Estimating relative abundance of whales from historical Antarctic whaling records

2014 ◽  
Vol 71 (1) ◽  
pp. 106-119 ◽  
Author(s):  
William K. de la Mare
Keyword(s):  
Maximum Likelihood ◽  
Relative Abundance ◽  
Expectation Maximization ◽  
Local Density ◽  
Operating Time ◽  
Handling Time ◽  
Maximum Likelihood Estimates ◽  
Catch Per Unit Effort ◽  
Additional Operating Time ◽  
Index Of Abundance

Catch per unit effort (CPUE) is often the only data available from historical fisheries for inferring distribution and abundance of exploited populations. CPUE underestimates variations in relative abundance when gross effort data are only measured in total operating days. Gross effort includes both searching time and handling time, but only searching time is useful for an index of abundance. A method is developed for estimating searching time by subtracting a maximum likelihood estimate of handling time from the gross effort. An expectation maximization (E-M) algorithm is used to combine maximum likelihood estimates of the handling time with the expected additional operating time due to handling the last catch of each day. Simulation tests show that the estimates of catch per unit of searching time (C/CSW) are much closer to proportionally related to local density than gross CPUE. Estimates of handling time are not unbiased, and some nonlinearity between local density and C/CSW may persist. The methods may be useful for other fisheries where historic gross catch and effort data involve both searching and handling.

scholarly journals Estimating the relative proportions of SARS-CoV-2 strains from wastewater samples

2022 ◽  
Author(s):  
Lenore Pipes ◽  
Zihao Chen ◽  
Svetlana Afanaseva ◽  
Rasmus Nielsen
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Expectation Maximization ◽  
Initial Step ◽  
Sequencing Depth ◽  
Maximum Likelihood Estimates ◽  
Reference Database ◽  
Wastewater Samples ◽  
Different Strains

Wastewater surveillance has become essential for monitoring the spread of SARS-CoV-2. The quantification of SARS-CoV-2 RNA in wastewater correlates with the Covid-19 caseload in a community. However, estimating the proportions of different SARS-CoV-2 strains has remained technically difficult. We present a method for estimating the relative proportions of SARS-CoV-2 strains from wastewater samples. The method uses an initial step to remove unlikely strains, imputation of missing nucleotides using the global SARS-CoV-2 phylogeny, and an Expectation-Maximization (EM) algorithm for obtaining maximum likelihood estimates of the proportions of different strains in a sample. Using simulations with a reference database of >3 million SARS-CoV-2 genomes, we show that the estimated proportions accurately reflect the true proportions given sufficiently high sequencing depth and that the phylogenetic imputation is highly accurate and substantially improves the reference database.

Estimation of historical stock sizes and recruitment anomalies from relative abundance time series

1995 ◽  
Vol 52 (7) ◽  
pp. 1523-1534 ◽  
Author(s):  
Carl Walters
Keyword(s):  
Time Series ◽  
Dynamic Programming ◽  
Maximum Likelihood ◽  
Relative Abundance ◽  
Measurement Errors ◽  
Dynamic Programming Algorithm ◽  
Maximum Likelihood Estimates ◽  
Programming Algorithm ◽  
Abundance Index ◽  
Stock Size

Often only simple relative abundance time series and basic growth and (or) survival estimates are available for assessing impacts of fishing and environmental factors. Assessment then involves fitting production models to the series, while forcing the model with observed catch or effort series. A key uncertainty in this approach is how to deal with recruitment variations due to factors other than stock size. A dynamic programming algorithm can be used to compute maximum likelihood estimates of the recruitment anomaly sequence, given prior knowledge of growth parameters, the natural survival rate, and proportion of the variation in the relative abundance index that is due to abundance measurement errors. The temporal pattern of anomaly estimates from the dynamic programming procedure is quite robust to uncertainties about the absolute stock size and average historical recruitment rate, so it can at least provide information for studies of factors affecting recruitment in cases where the abundance index measurement error is small compared with recruitment process errors (<10% of total error). Further, the procedure can easily be embedded within a Bayesian or maximum likelihood estimation of stock size and surplus production.

scholarly journals Parameter Estimation of a Multistate Model for an Aging Piece of Equipment under Condition-Based Maintenance

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Qihong Duan ◽  
Xiang Chen ◽  
Dengfu Zhao ◽  
Zheng Zhao
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Model Calculation ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Condition Based Maintenance ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Simulation Studies ◽  
Multistate Model

We study a multistate model for an aging piece of equipment under condition-based maintenance and apply an expectation maximization algorithm to obtain maximum likelihood estimates of the model parameters. Because of the monitoring discontinuity, we cannot observe any state's duration. The observation consists of the equipment's state at an inspection or right after a repair. Based on a proper construction of stochastic processes involved in the model, calculation of some probabilities and expectations becomes tractable. Using these probabilities and expectations, we can apply an expectation maximization algorithm to estimate the parameters in the model. We carry out simulation studies to test the accuracy and the efficiency of the algorithm.

scholarly journals Hybridization of Expectation-Maximization and K-Means Algorithms for Better Clustering Performance

2016 ◽  
Vol 16 (2) ◽  
pp. 16-34 ◽  
Author(s):  
D. Raja Kishor ◽  
N. B. Venkateswarlu
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Expectation Maximization ◽  
Execution Time ◽  
Maximum Likelihood Estimates ◽  
Fitness Value ◽  
Speed Up ◽  
Purdue University ◽  
Synthetic Datasets

