Estimating taxonomic durations and preservation probability

Paleobiology ◽  
1997 ◽  
Vol 23 (3) ◽  
pp. 278-300 ◽  
Author(s):  
Mike Foote
Keyword(s):  
Parameter Estimation ◽  
Estimation Method ◽  
Parameter Estimates ◽  
Extinction Rate ◽  
Mammal Species ◽  
The Face ◽  
Stratigraphic Ranges ◽  
Binned Data ◽  
Preservation Rate ◽  
Discrete Time Models

Paleontological completeness and stratigraphic ranges depend on extinction rate, origination rate, preservation rate, and the length of the interval of time over which observations can be made. I derive expressions for completeness and the distribution of durations and ranges as functions of these parameters, considering both continuous- and discrete-time models.Previous work has shown that, if stratigraphic ranges can be followed indefinitely forward, and if extinction and preservation occur at stochastically constant rates, then extinction rate and preservability can be estimated from (1) discrete (binned) stratigraphic ranges even if data on occurrences within ranges are unknown, and (2) continuous ranges if the number of occurrences within each range is known. I show that, regardless of whether the window of observation is finite or infinite, extinction and preservation rates can also be estimated from (3) continuous ranges when the number of occurrences is not known, and (4) discrete ranges when the number of occurrences is not known. One previous estimation method for binned data involves a sample-size bias. This is circumvented by using maximum likelihood parameter estimation. It is worth exploiting data on occurrences within ranges when these are available, since they allow preservation rate to be estimated with less variance. The various methods yield comparable parameter estimates when applied to Cambro-Ordovician trilobite species and Cenozoic mammal species.Stratigraphic gaps and variable preservation affect stratigraphic ranges predictably. In many cases, accurate parameter estimation is possible even in the face of these complications. The distribution of stratigraphic ranges can be used to estimate the sizes of gaps if their existence is known.

Fossil preservation and the stratigraphic ranges of taxa

Paleobiology ◽  
1996 ◽  
Vol 22 (2) ◽  
pp. 121-140 ◽  
Author(s):  
Mike Foote ◽  
David M. Raup
Keyword(s):  
Fossil Record ◽  
Mammalian Species ◽  
Evolutionary Rates ◽  
Extinction Rate ◽  
Mammal Species ◽  
Original Distribution ◽  
Lower Ordovician ◽  
Stratigraphic Ranges ◽  
Fossil Preservation ◽  
Rule Out

The incompleteness of the fossil record hinders the inference of evolutionary rates and patterns. Here, we derive relationships among true taxonomic durations, preservation probability, and observed taxonomic ranges. We use these relationships to estimate original distributions of taxonomic durations, preservation probability, and completeness (proportion of taxa preserved), given only the observed ranges. No data on occurrences within the ranges of taxa are required. When preservation is random and the original distribution of durations is exponential, the inference of durations, preservability, and completeness is exact. However, reasonable approximations are possible given non-exponential duration distributions and temporal and taxonomic variation in preservability. Thus, the approaches we describe have great potential in studies of taphonomy, evolutionary rates and patterns, and genealogy.Analyses of Upper Cambrian-Lower Ordovician trilobite species, Paleozoic crinoid genera, Jurassic bivalve species, and Cenozoic mammal species yield the following results: (1) The preservation probability inferred from stratigraphic ranges alone agrees with that inferred from the analysis of stratigraphic gaps when data on the latter are available. (2) Whereas median durations based on simple tabulations of observed ranges are biased by stratigraphic resolution, our estimates of median duration, extinction rate, and completeness are not biased. (3) The shorter geologic ranges of mammalian species relative to those of bivalves cannot be attributed to a difference in preservation potential. However, we cannot rule out the contribution of taxonomic practice to this difference. (4) In the groups studied, completeness (proportion of species [trilobites, bivalves, mammals] or genera [crinoids] preserved) ranges from 60% to 90%. The higher estimates of completeness at smaller geographic scales support previous suggestions that the incompleteness of the fossil record reflects loss of fossiliferous rock more than failure of species to enter the fossil record in the first place.

scholarly journals A QUASI-LIKELIHOOD APPROACH TO PARAMETER ESTIMATION FOR SIMULATABLE STATISTICAL MODELS

2014 ◽  
Vol 33 (2) ◽  
pp. 107 ◽  
Author(s):  
Markus Baaske ◽  
Felix Ballani ◽  
Karl Gerald Van den Boogaart
Keyword(s):  
Parameter Estimation ◽  
Statistical Models ◽  
Estimation Method ◽  
Score Function ◽  
Boolean Model ◽  
Parameter Estimates ◽  
Random Errors ◽  
Likelihood Functions ◽  
Simulation Based ◽  
Likelihood Approach

