In many areas of human practice, one needs to approximate a set of points P1, . . . , Pn ∈ R representing experimental data or observations by a simple geometric shape, such as a line, plane, circular arc, elliptic arc, and spherical surface. This problem is known as fitting amodel object line, circle, sphere, etc. to observed data points. The best fit is achieved when the geometric distances f...

We describe a Markov state model for a cloned potassium channel of the human heart ( 1 KvLQT I ). The parameters of the model are determined by a least-squares fit of predicted vs. measured data. The fitting process is achieved by using the “SPSA” optimizer to sequentially choose trial values of the parameters. At each choice of parameter value, a loss function is computed by simulating the act...

Piecewise affine systems serve as an important approximation of nonlinear systems. The identification of piecewise affine systems is here tackled by overparametrizing and assigning a regressor-parameter to each of the observations. Regressor parameters are then forced to be the same if that not causes a major increase in the fit term. The formulation takes the shape of a least-squares problem w...

We examine the capability of mean square displacement (MSD) analysis to extract reliable values of the diffusion coefficient D of a single particle undergoing Brownian motion in an isotropic medium in the presence of localization uncertainty. The theoretical results, supported by simulations, show that a simple unweighted least-squares fit of the MSD curve can provide the best estimate of D pro...

Least squares estimators are developed for the parameters in the autocorrelation function of a stationary process. Regularity conditions for consistency and asymptotic normality are given, and optimal weights are derived. It is shown how goodness of fit and model selection can be based on the distance between empirical and fitted autocorrelations. Examples of sums of Ornstein-Uhlenbeck type pro...

One of the most common questions about logistic regression is “How do I know if my model fits the data?” There are many approaches to answering this question, but they generally fall into two categories: measures of predictive power (like R-square) and goodness of fit tests (like the Pearson chi-square). This presentation looks first at R-square measures, arguing that the optional R-squares rep...

In this chapter, the authors present a systematic statistical analysis of cavity ring-down signal extraction. The traditional uncorrelated least squares fit can be generalized to the situation with data correlation (e.g. caused by data filtering, which is essential to minimize noise). If the data is sufficiently highly sampled, the effect of the data correlation can be included by introducing a...

Risk assessments of toxic chemicals currently rely heavily on the use of no-observed-effect concentrations (NOECs). Due to several crucial flaws in this concept, however, discussion of replacing NOECs with statistically estimated low-effect concentrations continues. This paper describes a general best-fit method for the estimation of effects and effect concentrations by the use of a pool of 10 ...

1. Abstract: The construction of facial composites by assembling individual facial features is common in criminal investigations. Arguably, the best known such method is E-FIT (electronic facial identication technique). However, although humans have excellent facial recognition ability, it is widely recognised that they often have great difficulty recalling facial characteristics in sufficient ...

June 1, 2010 Version 0.7-0 Date 2010-04-07 Title Non-supervised Regional Frequency Analysis Author Alberto Viglione Maintainer Alberto Viglione Depends stats, graphics Description A collection of statistical tools for objective (non-supervised) applications of the Regional Frequency Analysis methods in hydrology. The package refers to the index-value method and, mo...