Fisher's Rule Research Articles

Multiscale fuzzy entropy based on local mean decomposition and Fisher rule for EEG feature extraction in human motion analysis

Electroencephalogram (EEG) is a nonlinear, non-stationary, and random weak signal generated by a large number of neurons. It has great research value and practical significance in artificial intelligence, biomedical engineering and other fields. EEG feature extraction

Towards compositional geochemical potential mapping

Mineral potential mapping aims at defining target zones of future local mineral exploration efforts on the basis of regional geochemical and geological surveys. Geochemical potential mapping typically involves using a small set of elements to predict an anomalous presence of a mineral commodity related with them. In this context it is common to work with logarithmically transformed concentrations of elements. This contribution explores a compositionally compliant approach to potential mapping using geochemical evidences, in which the whole set of components is applied a log-ratio transformation before any potential mapping technique is used. In this way, candidate zones can be identified by its high value in a certain ratio of elements, implying that the important information is a contrast between two or more elements, and not an absolute concentration of one of them. Two different potential mapping techniques are used (a method equivalent to the Fisher rule, and a Poisson point process, both accounting for spatial dependence), with different results.

An experimental analysis of the behavior of forestry decision-makers — The example of timing in sales decisions

Despite the existing literature, it is still unclear whether and to what extent the behavior of forestry decision-makers can be predicted by means of normative models. To date, the actual decision-making behavior regarding logging has hence been only derived from the analysis of data gathered in surveys or on the basis of aggregated data. Currently, no studies exist that compare the individual timber harvesting behavior with a normative benchmark. The present study experimentally examines the behavior of decision-makers from forestry organizations by means of the example of selling a one-off property with a normative benchmark derived using the Jevons–Fisher rule. We investigate if the intuitive behavior shown by forestry decision-makers in an incentive-compatible experiment for the sale of a one-off property can be approximated to the optimal behavior according to the Jevons–Fisher rule. For determining the normative benchmark, the decision-maker's risk attitude measured by a Holt and Laury lottery is explicitly taken into account. The results reveal that, on average, participants decide earlier for selling the property than what would be expected according to the normative benchmark. This illustrates the importance of experimental investigations in order to better understand the decision-making behavior in a forestry setting. Furthermore, the findings indicate that risk-averse participants, males, participants who completed a forestry apprenticeship as well as participants with an economic-related educational background sell the property earlier. Older participants, participants holding a university degree, and participants interested in participating in further experiments sell the property rather later. Moreover, with progressive repetition of the property sale experiment, participants decide to sell the property earlier.

Performance and estimation of the true error rate of classification rules built with additional information. An application to a cancer trial

Classification rules that incorporate additional information usually present in discrimination problems are receiving certain attention during the last years as they perform better than the usual rules. Fernández, M. A., C. Rueda and B. Salvador (2006): "Incorporating additional information to normal linear discriminant rules," J. Am. Stat. Assoc., 101, 569-577, proved that these rules have lower total misclassification probability than the usual Fisher's rule. In this paper we consider two issues; on the one hand, we compare these rules with those based on shrinkage estimators of the mean proposed by Tong, T., L. Chen and H. Zhao (2012): "Improved mean estimation and its application to diagonal discriminant analysis," Bioinformatics, 28(4): 531-537. with regard to four criteria: total misclassification probability, area under ROC curve, well-calibratedness and refinement; on the other hand, we consider the estimation of the true error rate, which is a very interesting parameter in applications. We prove results on the apparent error rate of the rules that expose the need of new estimators of their true error rate. We propose four such new estimators. Two of them are defined incorporating the additional information into the leave-one-out-bootstrap. The other two are the corresponding cross-validation after bootstrap versions. We compare these estimators with the usual ones in a simulation study and in a cancer trial application, showing the good behavior of the rules that incorporate additional information and of the new leave-one-out bootstrap estimators of their true error rate.

