Precision Of Model Parameter Estimates Research Articles

Effects of missing observations on predictive capability of augmented Box-Behnken designs

In an experiment, there are many situations when some observations are missed, ignored or unavailable due to some accidents or high cost experiments. A missing observation can make the results of a response surface model quite misleading. It can have an adverse effect on desirable properties of a design like orthogonality, rotatability and optimality. Literature exhibits that some studies have investigated the effects of missing observations on prediction capabilities of response surface designs like Central Composite designs. This work investigates the impact of a missing observation on the estimation and prediction capabilities as well as on the relative A, D and G-efficiencies of augmented Box-Behnken designs. It has been observed that precision of model parameter estimates as well as relative A, D and G-efficiencies are less affected by missing a center run, but more by missing other design points. Prediction capability is adversely affected if we try to predict the response at the same location where we have missed the design point, however, when we capture the overall situation throughout the design region, a missing observation has smaller effect on the prediction capabilities of augment Box-Behnken designs. Missing a center run has less effect than missing other design points on prediction capability of these designs.

Influence of body mass, sociality, and movement behavior on improved detection probabilities when using a second camera trap

Maximizing detection probability is a common goal for occupancy studies using camera traps for data collection. Placing additional cameras at a survey station may improve precision of occupancy and detection estimates. However, these benefits are situational and potentially influenced by species' physical characteristics and behavior. We estimated null occupancy and detection probabilities for 20 mammalian species with >10 detections at multiple sites from one- and two-camera data sets from 63 stations set in a commercial forest reserve in Sabah, Malaysian Borneo during October–December 2015. We used a cross-validated absolute shrinkage and selection operator approach to model the effects of species’ body mass, social behavior, dietary niche, and foot posture on detection probability using one- and two-camera designs. The number of species detections, sites where species were detected, detection probability estimates, and precision of model parameter estimates for all species improved using two cameras. Our results showed that unguligrade species were associated with both high detection probability estimates with one camera and also the greatest improvements using the two-camera design in detection probability compared to all other species. Greater improvements in precision of model parameter estimates from two-camera designs were observed in species detected less frequently. Our data suggests that camera designs need to be adapted based on the focal species and we suggest that future occupancy studies collect preliminary information to maximize effectiveness of camera effort and ensure that data collection is efficient and meets project needs.

An integrated model of population genetics and community ecology

AbstractAimQuantifying abundance distributions is critical for understanding both how communities assemble, and how community structure varies through time and space, yet estimating abundances requires considerable investment in fieldwork. Community‐level population genetic data potentially offer a powerful way to indirectly infer richness, abundance and the history of accumulation of biodiversity within a community. Here we introduce a joint model linking neutral community assembly and comparative phylogeography to generate both community‐level richness, abundance and genetic variation under a neutral model, capturing both equilibrium and non‐equilibrium dynamics.LocationGlobal.MethodsOur model combines a forward‐time individual‐based community assembly process with a rescaled backward‐time neutral coalescent model of multi‐taxa population genetics. We explore general dynamics of genetic and abundance‐based summary statistics and use approximate Bayesian computation (ABC) to estimate parameters underlying the model of island community assembly. Finally, we demonstrate two applications of the model using community‐scale mtDNA sequence data and densely sampled abundances of an arachnid community on La Réunion. First, we use genetic data alone to estimate a summary of the abundance distribution, ground‐truthing this against the observed abundances. Then, we jointly use the observed genetic data and abundances to estimate the proximity of the community to equilibrium.ResultsSimulation experiments of our ABC procedure demonstrate that coupling abundance with genetic data leads to improved accuracy and precision of model parameter estimates compared with using abundance‐only data. We further demonstrate reasonable precision and accuracy in estimating a metric underlying the shape of the abundance distribution, temporal progress towards local equilibrium and several key parameters of the community assembly process. For the insular arachnid assemblage, we find the joint distribution of genetic diversity and abundance approaches equilibrium expectations, and that the Shannon entropy of the observed abundances can be estimated using genetic data alone.Main conclusionsThe framework that we present unifies neutral community assembly and comparative phylogeography to characterize the community‐level distribution of both abundance and genetic variation through time, providing a resource that should greatly enhance understanding of both the processes structuring ecological communities and the associated aggregate demographic histories.

JMASM45: A computer program for Bayesian D-optimal binary repeated measurements designs (Matlab)

Planners of longitudinal studies of binary responses in applied sciences have not yet benefitted from optimal designs, which have been shown to improve precision of model parameter estimates, due to absence of a computer program. An interactive computer program for Bayesian optimal binary repeated measurements designs is presented for this purpose.

