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The objective of this study was to identify potential recruitment sources of Prochilodus lineatus from freshwater areas (Paraná and Uruguay rivers) to estuarine population of the Río de la Plata Estuary (La Plata Basin, South America), considering young (age-1) and adult (age-7) fish. LA-ICP-MS chemical analysis of the otolith core (nine element:Ca ratios) of an unknown mixed sample from Río de la Plata Estuary (2011 and 2017) was compared with a young-of-year baseline data set (same cohort) and classified into freshwater nurseries (Paraná or Uruguay river) by using maximum classification-likelihood models (MLE and MCL) and quadratic discriminant analysis (QDA). Considering the three models used, the Uruguay River was the most important contributor for both young and adult populations. The young population (2011) was highly mixed with contributions between 31.7 to 68.3%, while the degree of mixing was found to decrease in 2017 (adult fish) from 97.1 to 100% contributions. The three employed methods showed comparable estimates, however, the QDA showed a high similarity with the MCL model, suggesting sensitivity to evaluate small contributions, unlike the MLE method. Our results show the potential application of maximum likelihood mixture models and QDA for determining the relative importance of recruitment sources of fish in estuarine waters of the La Plata Basin.
There are many sources of random and systematic error in composition quantification by atom probe microscopy, often, however, only statistical error is reported. Significantly larger errors can occur from the misidentification of ions and overlaps or interferences of peaks in the mass spectrum. These overlaps can be solved using maximum likelihood estimation (MLE), improving the accuracy of the result, but with an unknown effect on the precision. An analytical expression for the uncertainty of the MLE solution is presented and it is demonstrated to be much more accurate than the existing methods. In one example, the commonly used error estimate was five times too small.
Literature results containing overlaps most likely underestimate composition uncertainty because of the complexity of correctly dealing with stochastic effects and error propagation. The uncertainty depends on the amount of overlapped intensity, for example being ten times worse for the CO/Fe overlap than the Cr/Fe overlap. Using the methods described here, accurate estimation of error, and the minimization of this could be achieved, providing a key milestone in quantitative atom probe. Accurate estimation of the composition uncertainty in the presence of overlaps is crucial for planning experiments and scientific interpretation of the measurements.
Two new species of the genus Aporcelinus from the USA are described and illustrated. Aporcelinus floridensis sp. n. is characterized by its 1.12–1.52 mm long body, lip region offset by marked constriction and 14.5–17.0 μm broad with perioral liplets, odontostyle 16.5–20.0 μm at its ventral side and 1.1–1.2 times the lip region diameter, neck 316–395 μm long, pharyngeal expansion occupying 43–48% of total neck length, uterus simple and 33–56 μm long or 0.8–1.2 times the corresponding body diameter, V = 48–54, female tail conical (36–49 μm long, c = 27–41, c’ = 1.2–2.0) with finely rounded terminus and no hyaline portion, and male absent. Aporcelinus paolae sp. n. is characterized by its 1.29–1.80 mm long body, lip region offset by marked constriction and 14–16 μm broad, odontostyle 15–17 μm at its ventral side and 1.0–1.1 times the lip region diameter, neck 314–397 μm long, pharyngeal expansion occupying 43–53% of total neck length, uterus tripartite and 128–164 μm long or 2.6–3.6 times the corresponding body diameter, V = 53–57, female tail conical (30–39 μm long, c = 40–51, c’ = 1.1–1.3) with finely rounded terminus and variably re-curved dorsad, male tail conical (27–36 μm, c = 39–59, c’ = 0.9–1.2), ventrally straight and dorsally convex, spicules 48–54 μm long, and 7–9 irregularly spaced ventromedian supplements lacking hiatus. The analyses of the D2-D3 expansion segments of 28S rRNA (LSU) gene sequences of the two new species confirmed the monophyly of the genus, based upon currently available data, showing a close relationship between the genera Aporcelinus and Makatinus, and justified the placement of Aporcelaimellus, Makatinus and Aporcelinus under the subfamily Aporcelaimellinae.
