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"Galton's Statistical Methods" is an article from Publications of the American Statistical Association, Volume 1 . View more articles from Publications of the American Statistical Association . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2276500

"Galton's Statistical Methods" is an article from Publications of the American Statistical Association, Volume 1 . View more articles from Publications of the American Statistical Association . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2276500

"Galton's Statistical Methods" is an article from Publications of the American Statistical Association, Volume 1 . View more articles from Publications of the American Statistical Association . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2276500

"Galton's Statistical Methods" is an article from Publications of the American Statistical Association, Volume 1 . View more articles from Publications of the American Statistical Association . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2276500

"Galton's Statistical Methods" is an article from Publications of the American Statistical Association, Volume 1 . View more articles from Publications of the American Statistical Association . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2276500

"Galton's Statistical Methods" is an article from Publications of the American Statistical Association, Volume 1 . View more articles from Publications of the American Statistical Association . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2276500

"Galton's Statistical Methods" is an article from Publications of the American Statistical Association, Volume 1 . View more articles from Publications of the American Statistical Association . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2276500

"Galton's Statistical Methods" is an article from Publications of the American Statistical Association, Volume 1 . View more articles from Publications of the American Statistical Association . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2276500

"Galton's Statistical Methods" is an article from Publications of the American Statistical Association, Volume 1 . View more articles from Publications of the American Statistical Association . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2276500

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic purpose of the paper is the consideration of adaptive model selection for determining regularization parameters. This article introduces a new regularized estimator which has the best possible adaptive properties for a wide range of linear functionals. We derive non asymptotic upper bounds for the mean square error of the estimator and give the optimal convergence rates.

This volume was digitized and made accessible online due to deterioration of the original print copy.

The estimation of cosmological parameters from precision observables is an important industry with crucial ramifications for particle physics. This article discusses the statistical methods presently used in cosmological data analysis, highlighting the main assumptions and uncertainties. The topics covered are parameter estimation, model selection, multi-model inference, and experimental design, all primarily from a Bayesian perspective.

For there to be a successful measurement of the 21 cm Epoch of Reionization (EoR) power spectrum, it is crucial that strong foreground contaminants be robustly suppressed. These foregrounds come from a variety of sources (such as Galactic synchrotron emission and extragalactic point sources), but almost all share the property of being spectrally smooth, and when viewed through the chromatic response of an interferometer, occupy a signature "wedge" region in cylindrical $k_\perp k_\parallel$ Fourier space. The complement of the foreground wedge is termed the "EoR window", and is expected to be mostly foreground-free, allowing clean measurements of the power spectrum. This paper is a sequel to a previous paper that established a rigorous mathematical framework for describing the foreground wedge and the EoR window. Here, we use our framework to explore statistical methods by which the EoR window can be enlarged, thereby increasing the sensitivity of a power spectrum measurement. We adapt the FKP approximation (commonly used in galaxy surveys) for 21 cm cosmology, and also compare the optimal quadratic estimator to simpler estimators that ignore covariances between different Fourier modes. The optimal quadratic estimator is found to suppress foregrounds by an extra factor of $\sim 10^5$ in power at the peripheries of the EoR window, boosting the detection of the cosmological signal from $12\sigma$ to $50\sigma$ at the midpoint of reionization in our fiducial models. If numerical issues can be finessed, decorrelation techniques allow the EoR window to be further enlarged, enabling measurements to be made deep within the foreground wedge. These techniques do not assume that foreground are Gaussian-distributed, and we additionally prove that a final round of foreground subtraction can be performed after decorrelation in a way that is guaranteed to have no cosmological signal loss.

In quantum physics, all measured observables are subject to statistical uncertainties, which arise from the quantum nature as well as the experimental technique. We consider the statistical uncertainty of the so-called sampling method, in which one estimates the expectation value of a given observable by empirical means of suitable pattern functions. We show that if the observable can be written as a function of a single directly measurable operator, the variance of the estimate from the sampling method equals to the quantum mechanical one. In this sense, we say that the estimate is on the quantum mechanical level of uncertainty. In contrast, if the observable depends on non-commuting operators, e.g. different quadratures, the quantum mechanical level of uncertainty is not achieved. The impact of the results on quantum tomography is discussed, and different approaches to quantum tomographic measurements are compared. It is shown explicitly for the estimation of quasiprobabilities of a quantum state, that balanced homodyne tomography does not operate on the quantum mechanical level of uncertainty, while the unbalanced homodyne detection does.

