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Forensic Science International Apr 2019In the evaluation of measurements on characteristics of forensic trace evidence, Aitken and Lucy (2004) model the data as a two-level model using assumptions of... (Review)
Review
In the evaluation of measurements on characteristics of forensic trace evidence, Aitken and Lucy (2004) model the data as a two-level model using assumptions of normality where likelihood ratios are used as a measure for the strength of evidence. A two-level model assumes two sources of variation: the variation within measurements in a group (first level) and the variation between different groups (second level). Estimates of the variation within groups, the variation between groups and the overall mean are required in this approach. This paper discusses three estimators for the overall mean. In forensic science, two of these estimators are known as the weighted and unweighted mean. For an optimal choice between these estimators, the within- and between-group covariance matrices are required. In this paper a generalization to the latter two mean estimators is suggested, which is referred to as the generalized weighted mean. The weights of this estimator can be chosen such that they minimize the variance of the generalized weighted mean. These optimal weights lead to a "toy estimator", because they depend on the unknown within- and between-group covariance matrices. Using these optimal weights with estimates for the within- and between-group covariance matrices leads to the third estimator, the optimal "plug-in" generalized weighted mean estimator. The three estimators and the toy estimator are compared through a simulation study. Under conditions generally encountered in practice, we show that the unweighted mean can be preferred over the weighted mean. Moreover, in these situations the unweighted mean and the optimal generalized weighted mean behave similarly. An artificial choice of parameters is used to provide an example where the optimal generalized weighted mean outperforms both the weighted and unweighted mean. Finally, the three mean estimators are applied to real XTC data to illustrate the impact of the choice of overall mean estimator.
PubMed: 30903935
DOI: 10.1016/j.forsciint.2019.01.047 -
Critical Care Medicine Nov 1992To discuss the theoretical relationship of mean alveolar pressure to its most easily measured analog, mean airway pressure, and to describe the key determinants,... (Review)
Review
PURPOSES
To discuss the theoretical relationship of mean alveolar pressure to its most easily measured analog, mean airway pressure, and to describe the key determinants, measurement considerations, and clinical implications of this index.
DATA SOURCES
Relevant articles from the medical and physiological literature, as well as mathematical arguments developed in this article from first principles.
STUDY SELECTION
Theoretical, experimental, and clinical information that elucidates the physiologic importance, measurement, or adverse consequences of mean airway pressure.
DATA EXTRACTION
Mathematical models were used in conjunction with data from the published literature to develop a unified description of the physiological and clinical relevance of mean airway pressure.
SYNTHESIS
Geometrical and mathematical analyses demonstrate that shared elements comprise mean airway pressure and mean alveolar pressure, two variables that are related by the formula: mean alveolar pressure = mean airway pressure + (VE/60) x (RE - RI), where VE, RE, and RI are minute ventilation and expiratory and inspiratory resistances, respectively. Clear guidelines can be developed for selecting the site of mean airway pressure determination, for specifying technical requirements for mean airway pressure measurement, and for delineating clinical options to adjust the level of mean airway pressure. Problems in viewing mean airway pressure as a reflection of mean alveolar pressure can be interpreted against the theoretical basis of their interrelationship. In certain settings, mean airway pressure closely relates to levels of ventilation, arterial oxygenation, cardiovascular function, and barotrauma. Because mean airway pressure is associated with both beneficial and adverse actions, a thorough understanding of its theoretical and practical basis is integral to formulating an effective pressure-targeted strategy of ventilatory support.
CONCLUSIONS
Mean airway pressure closely reflects mean alveolar pressure, except when flow-resistive pressure losses differ greatly for the inspiratory and expiratory phases of the ventilatory cycle. Under conditions of passive inflation, mean airway pressure correlates with alveolar ventilation, arterial oxygenation, hemodynamic performance, and barotrauma. We encourage wider use of this index, appropriately measured and interpreted, as well as its incorporation into rational strategies for the ventilatory management of critical illness.
Topics: Adolescent; Airway Resistance; Hemodynamics; Humans; Lung Compliance; Manometry; Positive-Pressure Respiration; Pressure; Pulmonary Alveoli; Pulmonary Gas Exchange; Reproducibility of Results; Respiration, Artificial; Respiratory Function Tests; Time Factors; Work of Breathing
PubMed: 1424706
DOI: No ID Found -
Clinical Pharmacokinetics Nov 1989A mean time parameter in pharmacokinetics defines the average time taken for 1 or more kinetic events to occur. Due to the complexity of the subject, a great number of... (Review)
Review
A mean time parameter in pharmacokinetics defines the average time taken for 1 or more kinetic events to occur. Due to the complexity of the subject, a great number of different mean time parameters may be defined. Three of these parameters which appear to be of greatest interest are discussed: mean residence time (MRT), mean transit time (MTT) and mean arrival time (MAT). Formal definitions for these parameters are presented and various methods of evaluating them are described. The concepts of kinetic spaces, of importance in dealing with mean time parameters, are broadly defined. The discussion of the theory behind mean time parameters begins generally with fundamental core relationships, valid for both stochastic and non-stochastic systems, and successively introduces increasing degrees of kinetic specificity, ending with a discussion of mean time parameters of specific pharmacokinetic models. The limitations and assumptions involved in the use of mean time parameters in the various models are highlighted, with examples to clarify the concepts discussed. Area under the moment curve/area under the concentration-time curve (AUMC/AUC), commonly used as a definition for the MRT of drug molecules in the body, should not serve as a definition but should instead be considered as a method of evaluating this parameter. The literature on mean time parameters as they relate to absorption, distribution, elimination, metabolites, dosing times and drug accumulation is discussed. The clinical implications of mean time parameters are also considered, particularly in relation to the prediction, evaluation and interpretation of pharmacokinetic data.
