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Critical Care (London, England) Feb 2002The present review is the first in an ongoing guide to medical statistics, using specific examples from intensive care. The first step in any analysis is to describe and... (Comparative Study)
Comparative Study Review
The present review is the first in an ongoing guide to medical statistics, using specific examples from intensive care. The first step in any analysis is to describe and summarize the data. As well as becoming familiar with the data, this is also an opportunity to look for unusually high or low values (outliers), to check the assumptions required for statistical tests, and to decide the best way to categorize the data if this is necessary. In addition to tables and graphs, summary values are a convenient way to summarize large amounts of information. This review introduces some of these measures. It describes and gives examples of qualitative data (unordered and ordered) and quantitative data (discrete and continuous); how these types of data can be represented figuratively; the two important features of a quantitative dataset (location and variability); the measures of location (mean, median and mode); the measures of variability (range, interquartile range, standard deviation and variance); common distributions of clinical data; and simple transformations of positively skewed data.
Topics: Analysis of Variance; Critical Care; Hemoglobins; Humans; Hydrogen-Ion Concentration; Intensive Care Units; Models, Statistical; Statistical Distributions; Statistics as Topic; Urea
PubMed: 11940268
DOI: 10.1186/cc1455 -
ENeuro Jan 2023A central question in neuroscience is how sensory inputs are transformed into percepts. At this point, it is clear that this process is strongly influenced by prior... (Review)
Review
A central question in neuroscience is how sensory inputs are transformed into percepts. At this point, it is clear that this process is strongly influenced by prior knowledge of the sensory environment. Bayesian ideal observer models provide a useful link between data and theory that can help researchers evaluate how prior knowledge is represented and integrated with incoming sensory information. However, the statistical prior employed by a Bayesian observer cannot be measured directly, and must instead be inferred from behavioral measurements. Here, we review the general problem of inferring priors from psychophysical data, and the simple solution that follows from assuming a prior that is a Gaussian probability distribution. As our understanding of sensory processing advances, however, there is an increasing need for methods to flexibly recover the shape of Bayesian priors that are not well approximated by elementary functions. To address this issue, we describe a novel approach that applies to arbitrary prior shapes, which we parameterize using mixtures of Gaussian distributions. After incorporating a simple approximation, this method produces an analytical solution for psychophysical quantities that can be numerically optimized to recover the shapes of Bayesian priors. This approach offers advantages in flexibility, while still providing an analytical framework for many scenarios. We provide a MATLAB toolbox implementing key computations described herein.
Topics: Bayes Theorem; Probability; Sensation; Normal Distribution
PubMed: 36316119
DOI: 10.1523/ENEURO.0144-22.2022 -
Journal of Healthcare Engineering 2022At present, the incidence of emergencies in obstetric care environment is gradually increasing, and different obstetric wards often have a variety of situations....
At present, the incidence of emergencies in obstetric care environment is gradually increasing, and different obstetric wards often have a variety of situations. Therefore, it can provide great help in clinical medicine to give early warning and plan coping plans according to different situations. This paper studied an obstetrics central surveillance system based on a medical image segmentation algorithm. Images obtained by central obstetrics monitoring are segmented, magnified in detail, and image features are extracted, collated, and trained. The normal distribution rule is used to classify the features, which are included in the feature library of the obstetric central monitoring system. In the gray space of the medical image, the statistical distribution of gray features of the medical image is described by the mixture model of Rayleigh distribution and Gaussian distribution. In the gray space of the medical image, Taylor series expansion is used to describe the linear geometric structure of medicine. The eigenvalues of Hessian matrix are introduced to obtain high-order multiscale features of medicine. The multiscale feature energy function is introduced into Markov random energy objective function to realize medical image segmentation. Compared with other segmentation algorithms, the accuracy and sensitivity of the proposed algorithm are 87.98% and 86.58%, respectively, which can clearly segment small medical features.
Topics: Algorithms; Humans; Image Processing, Computer-Assisted; Normal Distribution
PubMed: 35529540
DOI: 10.1155/2022/3545831 -
Journal of the Experimental Analysis of... Jul 2002Ideal free distribution theory predicts that foragers will form groups proportional in number to the resources available in alternative resource sites or patches, a...