In quantum physics, all measured observables are subject to statistical uncertainties, which arise from the quantum nature as well as the experimental technique. We consider the statistical uncertainty of the so-called sampling method, in which one estimates the expectation value of a given observable by empirical means of suitable pattern functions. We show that if the observable can be written as a function of a single directly measurable operator, the variance of the estimate from the sampling method equals to the quantum mechanical one. In this sense, we say that the estimate is on the quantum mechanical level of uncertainty. In contrast, if the observable depends on non-commuting operators, e.g. different quadratures, the quantum mechanical level of uncertainty is not achieved. The impact of the results on quantum tomography is discussed, and different approaches to quantum tomographic measurements are compared. It is shown explicitly for the estimation of quasiprobabilities of a quantum state, that balanced homodyne tomography does not operate on the quantum mechanical level of uncertainty, while the unbalanced homodyne detection does.

In quantum physics, all measured observables are subject to statistical uncertainties, which arise from the quantum nature as well as the experimental technique. We consider the statistical uncertainty of the so-called sampling method, in which one estimates the expectation value of a given observable by empirical means of suitable pattern functions. We show that if the observable can be written as a function of a single directly measurable operator, the variance of the estimate from the sampling method equals to the quantum mechanical one. In this sense, we say that the estimate is on the quantum mechanical level of uncertainty. In contrast, if the observable depends on non-commuting operators, e.g. different quadratures, the quantum mechanical level of uncertainty is not achieved. The impact of the results on quantum tomography is discussed, and different approaches to quantum tomographic measurements are compared. It is shown explicitly for the estimation of quasiprobabilities of a quantum state, that balanced homodyne tomography does not operate on the quantum mechanical level of uncertainty, while the unbalanced homodyne detection does.

Bibliography: 572

Bibliography: 572

xxi, 482 p. 20 cm

xxi, 482 p. 20 cm

xxi, 482 p. 20 cm

xxi, 482 p. 20 cm

xxi, 482 p. 20 cm

xxi, 482 p. 20 cm

"Sources used for data and methods": p. 341-344; Bibliography: p. 345-352

Biological terrorism is a threat to the security and well-being of the United States. It is critical to detect the presence of these attacks in a timely manner, in order to provide sufficient and effective responses to minimize or contain the damage inflicted. Syndromic surveillance is the process of monitoring public health-related data and applying statistical tests to determine the potential presence of a disease outbreak in the observed system. Our research involved a comparative analysis of two multivariate statistical methods, the multivariate CUSUM (MCUSUM) and the multivariate exponentially weighted moving average (MEWMA), both modified to look only for increases in disease incidence. While neither of these methods is currently in use in a biosurveillance system, they are among the most promising multivariate methods for this application. Our analysis was based on a series of simulations using synthetic syndromic surveillance data that mimics various types of background disease incidence and outbreaks. We found that, similar to results for the univariate CUSUM and EWMA, the directionally-sensitive MCUSUM and MEWMA perform very similarly.

Biological terrorism is a threat to the security and well-being of the United States. It is critical to detect the presence of these attacks in a timely manner, in order to provide sufficient and effective responses to minimize or contain the damage inflicted. Syndromic surveillance is the process of monitoring public health-related data and applying statistical tests to determine the potential presence of a disease outbreak in the observed system. Our research involved a comparative analysis of two multivariate statistical methods, the multivariate CUSUM (MCUSUM) and the multivariate exponentially weighted moving average (MEWMA), both modified to look only for increases in disease incidence. While neither of these methods is currently in use in a biosurveillance system, they are among the most promising multivariate methods for this application. Our analysis was based on a series of simulations using synthetic syndromic surveillance data that mimics various types of background disease incidence and outbreaks. We found that, similar to results for the univariate CUSUM and EWMA, the directionally-sensitive MCUSUM and MEWMA perform very similarly.

Biological terrorism is a threat to the security and well-being of the United States. It is critical to detect the presence of these attacks in a timely manner, in order to provide sufficient and effective responses to minimize or contain the damage inflicted. Syndromic surveillance is the process of monitoring public health-related data and applying statistical tests to determine the potential presence of a disease outbreak in the observed system. Our research involved a comparative analysis of two multivariate statistical methods, the multivariate CUSUM (MCUSUM) and the multivariate exponentially weighted moving average (MEWMA), both modified to look only for increases in disease incidence. While neither of these methods is currently in use in a biosurveillance system, they are among the most promising multivariate methods for this application. Our analysis was based on a series of simulations using synthetic syndromic surveillance data that mimics various types of background disease incidence and outbreaks. We found that, similar to results for the univariate CUSUM and EWMA, the directionally-sensitive MCUSUM and MEWMA perform very similarly.