Application of Progressively Statistical Discriminant Models

Discriminant analysis is an important multivariate statistical analysis, and plays an important part in pattern classification, data mining, machine learning et al. In this paper, based on principle of progressively statistical discriminant analysis under Fisher rule, a progressively statistical discriminant model is set up. The authors analyzed the data about the occurrence of the second generation of the corn borer in 21 years from 1985 to 2006 (except 1990) at Linyi, Shandong Province, and then set up three graded recognition pattern. The results tested the pest data showed that the fitting rate is 95.24%, 92.31% and 100% respectively, and that accuracy of forecast is satisfactory.

Bayes Discriminant Rules with Ordered Predictors

We propose and discuss improved Bayes rules to discriminate between two populations using ordered predictors. To address the problem we propose an alternative formulation using a latent space that allows to introduce the information about the order in the theoretical rules. The rules are first defined when the marginal densities are fully known and then under normality when the parameters are unknown and training samples are available. Several numerical examples and simulations in the paper illustrate the methodology and show that the new rules handle the information appropriately. We compare the new rules with the classical Bayes and Fisher rules in these examples and we show that the misclassification probability is smaller for the new rules. The method is also applied to data from a diabetes study where we again show that the new rules improve over the usual Fisher rule.

Kernel-based Tracking Based on Adaptive Fusion of Multiple Cues

A scheme is proposed to integrate multiple cues with kernel tracking by adaptive fusion to improve the robustness of object tracking in the time-variant scenario.The tracked object is represented by a set of submodels of each cue,and then the multiple cues are combined by linear weighting to realize kernel-based tracking.According to the discriminability of each cue between target and background,measured by Fisher rule,an adaptive mechanism is presented to update the cue weight.Furthermore,a selective submodel update strategy is utilized to alleviate the model drift.In experiments,we employ color cue and local binary pattern(LBP)texture cue to implement the scheme,and the results demonstrate the effectiveness of the proposed method in several real sequences testing.

Regularization through variable selection and conditional MLE with application to classification in high dimensions

It is often the case that high-dimensional data consist of only a few informative components. Standard statistical modeling and estimation in such a situation is prone to inaccuracies due to overfitting, unless regularization methods are practiced. In the context of classification, we propose a class of regularization methods through shrinkage estimators. The shrinkage is based on variable selection coupled with conditional maximum likelihood. Using Stein's unbiased estimator of the risk, we derive an estimator for the optimal shrinkage method within a certain class. A comparison of the optimal shrinkage methods in a classification context, with the optimal shrinkage method when estimating a mean vector under a squared loss, is given. The latter problem is extensively studied, but it seems that the results of those studies are not completely relevant for classification. We demonstrate and examine our method on simulated data and compare it to feature annealed independence rule and Fisher's rule.

Robustness of classification rules that incorporate additional information

The discrimination problem for two normal populations with the same covariance matrix when additional information on the population is available is considered. A study of the robustness properties against training sample contamination of classification rules that incorporate this additional information is performed. These rules have received recently attention where their total misclassification probability (TMP) is proved to be lower than Fisher's linear discriminant rule. The results of a simulation study on the TMP which compares the behaviour of the new rules against Fisher's rule and some of its robustified versions under different types of contamination are presented. These results show that the rules that incorporate the additional information not only have lower TMP, but they also prevent against some types of contamination. In order to achieve prevention from all types of contamination a robustifed version of these rules is recommended.