Topics: Humans; Mathematical Computing; Models, Biological; Pharmaceutical Preparations; Pharmacokinetics; Stochastic Processes; Time Factors
PubMed: 2684472
DOI: 10.2165/00003088-198917050-00004 -
Entropy (Basel, Switzerland) May 2021In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or...
In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov-Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.
PubMed: 34070385
DOI: 10.3390/e23060662 -
The American Naturalist Aug 2019The mean age at which parents give birth is an important notion in demography, ecology, and evolution, where it is used as a measure of generation time. A standard way...
The mean age at which parents give birth is an important notion in demography, ecology, and evolution, where it is used as a measure of generation time. A standard way to quantify it is to compute the mean age of the parents of all offspring produced by a cohort, and the resulting measure is thought to represent the mean age at which a typical parent produces offspring. In this note, I explain why this interpretation is problematic. I also introduce a new measure of the mean age at reproduction and show that it can be very different from the mean age of parents of offspring of a cohort. In particular, the mean age of parents of offspring of a cohort systematically overestimates the mean age at reproduction and can even be greater than the expected life span of parents.
Topics: Animals; Female; Male; Maternal Age; Models, Statistical; Paternal Age; Plants; Reproduction
PubMed: 31318291
DOI: 10.1086/704110 -
Frontiers in Psychology 2021Individuals can perceive the mean emotion or mean identity of a group of faces. It has been considered that individual representations are discarded when extracting a...
Individuals can perceive the mean emotion or mean identity of a group of faces. It has been considered that individual representations are discarded when extracting a mean representation; for example, the "element-independent assumption" asserts that the extraction of a mean representation does not depend on recognizing or remembering individual items. The "element-dependent assumption" proposes that the extraction of a mean representation is closely connected to the processing of individual items. The processing mechanism of mean representations and individual representations remains unclear. The present study used a classic member-identification paradigm and manipulated the exposure time and set size to investigate the effect of attentional resources allocated to individual faces on the processing of both the mean emotion representation and individual representations in a set and the relationship between the two types of representations. The results showed that while the precision of individual representations was affected by attentional resources, the precision of the mean emotion representation did not change with it. Our results indicate that two different pathways may exist for extracting a mean emotion representation and individual representations and that the extraction of a mean emotion representation may have higher priority. Moreover, we found that individual faces in a group could be processed to a certain extent even under extremely short exposure time and that the precision of individual representations was relatively poor but individual representations were not discarded.
PubMed: 34671297
DOI: 10.3389/fpsyg.2021.713212 -
IEEE Transactions on Systems, Man, and... 1996We introduce and define the concept of mean aggregation of a collection of n numbers. We point out that the lack of associativity of this operation compounds the problem...
We introduce and define the concept of mean aggregation of a collection of n numbers. We point out that the lack of associativity of this operation compounds the problem of the extending mean of n numbers to n+1 numbers. The closely related concepts of self identity and the centering property are introduced as one imperative for extending mean aggregation operators. The problem of weighted mean aggregation is studied. A new concept of prioritized mean aggregation is then introduced. We next show that the technique of selecting an element based upon the performance of a random experiment can be considered as a mean aggregation operation.
PubMed: 18263024
DOI: 10.1109/3477.485833 -
Turkish Journal of Emergency Medicine Mar 2015Acute appendicitis (AA) is the most common indication for emergency abdominal surgery, although it remains difficult to diagnose. In this study, we investigated the the...
OBJECTIVES
Acute appendicitis (AA) is the most common indication for emergency abdominal surgery, although it remains difficult to diagnose. In this study, we investigated the the clinical utility of mean platelet volume in the diagnosis of acute appendicitis.
METHODS
The medical records of 241 patients who had undergone appendectomy between June 2013 and March 2014 were investigated retrospectively. Sixty patients who had undergone at least one complete blood count during preoperative hospital admission and who had no other active inflammatory conditions at the time the sample was taken were included in the study. Mean platelet volume and leukocyte count values were determined in each patient at hospital admission and during active acute appendicitis. Age, sex, mean platelet volume and leukocyte counts were recorded for each patient.
