A maximum likelihood approach for estimating growth from tag–recapture data

The Fabens method is commonly used to estimate growth parameters k and l infinity in the von Bertalanffy model from tag-recapture data. However, the Fabens method of estimation has an inherent bias when individual growth is variable. This paper presents an asymptotically unbiassed method using a maximum likelihood approach that takes account of individual variability in both maximum length and age-at-tagging. It is assumed that each individual's growth follows a von Bertalanffy curve with its own maximum length and age-at-tagging. The parameter k is assumed to be a constant to ensure that the mean growth follows a von Bertalanffy curve and to avoid overparameterization. Our method also makes more efficient use nf thp measurements at tno and recapture and includes diagnostic techniques for checking distributional assumptions. The method is reasonably robust and performs better than the Fabens method when individual growth differs from the von Bertalanffy relationship. When measurement error is negligible, the estimation involves maximizing the profile likelihood of one parameter only. The method is applied to tag-recapture data for the grooved tiger prawn (Penaeus semisulcatus) from the Gulf of Carpentaria, Australia.

Using rare mutations to estimate population divergence times: A maximum likelihood approach

In this paper we propose a method to estimate by maximum likelihood the divergence time between two populations, specifically designed for the analysis of nonrecurrent rare mutations. Given the rapidly growing amount of data, rare disease mutations affecting humans seem the most suitable candidates for this method. The estimator RD, and its conditional version RDc, were derived, assuming that the population dynamics of rare alleles can be described by using a birth–death process approximation and that each mutation arose before the split of a common ancestral population into the two diverging populations. The RD estimator seems more suitable for large sample sizes and few alleles, whose age can be approximated, whereas the RDc estimator appears preferable when this is not the case. When applied to three cystic fibrosis mutations, the estimator RD could not exclude a very recent time of divergence among three Mediterranean populations. On the other hand, the divergence time between these populations and the Danish population was estimated to be, on the average, 4,500 or 15,000 years, assuming or not a selective advantage for cystic fibrosis carriers, respectively. Confidence intervals are large, however, and can probably be reduced only by analyzing more alleles or loci.

A maximum-likelihood method for estimating natural mortality and catchability coefficient from catch-and-effort data

A simple stochastic model of a fish population subject to natural and fishing mortalities is described. The fishing effort is assumed to vary over different periods but to be constant within each period. A maximum-likelihood approach is developed for estimating natural mortality (M) and the catchability coefficient (q) simultaneously from catch-and-effort data. If there is not enough contrast in the data to provide reliable estimates of both M and q, as is often the case in practice, the method can be used to obtain the best possible values of q for a range of possible values of M. These techniques are illustrated with tiger prawn (Penaeus semisulcatus) data from the Northern Prawn Fishery of Australia.

Comparing sampling needs for variograms of soil properties computed by the method of moments and residual maximum likelihood

It has been generally accepted that the method of moments (MoM) variogram, which has been widely applied in soil science, requires about 100 sites at an appropriate interval apart to describe the variation adequately. This sample size is often larger than can be afforded for soil surveys of agricultural fields or contaminated sites. Furthermore, it might be a much larger sample size than is needed where the scale of variation is large. A possible alternative in such situations is the residual maximum likelihood (REML) variogram because fewer data appear to be required. The REML method is parametric and is considered reliable where there is trend in the data because it is based on generalized increments that filter trend out and only the covariance parameters are estimated. Previous research has suggested that fewer data are needed to compute a reliable variogram using a maximum likelihood approach such as REML, however, the results can vary according to the nature of the spatial variation. There remain issues to examine: how many fewer data can be used, how should the sampling sites be distributed over the site of interest, and how do different degrees of spatial variation affect the data requirements? The soil of four field sites of different size, physiography, parent material and soil type was sampled intensively, and MoM and REML variograms were calculated for clay content. The data were then sub-sampled to give different sample sizes and distributions of sites and the variograms were computed again. The model parameters for the sets of variograms for each site were used for cross-validation. Predictions based on REML variograms were generally more accurate than those from MoM variograms with fewer than 100 sampling sites. A sample size of around 50 sites at an appropriate distance apart, possibly determined from variograms of ancillary data, appears adequate to compute REML variograms for kriging soil properties for precision agriculture and contaminated sites. (C) 2007 Elsevier B.V. All rights reserved.

Maximum likelihood estimation of a migration matrix and effective population sizes in n subpopulations by using a coalescent approach

A maximum likelihood estimator based on the coalescent for unequal migration rates and different subpopulation sizes is developed. The method uses a Markov chain Monte Carlo approach to investigate possible genealogies with branch lengths and with migration events. Properties of the new method are shown by using simulated data from a four-population n-island model and a source–sink population model. Our estimation method as coded in migrate is tested against genetree; both programs deliver a very similar likelihood surface. The algorithm converges to the estimates fairly quickly, even when the Markov chain is started from unfavorable parameters. The method was used to estimate gene flow in the Nile valley by using mtDNA data from three human populations.

Extraction of road lanes from high-resolution stereo aerial imagery based on maximum likelihood segmentation and texture enhancement

Accurate road lane information is crucial for advanced vehicle navigation and safety applications. With the increasing of very high resolution (VHR) imagery of astonishing quality provided by digital airborne sources, it will greatly facilitate the data acquisition and also significantly reduce the cost of data collection and updates if the road details can be automatically extracted from the aerial images. In this paper, we proposed an effective approach to detect road lanes from aerial images with employment of the image analysis procedures. This algorithm starts with constructing the (Digital Surface Model) DSM and true orthophotos from the stereo images. Next, a maximum likelihood clustering algorithm is used to separate road from other ground objects. After the detection of road surface, the road traffic and lane lines are further detected using texture enhancement and morphological operations. Finally, the generated road network is evaluated to test the performance of the proposed approach, in which the datasets provided by Queensland department of Main Roads are used. The experiment result proves the effectiveness of our approach.

