A Symmetric Extended Logistic Model with Applications to Experimental Toxicity Data

The fit of the logit and probit models for quantal response data can be improved by embedding these classical models within a richer parametric family indexed by one or two shape parameters. In this paper, a symmetric extended logistic model indexed by a shape parameter λ is discussed with application to dose response curves. The usual maximum likelihood method is employed to estimate the parameters of the model. The need to include the shape parameter λ is illustrated by analyzing a set of real experimental data and comparing the fit of the extended logistic model to those obtained by the standard logit and probit models.     

Point estimation in quantal response models

In this article least-squares- and maximum-likelihood-estimators in quantal response models are presented in a standardized terminology. The large sample properties are derived and the convergence properties of the Newton-Raphson- and the Scoring-method for the iterative solution of the likelihood equations are investigated. Finally, it is shown that the iterative least-squares estimation methods are equivalent to the method of scoring.     

Incorporating time postinoculation into a dose–response model of Yersinia pestis in mice

Aims:  To develop a time-dependent dose–response model for describing the survival of animals exposed to Yersinia pestis.
Methods and Results:  Candidate time-dependent dose–response models were fitted to a survival data set for mice intraperitoneally exposed to graded doses of Y. pestis using the maximum likelihood estimation method. An exponential dose–response model with the model parameter modified by an inverse-power dependency of time postinoculation provided a statistically adequate fit to the experimental survival data. This modified model was verified by comparison with prior studies.
Conclusions:  The incorporated time dependency quantifies the expected temporal effect of in vivo bacteria growth in the dose–response relationship. The modified model describes the development of animal infectious response over time and represents observed responses accurately.
Significance and Impact of the Study:  This is the first study to incorporate time in a dose–response model for Y. pestis infection. The outcome may be used for the improved understanding of in vivo bacterial dynamics, improved postexposure decision making or as a component to better assist epidemiological investigations.     

kakusan: a computer program to automate the selection of a nucleotide substitution model and the configuration of a mixed model on multilocus data

The application of different substitution models to each gene (a.k.a. mixed model) should be considered in model‐based phylogenetic analysis of multigene sequences. However, a single molecular evolution model is still usually applied. There are no computer programs able to conduct model selection for multiple loci at the same time, though several recently developed types of software for phylogenetic inference can handle mixed model. Here, I have developed computer software named ‘kakusan’ that enables us to solve the above problems. Major running steps are briefly described, and an analysis of results with kakusan is compared to that obtained with other program.     

Bias and error in estimates of mean shape in geometric morphometrics

Sampling experiments were performed to investigate mean square error and bias in estimates of mean shape produced by different geometric morphometric methods. The experiments use the isotropic error model, which assumes equal and independent variation at each landmark. The case of three landmarks in the plane (i.e., triangles) was emphasized because it could be investigated systematically and the results displayed on the printed page. The amount of error in the estimates was displayed as RMSE surfaces over the space of all possible configurations of three landmarks. Patterns of bias were shown as vector fields over this same space. Experiments were also performed using particular combinations of four or more landmarks in both two and three dimensions.It was found that the generalized Procrustes analysis method produced estimates with the least error and no pattern of bias. Averages of Bookstein shape coordinates performed well if the longest edge was used as the baseline. The method of moments (Stoyan, 1990, Model. Biomet. J. 32, 843) used in EDMA (Lele, 1993, Math. Geol. 25, 573) exhibits larger errors. When variation is not small, it also shows a pattern of bias for isosceles triangles with one side much shorter than the other two and for triangles whose vertices are approximately collinear causing them to resemble their own reflections. Similar problems were found for the log-distance method of Rao and Suryawanshi (1996, Proc. Nat. Acad. Sci. 95, 4121). These results and their implications for the application of different geometric morphometric methods are discussed.     

Evaluating the performance of a successive-approximations approach to parameter optimization in maximum-likelihood phylogeny estimation

Almost all studies that estimate phylogenies from DNA sequencedata under the maximum-likelihood (ML) criterion employ an approximateapproach. Most commonly, model parameters are estimated on someinitial phylogenetic estimate derived using a rapid method (neighbor-joiningor parsimony). Parameters are then held constant during a treesearch, and ideally, the procedure is repeated until convergenceis achieved. However, the effectiveness of this approximationhas not been formally assessed, in part because doing so requirescomputationally intensive, full-optimization analyses. Here,we report both indirect and direct evaluations of the effectivenessof successive approximations. We obtained an indirect evaluationby comparing the results of replicate runs on real data thatuse random trees to provide initial parameter estimates. Forsix real data sets taken from the literature, all replicateiterative searches converged to the same joint estimates oftopology and model parameters, suggesting that the approximationis not starting-point dependent, as long as the heuristic searchesof tree space are rigorous. We conducted a more direct assessmentusing simulations in which we compared the accuracy of phylogeniesestimated using full optimization of all model parameters oneach tree evaluated to the accuracy of trees estimated via successiveapproximations. There is no significant difference between theaccuracy of the approximation searches relative to full-optimizationsearches. Our results demonstrate that successive approximationis reliable and provide reassurance that this much faster approachis safe to use for ML estimation of topology.     

The frequency of ion-pair substructures in proteins is quantitatively related to electrostatic potential: a statistical model for nonbonded interactions

A statistical analysis of ion pairs in protein crystal structures shows that their abundance with respect to uncharged controls is accurately predicted by a Boltzmann-like function of electrostatic potential. It appears that the mechanisms of protein folding and/or evolution combine to produce a "thermal" distribution of local nonbonded interactions, as has been suggested by statistical-mechanical theories. Using this relationship, we develop a maximum likelihood methodology for estimation of apparent energetic parameters from the data base of known structures, and we derive electrostatic potential functions that lead to optimal agreement of observed and predicted ion-pair frequencies. These are similar to potentials of mean force derived from electrostatic theory, but departure from Coulombic behavior is less than has been suggested.     

Stability and parameter dependency analysis of a facilitation tectal column (FTC) model

Mathematical models and computer simulations have been widely used to study the spatio-temporal characteristics of the processing of information carried out by the central nervous system. When trying to show whether or not a neural model accounts for the phenomena under study, if the number of parameters whose values need to be calculated becomes large, then computer simulations alone become very inefficient to define such values. Here, we developed stability and parameter dependency analyses of the mathematical representation of a single facilitation tectal column (FTC) model, to show how by using techniques from non-linear systems theory we can define the ranges of parameter values under which the model would explain the required performance of the neural net model. The benefits of these analyses can be grouped in two parts: first, the advantage of using non-linear systems techniques to analyze, analytically, the dynamics of neural net models; and second, we get a deeper understanding of why the hypotheses embedded in the models yield the appropriate behaviors and what are the critical situations (parametric combinations) under which these behaviors are displayed.