Tissue-Specific Effects of the Nuclear Factor κB Subunit p50 on Myocardial Ischemia-Reperfusion Injury

Nuclear factor kappaB (NF-kappaB) is a ubiquitous transcription factor activated by various stimuli implicated in ischemia-reperfusion injury. However, the role of NF-kappaB in cardiac ischemia-reperfusion injury has not yet been well defined. Therefore, we investigated reperfusion damage in mice with targeted deletion of the NF-kappaB subunit p50. Electrophoretic mobility shift assays validated NF-kappaB activation in wild-type (WT) but not p50 knockout (KO) mice. KO and WT animals underwent 30 minutes of coronary artery ligation and 24 hours of reperfusion in vivo. Ischemia-reperfusion damage was significantly reduced in the p50 KO when compared with matching WT mice. Although adhesion molecules such as intercellular adhesion molecule were up-regulated in left ventricles of p50 KO animals, fewer neutrophils infiltrated the infarct area, suggesting leukocytes as a potential mediator of the protection observed in the p50 KO. This was confirmed in adoptive transfer experiments: whereas transplantation of KO bone marrow in KO animals sustained the protective effect on ischemia-reperfusion injury, transplantation of WT bone marrow in KO animals abolished it. Thus, deletion of the NF-kappaB subunit p50 reduces ischemia-reperfusion injury in vivo, associated with less neutrophil infiltration. Bone marrow transplantation experiments indicate that impaired NF-kappaB activation in p50 KO leukocytes attenuates cardiac damage.

Inflation Expectations in the Czech Interbank Market

Monthly data on the inflation expectations of financial analysts in the Czech Republic exhibit a tendency for permanent bias and ineffectiveness which violates the rational expectations hypothesis assumed in macroeconomic models. This paper asks whether the surveyed data include any monetary-policy relevant information, in other words, whether the surveyed expectations correspond to the true market expectations, and hence should be reflected in macro models of the Czech economy instead of the rational expectations hypothesis. Using a methodology based on a simple Fisher rule, it is found that the difference between the surveyed and market expectations is not statistically significant.

Stabilizing the rouble: Is there a case for a new Fisher rule?

The management of the exchange rate by the Russian authorities obviously lacks both effectiveness and efficiency. “Black Tuesday” has vividly shown how vulnerable the rouble is to speculative attacks. In this article, a “classical” proposal is evoked and is discussed as an alternative to the present exchange-rate policy from the sustainability point of view.

Application of pattern recognition to ethylene production optimization

In this paper, a pattern recognition method has been applied to solving the problem of the optimization of ethylene production process. The basic point of the presented method is that the technological parameters are used as feature variables to construct the pattern space, and all samples are divided into two classes according to the production target to be optimized. In order to find out the key factors influencing the target, the method of feature extraction is adopted to reduce the dimensionality of the pattern space of the technological parameters. By using the Fisher rule and the fractional correction rule, a recognition model has been found, which can distinguish the operating conditions of high-quality product from that of low-quality product. Based on the recognition model, some specific methods are suggested for optimal production.

Dividend Policy under Asymmetric Information

ABSTRACTWe extend the standard finance model of the firm's dividend/investment/financing decisions by allowing the firm's managers to know more than outside investors about the true state of the firm's current earnings. The extension endogenizes the dividend (and financing) announcement effects amply documented in recent research. But once trading of shares is admitted to the model along with asymmetric information, the familiar Fisherian criterion for optimal investment becomes time inconsistent: the market's belief that the firm is following the Fisher rule creates incentives to violate the rule.We show that an informationally consistent signalling equilibrium exists under asymmetric information and the trading of shares that restores the time consistency of investment policy, but leads in general to lower levels of investment than the optimum achievable under full information and/or no trading. Contractual provisions that change the information asymmetry or the possibility of profiting from it could eliminate both the time inconsistency and the inefficiency in investment policies, but these contractual provisions too are likely to involve dead‐weight costs. Establishing which route or combination of routes serves in practice to maintain consistency remains for future research.