Abstract The present work proposes hybridization of Expectation-Maximization (EM) and K-means techniques as an attempt to speed-up the clustering process. Even though both the K-means and EM techniques look into different areas, K-means can be viewed as an approximate way to obtain maximum likelihood estimates for the means. Along with the proposed algorithm for hybridization, the present work also experiments with the Standard EM algorithm. Six different datasets, three of which synthetic datasets, are used for the experiments. Clustering fitness and Sum of Squared Errors (SSE) are computed for measuring the clustering performance. In all the experiments it is observed that the proposed algorithm for hybridization of EM and K-means techniques is consistently taking less execution time with acceptable Clustering Fitness value and less SSE than the standard EM algorithm. It is also observed that the proposed algorithm is producing better clustering results than the Cluster package of Purdue University.

scholarly journals Improving Equipment Reliability and System Maintenance and Repair Efficiency

2019 ◽  
Vol 5 (8) ◽  
pp. 1799-1811 ◽  
Author(s):  
Alexander Rusin ◽  
Yakov Baryshev
Keyword(s):  
Maximum Likelihood ◽  
Regression Models ◽  
Operating Time ◽  
Experimental Studies ◽  
Estimation Method ◽  
Maximum Likelihood Estimates ◽  
Automated System ◽  
Maintenance And Repair ◽  
Censored Samples ◽  
True Value

Mean time to failure of modern machinery and equipment, their individual parts and components can be calculated over the years. Methods for determining the optimal frequency of maintenance and repair, based on the collection and processing of information about the reliability of industrial facilities, during their testing in laboratories and at special sites, as well as through long, operational tests require considerable time and become expensive. The purpose of this work is to develop methods for processing information about the reliability of equipment in automated systems for maintenance and repair, which will reduce the time to collect information on equipment failures and improve the cost-effectiveness of maintenance and repair. Small, multiple-censored right-side samples of equipment operating time for failure are formed as a result of failure data collection in an automated system for equipment maintenance and repair. Calculation of reliability indicators for such samples is performed using the maximum likelihood estimation method. The article presents experimental studies of the accuracy of the maximum likelihood estimates of the parameter of the exponential distribution law for small, multiple right-censored samples. The studies were carried out by computer modeling of censored samples, similar to samples that are formed when monitoring equipment during operation. Methods of simulation modeling of random processes on a computer and methods of regression analysis were used. Analysis show that most of the maximum likelihood estimates obtained from small, multiple-censored right-side samples have significant deviations from the true values. A technique for improving the accuracy of maximum likelihood estimates is proposed. The scientific novelty is regression models are constructed that establish the relationship between the deviation of the maximum likelihood estimate from the true value and the parameters characterizing the sample structure. These models calculate and introduce corrections to maximum likelihood estimates. The use of the developed regression models will reduce the time to collect information about the reliability of the equipment, while maintaining the reliability of the results.

scholarly journals Expectation-maximization estimators for incompletely observed data

2004 ◽  
Vol 44 (161) ◽  
pp. 165-173
Author(s):  
Vladimir Vasic
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Incomplete Data ◽  
Maximum Likelihood Method ◽  
Complete Data ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Iterative Computation

Expectation-maximization is a broadly applicable approach to the iterative computation of maximum likelihood estimates. Each iteration of expectation-maximization method consists of two steps: the expectation step and the maximization step. Expectation-maximization method is useful in a variety of problems where the maximum likelihood estimates are very difficult to find. The basic idea of expectation-maximization method is to relate incomplete data problems to complete data problems where estimation by maximum likelihood method is much simpler.

Maximum likelihood estimation of fossil assemblage composition

Paleobiology ◽  
1979 ◽  
Vol 5 (2) ◽  
pp. 77-89 ◽  
Author(s):  
Richard C. Holtzman
Keyword(s):  
Maximum Likelihood ◽  
Relative Abundance ◽  
Relative Frequency ◽  
Sampling Error ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Fossil Assemblage ◽  
Minimum Number ◽  
Minimum Number Of Individuals ◽  
Number Of Individuals

The most common methods of estimating the relative abundance of species in a fossil assemblage are all maximum likelihood estimates. They differ from one another in their inherent assumptions made about the effects of fragmentation and differential preservation in the assemblage. For many fossil assemblages, relative abundance is best estimated by the relative frequency of specimens or relative frequency of elements. Monte Carlo simulations suggest, however, that in most other circumstances estimates based on frequency of elements divided by the number of elements in a complete individual provide greater accuracy than estimates based on minimum number of individuals. This relation results from an interaction between random sampling error and a variety of biases inherent in the two estimates.

Using Approximation Non-Bayesian Computation with Fuzzy Data to Estimation Inverse Weibull Parameters and Reliability Function

2018 ◽  
pp. 397
Author(s):  
Nadia Hashim Al-Noor ◽  
Shurooq A.K. Al-Sultany
Keyword(s):  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Mean Squared Error ◽  
Maximum Likelihood Estimators ◽  
Reliability Function ◽  
Fuzzy Data ◽  
Monte Carlo Simulation Study ◽  
Weibull Parameters ◽  
Squared Error ◽  
Newton Raphson

        In real situations all observations and measurements are not exact numbers but more or less non-exact, also called fuzzy. So, in this paper, we use approximate non-Bayesian computational methods to estimate inverse Weibull parameters and reliability function with fuzzy data. The maximum likelihood and moment estimations are obtained as non-Bayesian estimation. The maximum likelihood estimators have been derived numerically based on two iterative techniques namely “Newton-Raphson” and the “Expectation-Maximization” techniques. In addition, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the parameters and reliability function in terms of their mean squared error values and integrated mean squared error values respectively.

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