Refined parameter and uncertainty estimation when both variables are subject to error. Case study: estimation of Si consumption and regeneration rates in a marine environment

The problem of estimating parameters and their uncertainty from experimental measurements in marine ecosystems is a common task and often necessitates solving nonlinear equations. If the measurements are subject to individually varying errors (i.e., heteroscedastic data), the parameters are often estimated using a Weighted Least Squares (WLS) method. For estimating the parameter uncertainties, a linearized expression for the covariance matrix exists. Yet, both methods assume that the errors on the independent variable, also called “input”, is negligible, which is often not true. For instance, in order to determine uptake and regeneration rates of silicic acid by phytoplankton, concentration and isotopic abundance measurements are performed at the beginning (input) and at the end (output) of an incubation experiment. Here, the so-called input and output are measurements of the same quantities, i.e., determined in exactly the same way, only differing by the time at which the measurements were performed. Clearly, there is no reason to assume that the input measurements are subject to less error than the output measurements. We propose a refinement of the two abovementioned estimation methods which enlarges their applicability to cases where input noise is not negligible. The refined methods are evaluated on the uptake and regeneration processes of silicic acid and compared to the original procedures using Monte-Carlo simulations. The results reveal a smaller bias for the refined WLS estimator compared with the original one. An additional advantage of using the refined WLS cost function is that its residual value can be interpreted as a sample from a χ² distribution. This property is especially useful because it enables an internal quality control of the results. In addition, the parameter uncertainty estimation is significantly improved. By neglecting the effect of the input noise, a (potentially) important origin of the parameter variation is simply ignored. Therefore, without the refinement, the parameter uncertainties are systematically underestimated. Using the refined method, this systematic error disappears and on the whole, the parameter standard deviations are accurately estimated.     

Regional fishery management councils and the display of scientific authority

Abstract

Natural resource management entities such as the Regional Fishery Management Councils established by the Magnuson Fishery Conservation and Management Act of 1976 depend heavily on science to inform policymakers and to legitimate the policy process. This paper discusses the importance of fishery science to the council system, contrasts the functions of Scientific and Statistical Committees (SSCs) serving the Pacific Fishery Management Council and the New England Fishery Management Council, and remarks on the implications of differences in the display of scientific authority by these SSCs.     

The inverse power transformation logit and dogit mode choice models

This paper explores the properties of inverse Box-Cox and Box-Tukey transformations applied to the exponential functions of logit and dogit mode choice models. It is suggested that inverse power transformations allow for the introduction of modeler ignorance in the models and solve the “thin equal tails” problem of the logit model; it is also shown that they allow for asymmetry of response functions in both logit and dogit models by introducing alternative-specific parameters which make cross elasticities of demand among alternatives generally asymmetric. In the dogit model, modeler ignorance and consumer captivity remain conceptually distinct. Standard logit and dogit models appear as very special “perfect knowledge” cases in broad spectra of models which also include, among others, the reciprocal extreme value or log-Weibull variants. These improvements over the simple symmetric-thin-equal-tail-perfect-knowledge logit and the symmetric-pure-captivity dogit are achieved at the cost of introducing at the most two new parameters per alternative considered in the original logit and dogit mode choice models.     

The dogit model

This paper presents the dogit model. That model is flexible enough to permit the choice among specific pairs of alternatives to be consistent with the independence from irrelevant alternatives axiom, as in a logit model, but it simultaneously allows the choice among other pairs not to be. Dogit parameters add an “income effect” to the “substitution effect” already built into the logit model; alternatively, they allow for the joint presence of compulsive and discretionary elements in consumer behavior, or for the identification of captive markets. Eventual estimation of the values of the parameters of the dogit model appears simpler than for the probit model.     

拥有一辆福特,还是借一辆阿斯顿马丁?

打开任何一份报纸的经济版你会发现越来越多有关汽车行业现状的坏消息。就在笔者撰写此文之时．我们刚看到Dana档案的第11章．捷豹放弃了统一平台的计划．同时大众的CEO Bemd Pischetsrieder正忙于应对工会扬言要罢工的状况。