This paper introduces a parameter estimation method for a general class of statistical models. The method exclusively relies on the possibility to conduct simulations for the construction of interpolation-based metamodels of informative empirical characteristics and some subjectively chosen correlation structure of the underlying spatial random process. In the absence of likelihood functions for such statistical models, which is often the case in stochastic geometric modelling, the idea is to follow a quasi-likelihood (QL) approach to construct an optimal estimating function surrogate based on a set of interpolated summary statistics. Solving these estimating equations one can account for both the random errors due to simulations and the uncertainty about the meta-models. Thus, putting the QL approach to parameter estimation into a stochastic simulation setting the proposed method essentially consists of finding roots to a sequence of approximating quasiscore functions. As a simple demonstrating example, the proposed method is applied to a special parameter estimation problem of a planar Boolean model with discs. Here, the quasi-score function has a half-analytical, numerically tractable representation and allows for the comparison of the model parameter estimates found by the simulation-based method and obtained from solving the exact quasi-score equations.

Application of the Weighted Least Squares Parameter Estimation Method to the Robot Calibration

1994 ◽  
Vol 116 (3) ◽  
pp. 890-893 ◽  
Author(s):  
G. Zak ◽  
B. Benhabib ◽  
R. G. Fenton ◽  
I. Saban
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Kinematic Model ◽  
Measurement Data ◽  
Estimation Method ◽  
Kinematic Parameter ◽  
Measuring System ◽  
Parameter Estimates ◽  
Robot Calibration

Significant attention has been paid recently to the topic of robot calibration. To improve the robot’s accuracy, various approaches to the measurement of the robot’s position and orientation (pose) and correction of its kinematic model have been proposed. Little attention, however, has been given to the method of estimation of the kinematic parameters from the measurement data. Typically, a least-squares solution method is used to estimate the corrections to the parameters of the model. In this paper, a method of kinematic parameter estimation is proposed where a standard least-squares estimation procedure is replaced by weighted least-squares. The weighting factors are calculated based on all the a priori available statistical information about the robot and the pose-measuring system. By giving greater weight to the measurements made where the standard deviation of the noise in the data is expected to be lower, a significant reduction in the error of the kinematic parameter estimates is made possible. The improvement in the calibration results was verified using a calibration simulation algorithm.

scholarly journals Global synthesis of sea turtle von Bertalanffy growth parameters through Bayesian hierarchical modeling

2021 ◽  
Vol 657 ◽  
pp. 191-207
Author(s):  
MD Ramirez ◽  
T Popovska ◽  
EA Babcock
Keyword(s):  
Population Dynamics ◽  
Parameter Estimation ◽  
Body Size ◽  
Sea Turtles ◽  
Estimation Method ◽  
Growth Parameter ◽  
Sea Turtle ◽  
Parameter Estimates ◽  
Von Bertalanffy ◽  
Bayesian Hierarchical

Knowledge of sea turtle demographic rates is central to modeling their population dynamics, but few studies have quantitatively synthesized existing data globally. Here, we used a Bayesian hierarchical model to conduct a meta-analysis of published von Bertalanffy growth curve parameters (growth coefficient, K; asymptotic length, L∞) for chelonid sea turtles. We identified 34 studies for 5 of 6 extant chelonids that met minimum selection criteria. We implemented a suite of models that included a multivariate normal likelihood on the log-transformed values of the 2 parameters to evaluate the influence of species, population (regional management unit, RMU), parameter estimation method (mark-recapture, skeletochronology, length-frequency analysis), latitude, and sampled body size range (all sizes, no large, no small, no large or small) on growth parameter estimates. According to information criteria, the best model included a random effect of species. The second best model also included latitude as a fixed effect, but RMU, parameter estimation method, latitude, and sampled body size ultimately did not strongly influence the means or variances of K and L∞ among studies. The apparent lack of RMU effect on parameter estimates within species may be an artifact of the small number of RMUs with published growth parameter estimates. The species-specific, and in some cases RMU-specific, posterior means and standard deviations of K and L∞ from this study would be appropriate priors for future studies of growth in chelonid sea turtles or for models of population dynamics. We highlight the need for expanded study and synthesis of sea turtle somatic growth rates.

scholarly journals A time-dependent parameter estimation framework for crop modeling

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Faezeh Akhavizadegan ◽  
Javad Ansarifar ◽  
Lizhi Wang ◽  
Isaiah Huber ◽  
Sotirios V. Archontoulis
Keyword(s):  
Machine Learning ◽  
Parameter Estimation ◽  
Estimation Method ◽  
Time Dependent ◽  
Bayesian Optimization ◽  
Parameter Estimates ◽  
Crop Modeling ◽  
Bayesian Optimization Algorithm ◽  
Crop Models ◽  
Dependent Parameter