The current research paper describes the lateral-directional parameter estimation from flight data of a miniature Unmanned Aerial Vehicle (UAV) using Maximum Likelihood (ML), and Neural-Gauss-Newton (NGN) methods. An unmanned configuration with a cropped delta planform and thin rectangular cross-section has been designed, fabricated and instrumented. Exhaustive full-scale wind-tunnel tests were performed on the UAV to extract the form of aerodynamic model that has to be postulated a priori for parameter estimation. Rigorous flight tests have been performed to acquire the flight data for several prescribed manoeuvres. Four sets of compatible flight data have been used to carry out parameter estimation using classical ML and neural-network-based NGN methods. It is observed that the estimated parameters are consistent and the lower values of the Cramer-Rao bound for the corresponding estimates have shown significant confidence in the obtained parameters. Furthermore, to validate the aerodynamic model used and to enhance the confidence in the estimated parameters, a proof of match exercise has been carried out.
The item count technique (ICT-MLE) regression model for survey list experiments depends on assumptions about responses at the extremes (choosing no or all items on the list). Existing list experiment best practices aim to minimize strategic misrepresentation in ways that virtually guarantee that a tiny number of respondents appear in the extrema. Under such conditions both the “no liars” identification assumption and the computational strategy used to estimate the ICT-MLE become difficult to sustain. I report the results of Monte Carlo experiments examining the sensitivity of the ICT-MLE and simple difference-in-means estimators to survey design choices and small amounts of non-strategic respondent error. I show that, compared to the difference in means, the performance of the ICT-MLE depends on list design. Both estimators are sensitive to measurement error, but the problems are more severe for the ICT-MLE as a direct consequence of the no liars assumption. These problems become extreme as the number of treatment-group respondents choosing all the items on the list decreases. I document that such problems can arise in real-world applications, provide guidance for applied work, and suggest directions for further research.
The spread of African swine fever virus (ASFV) threatens to reach further parts of Europe. In countries with a large swine production, an outbreak of ASF may result in devastating economic consequences for the swine industry. Simulation models can assist decision makers setting up contingency plans. This creates a need for estimation of parameters. This study presents a new analysis of a previously published study. A full likelihood framework is presented including the impact of model assumptions on the estimated transmission parameters. As animals were only tested every other day, an interpretation was introduced to cover the weighted infectiousness on unobserved days for the individual animals (WIU). Based on our model and the set of assumptions, the within- and between-pen transmission parameters were estimated to βw = 1·05 (95% CI 0·62–1·72), βb = 0·46 (95% CI 0·17–1·00), respectively, and the WIU = 1·00 (95% CI 0–1). Furthermore, we simulated the spread of ASFV within a pig house using a modified SEIR-model to establish the time from infection of one animal until ASFV is detected in the herd. Based on a chosen detection limit of 2·55% equivalent to 10 dead pigs out of 360, the disease would be detected 13–19 days after introduction.
Unlike the mortality risk on which actuaries have been working for more than a century, the long-term care (LTC) risk is relatively new and as of today hardly mastered. Semi-Markov processes have been identified as an adequate tool to study this risk. Nevertheless, access to data is limited and the associated literature still scarce. Insurers mainly use discrete time methods directly inspired from the study of mortality in order to build experience tables. Those methods however are not perfectly suited for the study of competing risk situations. This article provides a theoretical framework to estimate biometric laws associated with a LTC insurance portfolio. The presented method relies on a continuous-time semi-Markov model with three states: autonomy, disability and death. The process describing the state of disability is defined through its transition intensities. We provide a formula to infer the mortality of autonomous people from the mortality of the whole portfolio, on which we have more reliable knowledge. We then propose a parametric expression for the remaining intensities of the model. In particular, incidence in LTC is described by a logistic formula. Under the assumption that the disabled population is a mixture of two latent populations with respect to the category of pathology that caused LTC, we show that the resulting intensity of mortality in LTC takes a very peculiar form and depends on time spent in the LTC state. Estimation of parameters relies on the maximum likelihood method. Our parametric approach, while inducing model uncertainty, eliminates issues related to segmentation in age categories, smoothing or extrapolation at higher ages and thus proves very convenient for the practitioner. Finally, we provide an application using data from a real LTC insurance portfolio.