Estimation and Verification of Hypotheses in Some Zyskind‐Martin Models with Missing Values

AbstractSeveral theorems on estimation and verification of linear hypotheses in some Zyskind‐Martin (ZM) models are given. The assumptions are as follows. Let y = Xβ + e or (y, Xβ, σ2V) be a fixed model where y is a vector of n observations, X is a known matrix nXp with rank r(X) = r ≦ p < n, where p is a number of coordinates of the unknown parameter vector β, e is a random vector of errors with covariance matrix σ2V, where σ2 is unknown scalar parameter, V is a known non‐negative definite matrix such that R(X) ⊂ R(V). Symbol R(A) denotes a vector space generated by columns of matrix A. The expected value of y is Xβ. In this paper four following Zyskind‐Martin (ZM) models are considered: ZMd, ZMa, ZMc and ZMqd (definitions in sec. 1) when vector y y1 y2 involves a vector y1 of m missing values and a vector y2 with (n — m) observed values.A special transformation of ZM model gives again ZM model (cf. theorem 2.1). Ten properties of actual (ZMa) and complete (ZMc) Zyskind‐Martin models with missing values (cf. theorem 2.2) test functions F are given in (2.11)) are presented.The third propriety constitutes a generalization of R. A. Fisher's rule from standard model (y, Xβ, σ2I) to ZM model.Estimation of vector y1 (cf. 3.3) of vector β (cf. th. 3.2) and of scalar σ2 (cf. th. 3.4) in actual ZMa model and in diagonal quasi‐ZM model (ZMqd) are presented. Relation between y̌ 1 and β is given in theorem 3.1. The results of section 2 are illustrated by numerical example in section 4.

The Red Queen

Editor. —I do not know type of playing cards used in Chicago or which edition of Alice in Wonderland Dr Caplan (Archives1982;39:389-390) reads, but in Bronx suits are spades, hearts, diamonds, and clubs, and Lewis Carroll referred to of Hearts, not of Chess. Fisher's Rule No. 6 is, Describe quantitatively and precisely. Rule No. 7 is, the details of case are important; their analysis distinguishes expert from journey-man. Rule No. 18 should be, To publish is to risk being shot at in streets. Curiouser and curiouser! Like most things in life there is a little right and a little wrong, as both Dr Caplan's quote and Dr Scheinberg's rejoinder illustrate. The statement was made by Red Queen (of chess) but appeared in Through Looking Glass, not in Alice's Adventures in Wonderland. I do

Missing data in linear models with correlated errors

One common method for analyzing data in experimental designs when observations are missing was devised by Yates (1933), who developed his procedure based upon a suggestion by R. A. Fisher. Considering a linear model with independent, equi-variate errors, Yates substituted algebraic values for the missing data and then minimized the error sum of squares with respect to both the unknown parameters and the algebraic values. Yates showed that this procedure yielded the correct error sum of squares and a positively biased hypothesis sum of squares. Others have elaborated on this technique. Chakrabarti (1962) gave a formal proof of Fisher's rule that produced a way to simplify the calculations of the auxiliary values to be used in place of the missing observations. Kshirsagar (1971) proved that the hypothesis sum of squares based on these values was biased, and developed an easy way to compute that bias. Sclove

Beverton-Holt Model of a Commercial Fishery: Optimal Dynamics

The problem of optimal regulation of a fishery is discussed. Of special interest is the problem of regulating an overexploited fishery by reducing effort to allow the fish population to build up to a suitable level.We first argue that the problem requires an economic analysis based on the concept of maximization of present value. From this concept we then deduce a simple, general rule, the "Fisher Rule," which we subsequently use to determine optimal exploitation. Among the principal results are the following: (a) an optimal mesh-size is determined, which, because of the discounting of future revenues, is smaller than the size corresponding to maximum sustainable yield; (b) the optimal recovery policy for an overexploited fishery is deduced; it consists of a fishing closure permitting the fish population to reach an optimal age; (c) the optimal development of an unexploited fishery is deduced; an initial development stage characterized by large landings and profits is rapidly transformed into a situation of optimal sustained yield, in which both landings and profits may be significantly reduced; (d) the optimal policy is deduced for a fishery in which gear limitations are impractical; the result may be a strongly unstable fishing industry; (e) the effect of high discount rates, which might be employed by private fishing interests, is discussed; such rates may result in overfishing similar to the case of a common-property fishery.