Effects of Missing Observations on Predictive Capability of Central Composite Designs

Quite often in experimental work, many situations arise where some observations are lost or become unavailable due to some accidents or cost constraints. When there are missing observations, some desirable design properties like orthogonality, rotatability and optimality can be adversely affected. Some attention has been given, in literature, to investigating the prediction capability of response surface designs; however, little or no effort has been devoted to investigating same for such designs when some observations are missing. This work therefore investigates the impact of a single missing observation of the various design points: factorial, axial and center points, on the estimation and predictive capability of Central Composite Designs (CCDs). It was observed that for each of the designs considered, precision of model parameter estimates and the design prediction properties were adversely affected by the missing observations and that the largest loss in precision of parameters corresponds to a missing factorial point.

A Designed Screening Study with Prespecified Combinations of Factor Settings

ABSTRACT In many applications, the experimenter has limited options about what factor combinations can be chosen for a designed study. Consider a screening study for a production process involving five input factors whose levels have been previously established. The goal of the study is to understand the effect of each factor on the response, a variable that is expensive to measure and results in destruction of the part. From an inventory of available parts with known factor values, we wish to identify a best collection of factor combinations with which to estimate the factor effects. Though the observational nature of the study cannot establish a causal relationship involving the response and the factors, the study can increase understanding of the underlying process. The study can also help determine where investment should be made to control input factors during production that will maximally influence the response. Because the factor combinations are observational, the chosen model matrix will be nonorthogonal and will not allow independent estimation of factor effects. In this manuscript we borrow principles from design of experiments to suggest an “optimal” selection of factor combinations. Specifically, we consider precision of model parameter estimates, the issue of replication, and abilities to detect lack of fit and to estimate two-factor interactions. Through an example, we present strategies for selecting a subset of factor combinations that simultaneously balance multiple objectives, conduct a limited sensitivity analysis, and provide practical guidance for implementing our techniques across a variety of quality engineering disciplines.

To triplicate or not to triplicate?

A common practice in scientific experimentation in areas such as Medicine, Pharmacy, Nutrition, among others, is to measure each sample unit three times (in triplicate) or more generally, m times (in m–plicate) and take the average of such measurements as the response variable. This is generally done to improve the precision of model parameter estimates. When the objective is to estimate the population mean, we use a random effects model to show that the efficiency of working with m-plicates is related to the magnitude of the intraclass correlation coefficient, which essentially measures the contribution of the variance between sample units to the total variance. We show that above certain values of this parameter, the use of m-plicates does not bring significant improvement (say, of 10% or more) to the precision of the estimates. Additionally, taking the costs of sampling units and making measurements into account, we compare sampling schemes with and without m-plicates designed to obtain fixed width confidence intervals for the mean. We illustrate the results through a practical example.

Biomodel Formulation and Identification Using Optimal and Other Effective Experiment Designs

Several inten'clated methodological issues of this symposium are addressed, with the focus of formulating and quantifying kinetic models whose purpose is to answer particular quantitative questions about living systems. The unifying concept is kinetic experiment design, that is, decisions about what to do in the experimental laboratory to achieve this goal, and also how to do it “best.” The overriding factor in this endeavor is the paucity of “good-enough” data available from many types of biosystem studies. More often than not, the data are too few, too noisy, or both, and the number of output “ports” available to experimental probes are also too few. Optimal sampling schedule (OSS) design, based in information theory and asymptotic theory of mathematical statistics, represents one approach to optimizing the precision of model parameter estimates from small data sets. Some practical results of kinetic experiments perfomied with optimal sampling schedule designs are discussed, based on experiences in real endocrine and metabolic system studies in several animal species. Some potential pitfalls of this ap-proach are also discussed. A related problem is how to quantify unidentifiable models, i.e., models with “too many parameters”, more parameters than the number or variety of data available to quantify all or even some of them. Interval identifiahility and parameter interval analysis methods and results are reviewed, for several classes of multicompartmental models, because this is one approach to circumventing the unidentifiability problem, without the need for distorting or further abstracting relatively realistic model structures by reducing the dimensionality of their state variables or parameters. Finally, for models and systems with more than just a few pools, i.e., complex models, a case is made for using easier steady state experiment designs and models, rather than more complicated transient response studies, to reduce the dimensionality of the parameter estimation problem, rendering it more identifiable, or completely identifiable. Cut-set analysis, a graph theoretic approach, is used to help solve this problem. This is all done in the context of matching the model and the experiment design to the goals of a study, and an example is presented illustrating how a multidimensional system can be explored so that a 1-dimensional model fits the data best, and helps to answer some common questions in kinetic analysis.

The relationship between data and the precision of parameter estimates of hydrologic models

This paper presents a discussion of the relationship between data used for hydrologic model calibration and the precision of model parameter estimates. The analysis is conducted within the framework of the maximum likelihood approach to model selection. The concept of “information” is discussed and the relationship between information and parameter uncertainty is examined. This analysis provides some interesting insights into the role that the quantity and quality of the data used play in the identification procedure. Based on this, a method for selecting data sets suitable for model calibration is suggested. The ideas discussed are illustrated by means of simulation studies using a conceptual-type rainfall-runoff model.