A general class of Markovian non-Gaussian bifurcating models for cell lineage data is presented. Examples include bifurcating autoregression, random coefficient autoregression, bivariate exponential, bivariate gamma, and bivariate Poisson models. Quasi-likelihood estimation for the model parameters and large-sample properties of the estimates are discussed.
In this paper, we explore some of the various issues that may occur in attempting to fit a dynamical systems (either agent- or continuum-based) model of urban crime to data on just the attack times and locations. We show how one may carry out a regression analysis for the model described by Short et al. (2008, Math. Mod. Meth. Appl. Sci.) by using simulated attack data from the agent-based model. It is discussed how one can incorporate the attack data into the partial differential equations for the expected attractiveness to burgle and the criminal density to predict crime rates between attacks. Using this predicted crime rate, we derive a likelihood function that one can maximise in order to fit parameters and/or initial conditions for the model. We focus on carrying out data assimilation for two different parameter regions, namely in the case where stationary and non-stationary crime hotspots form. It is found that the likelihood function is ‘flat’ for large ranges of parameters, and that this has major implications for crime forecasting. Hence, we look at how one might carry out a goodness-of-fit and forecasting analysis for crime rates given the range of parameter fits. We show how one can use the Kolmogorov–Smirnov statistic to assess the goodness-of-fit. The dynamical systems analysis of the partial differential equations proves invaluable to understanding how the crime rate forecasts depend on the parameters and their sensitivity. Finally, we outline several interesting directions for future research in this area where we believe that the combination of dynamical systems modelling, analysis, and data assimilation can prove effective in developing policing strategies for urban crime.
Electronic communications, as well as other categories of interactions within social networks, exhibit bursts of activity localised in time. We adopt a self-exciting Hawkes process model for this behaviour. First we investigate parameter estimation of such processes and find that, in the parameter regime we encounter, the choice of triggering function is not as important as getting the correct parameters once a choice is made. Then we present a relaxed maximum likelihood method for filling in missing data in records of communications in social networks. Our optimisation algorithm adapts a recent curvilinear search method to handle inequality constraints and a non-vanishing derivative. Finally we demonstrate the method using a data set composed of email records from a social network based at the United States Military Academy. The method performs differently on this data and data from simulations, but the performance degrades only slightly as more information is removed. The ability to fill in large blocks of missing social network data has implications for security, surveillance, and privacy.
We discuss how to fit mixtures of Erlangs to censored and truncated data by iteratively using the EM algorithm. Mixtures of Erlangs form a very versatile, yet analytically tractable, class of distributions making them suitable for loss modeling purposes. The effectiveness of the proposed algorithm is demonstrated on simulated data as well as real data sets.
In earlier studies, scientists have attempted to identify genetic and environmental factors affecting the rate of multiple maternities among humans. We contribute to these studies by analysing the frequencies of multiple maternities in sibships containing triplets. Use of the Hellin transformation is included in evaluation of the triplet rate. Our results indicate greater frequencies of repeated multiple maternities in the sibships than expected, based on population frequencies. The excesses obtained are more marked in triplet maternities than in twin maternities. The transformed triplet rate shows results similar to the twinning rate. The findings also indicate that in families, the influence of maternal factors on the frequencies of multiple maternities is stronger than the influence of paternal factors.
In empirical studies of friendship networks, participants are typically asked, in interviews or questionnaires, to identify some or all of their close friends, resulting in a directed network in which friendships can, and often do, run in only one direction between a pair of individuals. Here we analyze a large collection of such networks representing friendships among students at US high and junior-high schools and show that the pattern of unreciprocated friendships is far from random. In every network, without exception, we find that there exists a ranking of participants, from low to high, such that almost all unreciprocated friendships consist of a lower ranked individual claiming friendship with a higher ranked one. We present a maximum-likelihood method for deducing such rankings from observed network data and conjecture that the rankings produced reflect a measure of social status. We note in particular that reciprocated and unreciprocated friendships obey different statistics, suggesting different formation processes, and that rankings are correlated with other characteristics of the participants that are traditionally associated with status, such as age and overall popularity as measured by total number of friends.