Ideal free distribution theory predicts that foragers will form groups proportional in number to the resources available in alternative resource sites or patches, a phenomenon termed habitat matching. Three experiments tested this prediction with college students in discrete-trial simulations and a free-operant simulation. Sensitivity to differences in programmed reinforcement rates was quantified by using the sensitivity parameter of the generalized matching law (s). The first experiment, replicating prior published experiments, produced a greater degree of undermatching for the initial choice (s = 0.59) compared to final choices (s = 0.86). The second experiment, which extended prior findings by allowing only one choice per trial, produced comparable undermatching (s = 0.82). The third experiment used free-operant procedures more typical of laboratory studies of habitat matching with other species and produced the most undermatching (s = 0.71). The results of these experiments replicated previous results with human groups, supported predictions of the ideal free distribution, and suggested that undermatching represents a systematic deviation from the ideal free distribution. These results are consistent with a melioration account of individual behavior as the basis for group choice.
Topics: Adolescent; Adult; Choice Behavior; Competitive Behavior; Female; Group Processes; Humans; Male; Motivation; Reinforcement Schedule; Statistical Distributions; Students
PubMed: 12144309
DOI: 10.1901/jeab.2002.78-1 -
PloS One 2023In this study, we propose a generalized Marshall-Olkin exponentiated exponential distribution as a submodel of the family of generalized Marshall-Olkin distribution....
In this study, we propose a generalized Marshall-Olkin exponentiated exponential distribution as a submodel of the family of generalized Marshall-Olkin distribution. Some statistical properties of the proposed distribution are examined such as moments, the moment-generating function, incomplete moment, and Lorenz and Bonferroni curves. We give five estimators for the unknown parameters of the proposed distribution based on maximum likelihood, least squares, weighted least squares, and the Anderson-Darling and Cramer-von Mises methods of estimation. To investigate the finite sample properties of the estimators, a comprehensive Monte Carlo simulation study is conducted for the models with three sets of randomly selected parameter values. Finally, four different real data applications are presented to demonstrate the usefulness of the proposed distribution in real life.
Topics: Computer Simulation; Statistical Distributions; Monte Carlo Method; Least-Squares Analysis
PubMed: 36652462
DOI: 10.1371/journal.pone.0280349 -
Cerebral Cortex (New York, N.Y. : 1991) Aug 2023Numbers of neurons and their spatial variation are fundamental organizational features of the brain. Despite the large corpus of cytoarchitectonic data available in the...
Numbers of neurons and their spatial variation are fundamental organizational features of the brain. Despite the large corpus of cytoarchitectonic data available in the literature, the statistical distributions of neuron densities within and across brain areas remain largely uncharacterized. Here, we show that neuron densities are compatible with a lognormal distribution across cortical areas in several mammalian species, and find that this also holds true within cortical areas. A minimal model of noisy cell division, in combination with distributed proliferation times, can account for the coexistence of lognormal distributions within and across cortical areas. Our findings uncover a new organizational principle of cortical cytoarchitecture: the ubiquitous lognormal distribution of neuron densities, which adds to a long list of lognormal variables in the brain.
Topics: Animals; Neurons; Brain; Mammals; Cerebral Cortex; Statistical Distributions
PubMed: 37409647
DOI: 10.1093/cercor/bhad160 -
Biochemia Medica 2015Computer-intensive resampling/bootstrap methods are feasible when calculating reference intervals from non-Gaussian or small reference samples. Microsoft Excel® in... (Review)
Review
Computer-intensive resampling/bootstrap methods are feasible when calculating reference intervals from non-Gaussian or small reference samples. Microsoft Excel® in version 2010 or later includes natural functions, which lend themselves well to this purpose including recommended interpolation procedures for estimating 2.5 and 97.5 percentiles. The purpose of this paper is to introduce the reader to resampling estimation techniques in general and in using Microsoft Excel® 2010 for the purpose of estimating reference intervals in particular. Parametric methods are preferable to resampling methods when the distributions of observations in the reference samples is Gaussian or can transformed to that distribution even when the number of reference samples is less than 120. Resampling methods are appropriate when the distribution of data from the reference samples is non-Gaussian and in case the number of reference individuals and corresponding samples are in the order of 40. At least 500-1000 random samples with replacement should be taken from the results of measurement of the reference samples.