AbstractThe performance of crop models in simulating various aspects of the cropping system is sensitive to parameter calibration. Parameter estimation is challenging, especially for time-dependent parameters such as cultivar parameters with 2–3 years of lifespan. Manual calibration of the parameters is time-consuming, requires expertise, and is prone to error. This research develops a new automated framework to estimate time-dependent parameters for crop models using a parallel Bayesian optimization algorithm. This approach integrates the power of optimization and machine learning with prior agronomic knowledge. To test the proposed time-dependent parameter estimation method, we simulated historical yield increase (from 1985 to 2018) in 25 environments in the US Corn Belt with APSIM. Then we compared yield simulation results and nine parameter estimates from our proposed parallel Bayesian framework, with Bayesian optimization and manual calibration. Results indicated that parameters calibrated using the proposed framework achieved an 11.6% reduction in the prediction error over Bayesian optimization and a 52.1% reduction over manual calibration. We also trained nine machine learning models for yield prediction and found that none of them was able to outperform the proposed method in terms of root mean square error and R2. The most significant contribution of the new automated framework for time-dependent parameter estimation is its capability to find close-to-optimal parameters for the crop model. The proposed approach also produced explainable insight into cultivar traits’ trends over 34 years (1985–2018).

scholarly journals Sampling Plans for Fitting the Psychometric Function

2005 ◽  
Vol 8 (2) ◽  
pp. 256-289 ◽  
Author(s):  
Miguel A. García-Pérez ◽  
Rocío Alcalá-Quintana
Keyword(s):  
Parameter Estimation ◽  
Psychometric Function ◽  
Estimation Method ◽  
Forced Choice ◽  
Estimation Methods ◽  
Parameter Estimates ◽  
Mathematical Form ◽  
Sampling Plans ◽  
Forced Choice Tasks ◽  
Choice Tasks

Research on estimation of a psychometric function Ψ has usually focused on comparing alternative algorithms to apply to the data, rarely addressing how best to gather the data themselves (i.e., what sampling plan best deploys the affordable number of trials). Simulation methods were used here to assess the performance of several sampling plans in yes–no and forced-choice tasks, including the QUEST method and several variants of up–down staircases and of the method of constant stimuli (MOCS). We also assessed the efficacy of four parameter estimation methods. Performance comparisons were based on analyses of usability (i.e., the percentage of times that a plan yields usable data for the estimation of all the parameters of Ψ) and of the resultant distributions of parameter estimates. Maximum likelihood turned out to be the best parameter estimation method. As for sampling plans, QUEST never exceeded 80% usability even when 1000 trials were administered and rendered accurate estimates of threshold but misestimated the remaining parameters. MOCS and up–down staircases yielded similar and acceptable usability (above 95% with 400–500 trials) and, although neither type of plan allowed estimating all parameters with optimal precision, each type appeared well suited to estimating a distinct subset of parameters. An analysis of the causes of this differential suitability allowed designing alternative sampling plans (all based on up–down staircases) for yes–no and forced-choice tasks. These alternative plans rendered near optimal distributions of estimates for all parameters. The results just described apply when the fitted Ψ has the same mathematical form as the actual Ψ generating the data; in case of form mismatch, all parameters except threshold were generally misestimated but the relative performance of all the sampling plans remained identical. Detailed practical recommendations are given.

scholarly journals A two-stage approach for estimating the parameters of an age-group epidemic model from incidence data

2017 ◽  
Vol 27 (7) ◽  
pp. 1999-2014 ◽  
Author(s):  
Rami Yaari ◽  
Itai Dattner ◽  
Amit Huppert
Keyword(s):  
Parameter Estimation ◽  
Infectious Diseases ◽  
Estimation Method ◽  
Parameter Estimates ◽  
Age Group ◽  
Next Generation ◽  
Two Stage ◽  
Incidence Data ◽  
Highly Nonlinear ◽  
Next Generation Matrix

Age-dependent dynamics is an important characteristic of many infectious diseases. Age-group epidemic models describe the infection dynamics in different age-groups by allowing to set distinct parameter values for each. However, such models are highly nonlinear and may have a large number of unknown parameters. Thus, parameter estimation of age-group models, while becoming a fundamental issue for both the scientific study and policy making in infectious diseases, is not a trivial task in practice. In this paper, we examine the estimation of the so-called next-generation matrix using incidence data of a single entire outbreak, and extend the approach to deal with recurring outbreaks. Unlike previous studies, we do not assume any constraints regarding the structure of the matrix. A novel two-stage approach is developed, which allows for efficient parameter estimation from both statistical and computational perspectives. Simulation studies corroborate the ability to estimate accurately the parameters of the model for several realistic scenarios. The model and estimation method are applied to real data of influenza-like-illness in Israel. The parameter estimates of the key relevant epidemiological parameters and the recovered structure of the estimated next-generation matrix are in line with results obtained in previous studies.

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