Maximum likelihood estimation of natural mortality and quantification of temperature effects on catchability of brown tiger prawn (Penaeus esculentus) in Moreton Bay (Australia) using logbook data

It is common to model the dynamics of fisheries using natural and fishing mortality rates estimated independently using two separate analyses. Fishing mortality is routinely estimated from widely available logbook data, whereas natural mortality estimations have often required more specific, less frequently available, data. However, in the case of the fishery for brown tiger prawn (Penaeus esculentus) in Moreton Bay, both fishing and natural mortality rates have been estimated from logbook data. The present work extended the fishing mortality model to incorporate an eco-physiological response of tiger prawn to temperature, and allowed recruitment timing to vary from year to year. These ecological characteristics of the dynamics of this fishery were ignored in the separate model that estimated natural mortality. Therefore, we propose to estimate both natural and fishing mortality rates within a single model using a consistent set of hypotheses. This approach was applied to Moreton Bay brown tiger prawn data collected between 1990 and 2010. Natural mortality was estimated by maximum likelihood to be equal to 0.032 ± 0.002 week−1, approximately 30% lower than the fixed value used in previous models of this fishery (0.045 week−1).

MRT Letter: A Unified Accelerated Maximum Likelihood Technique for Widefield, Confocal, and Super-Resolution 4Pi Microscopy

We propose an algorithmic technique for accelerating maximum likelihood (ML) algorithm for image reconstruction in fluorescence microscopy. This is made possible by integrating Biggs-Andrews (BA) method with ML approach. The results on widefield, confocal, and super-resolution 4Pi microscopy reveal substantial improvement in the speed of 3D image reconstruction (the number of iterations has reduced by approximately one-half). Moreover, the quality of reconstruction obtained using accelerated ML closely resembles with nonaccelerated ML method. The proposed technique is a step closer to realize real-time reconstruction in 3D fluorescence microscopy. Microsc. Res. Tech. 78:331-335, 2015. (c) 2015 Wiley Periodicals, Inc.

Implementation of the EM Algorithm for Maximum Likelihood Estimation of a Random Effects Model for One Longitudinal Ordinal Outcome

2010 Mathematics Subject Classification: 62J99.

BIAS-CORRECTED MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF THE WEIGHTED LINDLEY DISTRIBUTION

This report discusses the calculation of analytic second-order bias techniques for the maximum likelihood estimates (for short, MLEs) of the unknown parameters of the distribution in quality and reliability analysis. It is well-known that the MLEs are widely used to estimate the unknown parameters of the probability distributions due to their various desirable properties; for example, the MLEs are asymptotically unbiased, consistent, and asymptotically normal. However, many of these properties depend on an extremely large sample sizes. Those properties, such as unbiasedness, may not be valid for small or even moderate sample sizes, which are more practical in real data applications. Therefore, some bias-corrected techniques for the MLEs are desired in practice, especially when the sample size is small. Two commonly used popular techniques to reduce the bias of the MLEs, are ‘preventive’ and ‘corrective’ approaches. They both can reduce the bias of the MLEs to order O(n−2), whereas the ‘preventive’ approach does not have an explicit closed form expression. Consequently, we mainly focus on the ‘corrective’ approach in this report. To illustrate the importance of the bias-correction in practice, we apply the bias-corrected method to two popular lifetime distributions: the inverse Lindley distribution and the weighted Lindley distribution. Numerical studies based on the two distributions show that the considered bias-corrected technique is highly recommended over other commonly used estimators without bias-correction. Therefore, special attention should be paid when we estimate the unknown parameters of the probability distributions under the scenario in which the sample size is small or moderate.

Novel methods and the maximum likelihood estimation technique for estimating traffic critical gap

Most unsignalised intersection capacity calculation procedures are based on gap acceptance models. Accuracy of critical gap estimation affects accuracy of capacity and delay estimation. Several methods have been published to estimate drivers’ sample mean critical gap, the Maximum Likelihood Estimation (MLE) technique regarded as the most accurate. This study assesses three novel methods; Average Central Gap (ACG) method, Strength Weighted Central Gap method (SWCG), and Mode Central Gap method (MCG), against MLE for their fidelity in rendering true sample mean critical gaps. A Monte Carlo event based simulation model was used to draw the maximum rejected gap and accepted gap for each of a sample of 300 drivers across 32 simulation runs. Simulation mean critical gap is varied between 3s and 8s, while offered gap rate is varied between 0.05veh/s and 0.55veh/s. This study affirms that MLE provides a close to perfect fit to simulation mean critical gaps across a broad range of conditions. The MCG method also provides an almost perfect fit and has superior computational simplicity and efficiency to the MLE. The SWCG method performs robustly under high flows; however, poorly under low to moderate flows. Further research is recommended using field traffic data, under a variety of minor stream and major stream flow conditions for a variety of minor stream movement types, to compare critical gap estimates using MLE against MCG. Should the MCG method prove as robust as MLE, serious consideration should be given to its adoption to estimate critical gap parameters in guidelines.

A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions

A quasi-maximum likelihood procedure for estimating the parameters of multi-dimensional diffusions is developed in which the transitional density is a multivariate Gaussian density with first and second moments approximating the true moments of the unknown density. For affine drift and diffusion functions, the moments are exactly those of the true transitional density and for nonlinear drift and diffusion functions the approximation is extremely good and is as effective as alternative methods based on likelihood approximations. The estimation procedure generalises to models with latent factors. A conditioning procedure is developed that allows parameter estimation in the absence of proxies.