Topics: Humans; Models, Statistical; Normal Distribution; Reference Values; Software
PubMed: 26527366
DOI: 10.11613/BM.2015.031 -
Topics in Cognitive Science Jan 2013Most empirical work in human categorization has studied learning in either fully supervised or fully unsupervised scenarios. Most real-world learning scenarios, however,... (Review)
Review
Most empirical work in human categorization has studied learning in either fully supervised or fully unsupervised scenarios. Most real-world learning scenarios, however, are semi-supervised: Learners receive a great deal of unlabeled information from the world, coupled with occasional experiences in which items are directly labeled by a knowledgeable source. A large body of work in machine learning has investigated how learning can exploit both labeled and unlabeled data provided to a learner. Using equivalences between models found in human categorization and machine learning research, we explain how these semi-supervised techniques can be applied to human learning. A series of experiments are described which show that semi-supervised learning models prove useful for explaining human behavior when exposed to both labeled and unlabeled data. We then discuss some machine learning models that do not have familiar human categorization counterparts. Finally, we discuss some challenges yet to be addressed in the use of semi-supervised models for modeling human categorization.
Topics: Artificial Intelligence; Classification; Concept Formation; Decision Making; Empirical Research; Humans; Knowledge of Results, Psychological; Learning; Models, Psychological; Models, Statistical; Probability; Statistical Distributions
PubMed: 23335577
DOI: 10.1111/tops.12010 -
BMC Medical Research Methodology Dec 2017The statistical analysis of health care cost data is often problematic because these data are usually non-negative, right-skewed and have excess zeros for non-users....
BACKGROUND
The statistical analysis of health care cost data is often problematic because these data are usually non-negative, right-skewed and have excess zeros for non-users. This prevents the use of linear models based on the Gaussian or Gamma distribution. A common way to counter this is the use of Two-part or Tobit models, which makes interpretation of the results more difficult. In this study, I explore a statistical distribution from the Tweedie family of distributions that can simultaneously model the probability of zero outcome, i.e. of being a non-user of health care utilization and continuous costs for users.
METHODS
I assess the usefulness of the Tweedie model in a Monte Carlo simulation study that addresses two common situations of low and high correlation of the users and the non-users of health care utilization. Furthermore, I compare the Tweedie model with several other models using a real data set from the RAND health insurance experiment.
RESULTS
I show that the Tweedie distribution fits cost data very well and provides better fit, especially when the number of non-users is low and the correlation between users and non-users is high.
CONCLUSION
The Tweedie distribution provides an interesting solution to many statistical problems in health economic analyses.
Topics: Algorithms; Computer Simulation; Health Care Costs; Health Services Research; Humans; Models, Economic; Monte Carlo Method; Patient Acceptance of Health Care; Statistical Distributions
PubMed: 29258428
DOI: 10.1186/s12874-017-0445-y -
PloS One 2022Contagious statistical distributions are a valuable resource for managing contagion by means of k-connected chains of distributions. Binomial, hypergeometric, Pólya,...
Contagious statistical distributions are a valuable resource for managing contagion by means of k-connected chains of distributions. Binomial, hypergeometric, Pólya, uniform distributions with the same values for all parameters except sample size n are known to be strongly associated. This paper describes how the relationship can be obtained via factorial moments, simplifying the process by including novel elements. We describe the properties of these distributions and provide examples of their real-world application, and then define a chain of k-connected distributions, which generalises the relationship among samples of any size for a given population and the Pólya urn model.
Topics: Communicable Diseases; Humans; Poly A; Sample Size; Statistical Distributions
PubMed: 35622844
DOI: 10.1371/journal.pone.0268810