habitat and fish density produced estimates with the least design-bias for all species in all years and the lowest variance when stratum sample sizes were sufficient. Third, mixed model linear regression (MMLR), empirical Bayes (EB) and hierarchical Bayes (HB) estimation methods were used to incorporate historical trends of yellowfin sole, Limanda aspera biomass from the eastern Bering Sea trawl survey into annual biomass estimates. Using MMLR, EB, and HB methods resulted in biomass estimates that were less anomalous than survey estimates with respect to a linear regression trend. Estimates for all three methods had lower CV s than surveys in most years. The results of this thesis suggest that incorporating additional information into survey design and estimation can decrease the variability of survey estimates and/or correct for possible bias. Methods that can incorporate additional information, therefore, have the potential to improve survey assessments for management use.Introduction -- Multispecies survey designs with habitat and fish density information -- Using poststratification to improve multispecies survey assessments : case study of juvenile flatfishes -- A comparison of models for incorporating multiple years of information into annual estimates of biomass from multispecies trawl surveys -- Conclusions

Non-Bayes, Bayes and Empirical Bayes Estimators for the Shape Parameter of Lomax Distribution

Point estimation is one of the core topics in mathematical statistics. In this paper we consider the most common methods of point estimation: non-Bayes, Bayes and empirical Bayes methods to estimate the shape parameter of Lomax distribution based on complete data. The maximum likelihood, moment and uniformly minimum variance unbiased estimators are obtained as non-Bayes estimators. Bayes and empirical Bayes estimators are obtained corresponding to three informative priors "gamma, chi-square and inverted Levy" based on symmetric "squared error" and asymmetric "LINEX and general entropy" loss functions. The estimates of the shape parameter were compared empirically via Monte Carlo simulation study based upon the mean squared error. Among the set of conclusions that have been reached, it is observed that, for all sample sizes and different cases, the performance of uniformly minimum variance unbiased estimator is better than other non-Bayes estimators. Further that, Monte Carlo simulation results indicate that the performance of Bayes and empirical Bayes estimator in some cases are better than non-Bayes for some appropriate of prior distribution, loss function, values of parameters and sample size. Keywords: Lomax distribution; maximum likelihood estimator; moment estimator; uniformly minimum variance unbiased estimator; Bayes estimator; empirical Bayes estimator; informative prior; squared error loss function; LINEX  loss  function;  general  entropy  loss  function;  mean  squared  error

Application of Faulkenberry (2018) Bayes Factor to a Balanced Two Way Analysis of Variance with Random Effects

The Analysis of Variance technique estimates variance components by comparing their mean squares to their expected values. Nevertheless, this method could give variance component estimates that are found outside the parameter space, i.e. negative estimates. In a bid to overcome this deficiency, alternate approaches are essential, and likelihood-based approaches have become common over time. Bayesian techniques have also been proposed and Bayes factors developed for examining various models. We applied the Bayes factor proposed by Faulkenberry (2018) to a Balanced Two Way ANOVA under three (3) cases, namely Case 1: the levels of the two factors are fixed; Case 2: the levels of the two factors are random; and Case 3: the levels of one factor are considered as fixed, while the levels of the other factor are considered as random. We realized that when the levels of the two factors are fixed, the Bayesian conclusion about the variability in the effects is in line with that of a frequentist. But when the same data set was considered to be wholly or partly as sample observations drawn randomly from a given population of interest, the Bayesian conclusion differed slightly from that of the frequentist. Keywords: Bayes Factor; Bayesian; Frequentist, Fixed; Random

Performance different uninformative efficiency of priors for binomial model

The current paper studies the performance efficiency of two uninformative priors, namely Bayes-Laplace (Uniform) prior and Jeffrey’s prior for Binomial model. Several performance measures, such as the Bayes estimators under different loss functions, the posterior distribution skewness coefficient, the Bayesian point estimates, and the posterior variance, are used for comparison. Using these two uninformative priors, we conducted numerical simulation which showed that they perform extreme similarly

Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a thermodynamic integration scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods

Parameters and Reliability Estimation of Left Truncated Gumbel Distribution under Progressive Type II Censored with Repairable Mechanical Equipment Data

The estimation of two parameters of the left truncated Gumbel distribution using the progressive type II censoring scheme is discussed. We first derived the maximum likelihood estimators of the unknown parameters. The approximate asymptotic variance-covariance matrix and approximate confidence intervals based on the asymptotic normality of the classical estimators are calculated. Also, the survival and hazard functions are derived. Further, the delta method is used to construct approximate confidence intervals for survival and hazard functions. Using the left truncated normal prior for the location parameter and an inverted gamma prior for the scale parameter, several Bayes estimates based on squared error and general entropy loss functions are computed. Bayes estimators of the unknown parameters cannot be calculated in closed forms. Markov chain Monte Carlo method, namely Metropolis-Hastings algorithm, has been used to derive the approximate Bayes estimates. Also, the credible intervals are constructed by using Markov chain Monte Carlo samples. Finally, The Monte Carlo simulation study compares the performances among various estimates in terms of their root mean squared errors, mean absolute biased, average confidence lengths, and coverage probabilities under different sets of values of sample sizes, number of failures and censoring schemes. Moreover, a numerical example with a real data set and Markov chain Monte Carlo data sets are tackled to highlight the importance of the proposed methods. Bayes Markov chain Monte Carlo estimates have performed better than those obtained based on the likelihood function