This article is from BMC Systems Biology , volume 5 . Abstract Background: Comparing metabolic profiles under different biological perturbations has become a powerful approach to investigating the functioning of cells. The profiles can be taken as single snapshots of a system, but more information is gained if they are measured longitudinally over time. The results are short time series consisting of relatively sparse data that cannot be analyzed effectively with standard time series techniques, such as autocorrelation and frequency domain methods. In this work, we study longitudinal time series profiles of glucose consumption in the yeast Saccharomyces cerevisiae under different temperatures and preconditioning regimens, which we obtained with methods of in vivo nuclear magnetic resonance (NMR) spectroscopy. For the statistical analysis we first fit several nonlinear mixed effect regression models to the longitudinal profiles and then used an ANOVA likelihood ratio method in order to test for significant differences between the profiles. Results: The proposed methods are capable of distinguishing metabolic time trends resulting from different treatments and associate significance levels to these differences. Among several nonlinear mixed-effects regression models tested, a three-parameter logistic function represents the data with highest accuracy. ANOVA and likelihood ratio tests suggest that there are significant differences between the glucose consumption rate profiles for cells that had been--or had not been--preconditioned by heat during growth. Furthermore, pair-wise t-tests reveal significant differences in the longitudinal profiles for glucose consumption rates between optimal conditions and heat stress, optimal and recovery conditions, and heat stress and recovery conditions (p-values

This article is from BMC Systems Biology , volume 5 . Abstract Background: Comparing metabolic profiles under different biological perturbations has become a powerful approach to investigating the functioning of cells. The profiles can be taken as single snapshots of a system, but more information is gained if they are measured longitudinally over time. The results are short time series consisting of relatively sparse data that cannot be analyzed effectively with standard time series techniques, such as autocorrelation and frequency domain methods. In this work, we study longitudinal time series profiles of glucose consumption in the yeast Saccharomyces cerevisiae under different temperatures and preconditioning regimens, which we obtained with methods of in vivo nuclear magnetic resonance (NMR) spectroscopy. For the statistical analysis we first fit several nonlinear mixed effect regression models to the longitudinal profiles and then used an ANOVA likelihood ratio method in order to test for significant differences between the profiles. Results: The proposed methods are capable of distinguishing metabolic time trends resulting from different treatments and associate significance levels to these differences. Among several nonlinear mixed-effects regression models tested, a three-parameter logistic function represents the data with highest accuracy. ANOVA and likelihood ratio tests suggest that there are significant differences between the glucose consumption rate profiles for cells that had been--or had not been--preconditioned by heat during growth. Furthermore, pair-wise t-tests reveal significant differences in the longitudinal profiles for glucose consumption rates between optimal conditions and heat stress, optimal and recovery conditions, and heat stress and recovery conditions (p-values

This article is from BMC Systems Biology , volume 5 . Abstract Background: Comparing metabolic profiles under different biological perturbations has become a powerful approach to investigating the functioning of cells. The profiles can be taken as single snapshots of a system, but more information is gained if they are measured longitudinally over time. The results are short time series consisting of relatively sparse data that cannot be analyzed effectively with standard time series techniques, such as autocorrelation and frequency domain methods. In this work, we study longitudinal time series profiles of glucose consumption in the yeast Saccharomyces cerevisiae under different temperatures and preconditioning regimens, which we obtained with methods of in vivo nuclear magnetic resonance (NMR) spectroscopy. For the statistical analysis we first fit several nonlinear mixed effect regression models to the longitudinal profiles and then used an ANOVA likelihood ratio method in order to test for significant differences between the profiles. Results: The proposed methods are capable of distinguishing metabolic time trends resulting from different treatments and associate significance levels to these differences. Among several nonlinear mixed-effects regression models tested, a three-parameter logistic function represents the data with highest accuracy. ANOVA and likelihood ratio tests suggest that there are significant differences between the glucose consumption rate profiles for cells that had been--or had not been--preconditioned by heat during growth. Furthermore, pair-wise t-tests reveal significant differences in the longitudinal profiles for glucose consumption rates between optimal conditions and heat stress, optimal and recovery conditions, and heat stress and recovery conditions (p-values