Dose–response analysis is widely used in biological sciences and has application to a variety of risk assessment, bioassay, and calibration problems. In weed science, dose–response methodologies have typically relied on least squares estimation under the assumptions of normal, homoscedastic, and independent errors. Advances in computational abilities and available software, however, have given researchers more flexibility and choices for data analysis when these assumptions are not appropriate. This article will explore these techniques and demonstrate their use to provide researchers with an up-to-date set of tools necessary for analysis of dose–response problems. Demonstrations of the techniques are provided using a variety of data examples from weed science.
We give a stochastic expansion for estimates
that minimise the arithmetic mean of (typically independent) random functions of a known parameter θ.
Examples include least squares estimates, maximum likelihood estimates and more generally M-estimates.
This is used to obtain leading cumulant coefficients of
needed for the Edgeworth expansions for the distribution and density n1/2 (
− θ0) to magnitude n−3/2 (or to n−2 for the symmetric case),
where θ0 is the true parameter value and n is typically the sample size.
Applications are given to least squares estimates for both real and complex models.
An alternative approach is given when the linear parameters of the model are nuisance parameters.
The methods are illustrated with the problem of estimating the frequencies
when the signal consists of the sum of sinusoids of unknown amplitudes.
Non-life insurance payouts consist of two factors: claimsizes and claim frequency. When calculating e.g. next years premium, it is vital to correctly model these factors and to estimate the unknown parameters. A standard way is to separately estimate in the claimsize and the claim frequency models.
Often there is a deductible with each single claim, and this deductible can be quite large, particularly in inhomogeneous cases such as industrial fire insurance or marine insurance. Not taking the deductibles into account can lead to serious bias in the estimates and consequent implications when applying the model.
When the deductibles are nonidentical, in a full maximum likelihood estimation all unknown parameters have to be estimated simultaneously. An alternative is to use pseudo-maximum likelihood, i.e. first estimate the claimsize model, taking the deductibles into account, and then use the estimated probability that a claim exceeds the deductible as an offset in the claim frequency estimation. This latter method is less efficient, but due to complexity or time considerations, it may be the preferred option.
In this paper we will provide rather general formulas for the relative efficiency of the pseudo maximum likelihood estimators in the i.i.d. case. Two special cases will be studied in detail, and we conclude the paper by comparing the methods on some marine insurance data.
The chain ladder is considered in relation to certain recursive and non-recursive models of claim observations. The recursive models resemble the (distribution free) Mack model but are augmented with distributional assumptions. The non-recursive models are generalisations of Poisson cross-classified structure for which the chain ladder is known to be maximum likelihood. The error distributions considered are drawn from the exponential dispersion family.
Each of these models is examined with respect to sufficient statistics and completeness (Section 5), minimum variance estimators (Section 6) and maximum likelihood (Section 7). The chain ladder is found to provide maximum likelihood and minimum variance unbiased estimates of loss reserves under a wide range of recursive models. Similar results are obtained for a much more restricted range of non-recursive models.
These results lead to a full classification of this paper's chain ladder models with respect to the estimation properties (bias, minimum variance) of the chain ladder algorithm (Section 8).
This paper develops models of the initial impact of marine aggregate extraction on a benthic assemblage. We predict the effect of dredging on species numbers and abundance assuming spatial randomness of individuals. We extend the model to allow for spatial clustering of individuals using a Matern process. Data from a controlled field experiment are used to develop a framework for estimating species reduction. This involves modelling the spatial pattern of individuals before dredging using a Matern process, the impact of dredging at an individual level, and the probability that a species is not seen in a post-dredging survey. The framework was used to estimate that, of the 41 species that were seen in a pre-dredging survey but not in a post-dredging survey, between 0 and 14 were eliminated (with 95% likelihood) rather than escaped detection. The most likely number eliminated was 4.
It has long been known that maximum likelihood estimation in a Poisson model reproduces the chain-ladder technique. We revisit this model. A new canonical parametrisation is proposed to circumvent the inherent identification problem in the parametrisation. The maximum likelihood estimators for the canonical parameter are simple, interpretable and easy to derive. The boundary problem where all observations in one particular development year or on particular underwriting year is zero is also analysed.