RESULTS
The mean age of patients was 33.15±10.94 years and the male to female ratio was 1.5:1. The mean leukocyte count prior to acute appendicitis was 7.42±2.12×10(3)/mm(3). Mean leukocyte count was significantly higher (13.14±2.99×10(3)/mm(3)) in acute appendicitis. The optimal leukocyte count cutoff point for the diagnosis of acute appendicitis was 10.10×10(3)/mm(3), with sensitivity of 94% and a specificity of 75%. The mean platelet volume prior to acute appendicitis was 7.58±1.11 fL. Mean platelet volume was significantly lower (7.03±0.8 fL) in acute appendicitis. The optimal mean platelet volume cutoff point for the diagnosis of AA was 6.10 fL, with a sensitivity of 83% and a specificity of 42%. Area under the curve for leukocyte count diagnosis was 0.67 and 0.69 for the diagnosis of AA by mean platelet volume.
CONCLUSIONS
Mean platelet volume was significantly decreased in acute appendicitis. Mean platelet volume can be used as a supportive diagnostic parameter in the diagnosis of acute appendicitis.
PubMed: 27331191
DOI: 10.5505/1304.7361.2015.32657 -
Critical Care Medicine Oct 1992To discuss the theoretical relationship of mean alveolar pressure to its most easily measured analog, the mean airway pressure, and to describe the key determinants,...
PURPOSES
To discuss the theoretical relationship of mean alveolar pressure to its most easily measured analog, the mean airway pressure, and to describe the key determinants, measurement considerations, and clinical implications of this index.
DATA SOURCES
Relevant articles from the medical and physiologic literature, as well as mathematical arguments developed in this article from first principles.
STUDY SELECTION
Theoretical, experimental, and clinical information that elucidates the physiologic importance, measurement, or adverse consequences of mean airway pressure.
DATA EXTRACTION
Mathematical models were used in conjunction with data from the published literature to develop a unified description of the physiological and clinical relevance of mean airway pressure.
SYNTHESIS
Geometrical and mathematical analyses demonstrate that shared elements comprise mean airway pressure and mean alveolar pressure, two variables that are related by the formula: mean alveolar pressure = mean airway pressure + (VE/60) x (RE-RI), where VE, RE, and RI are minute ventilation and expiratory and inspiratory resistances, respectively. Clear guidelines can be developed for selecting the site of mean airway pressure determination, for specifying technical requirements for mean airway pressure measurement, and for delineating clinical options to adjust the level of mean airway pressure. Problems in viewing mean airway pressure as a reflection of mean alveolar pressure can be interpreted against the theoretical basis of their interrelationship. In certain settings, mean airway pressure closely relates to levels of ventilation, arterial oxygenation, cardiovascular function, and barotrauma. Because mean airway pressure is associated with both beneficial and adverse effects, a thorough understanding of its theoretical and practical basis is integral to formulating an effective pressure-targeted strategy of ventilatory support.
CONCLUSIONS
Mean airway pressure closely reflects mean alveolar pressure, except when flow-resistive pressure losses differ greatly for the inspiratory and expiratory phases of the ventilatory cycle. Under conditions of passive inflation, mean airway pressure correlates with alveolar ventilation, arterial oxygenation, hemodynamic performance, and barotrauma. We encourage wider use of this index, appropriately measured and interpreted, as well as its incorporation into rational strategies for the ventilatory management of critical illness.
Topics: Airway Resistance; Evaluation Studies as Topic; Humans; Lung Compliance; Manometry; Mathematics; Models, Statistical; Positive-Pressure Respiration; Pulmonary Alveoli; Reproducibility of Results; Respiration; Respiratory Function Tests; Thermodynamics; Tidal Volume; Time Factors
PubMed: 1395670
DOI: No ID Found -
Vision Research Feb 2020When there are many visual items, the visual system could represent their summary statistics (e.g., mean, variance) to process them efficiently. Although many previous...
When there are many visual items, the visual system could represent their summary statistics (e.g., mean, variance) to process them efficiently. Although many previous studies have investigated the mean or variance representation itself, a relationship between these two ensemble representations has not been investigated much. In this study, we tested the potential interaction between mean and variance representations by using a visual adaptation method. We reasoned that if mean and variance representations interact with each other, an adaptation aftereffect to either mean or variance would influence the perception of the other. Participants watched a sequence of orientation arrays containing a specific statistical property during the adaptation period. To produce an adaptation aftereffect specific to variance or mean, one property of the adaptor arrays (variance or mean) had a fixed value while the other property was randomly varied. After the adaptation, participants were asked to discriminate the property of the test array that was randomly varied during the adaptation. We found that the adaptation aftereffect of orientation variance influenced the sensitivity of mean orientation discrimination (Experiment 1), and that the adaptation aftereffect of mean orientation influenced the bias of orientation variance discrimination (Experiment 2). These results suggest that mean and variance representations do closely interact with each other. Considering that mean and variance reflect the representative value and dispersion of multiple items respectively, the interactions between mean and variance representations may reflect their complementary roles to summarize complex visual information effectively.
Topics: Adaptation, Ocular; Female; Figural Aftereffect; Humans; Male; Orientation, Spatial; Psychophysics; Visual Perception
PubMed: 31954877
DOI: 10.1016/j.visres.2020.01.002