This article is from BMC Systems Biology , volume 5 . Abstract Background: For RNA-seq data, the aggregated counts of the short reads from the same gene is used to approximate the gene expression level. The count data can be modelled as samples from Poisson distributions with possible different parameters. To detect differentially expressed genes under two situations, statistical methods for detecting the difference of two Poisson means are used. When the expression level of a gene is low, i.e., the number of count is small, it is usually more difficult to detect the mean differences, and therefore statistical methods which are more powerful for low expression level are particularly desirable. In statistical literature, several methods have been proposed to compare two Poisson means (rates). In this paper, we compare these methods by using simulated and real RNA-seq data. Results: Through simulation study and real data analysis, we find that the Wald test with the data being log-transformed is more powerful than other methods, including the likelihood ratio test, which has similar power as the variance stabilizing transformation test; both are more powerful than the conditional exact test and Fisher exact test. Conclusions: When the count data in RNA-seq can be reasonably modelled as Poisson distribution, the Wald-Log test is more powerful and should be used to detect the differentially expressed genes.

This article is from PLoS ONE , volume 9 . Abstract Accurately quantifying soil organic carbon (SOC) is considered fundamental to studying soil quality, modeling the global carbon cycle, and assessing global climate change. This study evaluated the uncertainties caused by up-scaling of soil properties from the county scale to the provincial scale and from lower-level classification of Soil Species to Soil Group, using four methods: the mean, median, Soil Profile Statistics (SPS), and pedological professional knowledge based (PKB) methods. For the SPS method, SOC stock is calculated at the county scale by multiplying the mean SOC density value of each soil type in a county by its corresponding area. For the mean or median method, SOC density value of each soil type is calculated using provincial arithmetic mean or median. For the PKB method, SOC density value of each soil type is calculated at the county scale considering soil parent materials and spatial locations of all soil profiles. A newly constructed 1∶50,000 soil survey geographic database of Zhejiang Province, China, was used for evaluation. Results indicated that with soil classification levels up-scaling from Soil Species to Soil Group, the variation of estimated SOC stocks among different soil classification levels was obviously lower than that among different methods. The difference in the estimated SOC stocks among the four methods was lowest at the Soil Species level. The differences in SOC stocks among the mean, median, and PKB methods for different Soil Groups resulted from the differences in the procedure of aggregating soil profile properties to represent the attributes of one soil type. Compared with the other three estimation methods (i.e., the SPS, mean and median methods), the PKB method holds significant promise for characterizing spatial differences in SOC distribution because spatial locations of all soil profiles are considered during the aggregation procedure.

This article is from PLoS ONE , volume 9 . Abstract Accurately quantifying soil organic carbon (SOC) is considered fundamental to studying soil quality, modeling the global carbon cycle, and assessing global climate change. This study evaluated the uncertainties caused by up-scaling of soil properties from the county scale to the provincial scale and from lower-level classification of Soil Species to Soil Group, using four methods: the mean, median, Soil Profile Statistics (SPS), and pedological professional knowledge based (PKB) methods. For the SPS method, SOC stock is calculated at the county scale by multiplying the mean SOC density value of each soil type in a county by its corresponding area. For the mean or median method, SOC density value of each soil type is calculated using provincial arithmetic mean or median. For the PKB method, SOC density value of each soil type is calculated at the county scale considering soil parent materials and spatial locations of all soil profiles. A newly constructed 1∶50,000 soil survey geographic database of Zhejiang Province, China, was used for evaluation. Results indicated that with soil classification levels up-scaling from Soil Species to Soil Group, the variation of estimated SOC stocks among different soil classification levels was obviously lower than that among different methods. The difference in the estimated SOC stocks among the four methods was lowest at the Soil Species level. The differences in SOC stocks among the mean, median, and PKB methods for different Soil Groups resulted from the differences in the procedure of aggregating soil profile properties to represent the attributes of one soil type. Compared with the other three estimation methods (i.e., the SPS, mean and median methods), the PKB method holds significant promise for characterizing spatial differences in SOC distribution because spatial locations of all soil profiles are considered during the aggregation procedure.

We provide an introductory review of Bayesian data analytical methods, with a focus on applications for linguistics, psychology, psycholinguistics, and cognitive science. The empirically oriented researcher will benefit from making Bayesian methods part of their statistical toolkit due to the many advantages of this framework, among them easier interpretation of results relative to research hypotheses, and flexible model specification. We present an informal introduction to the foundational ideas behind Bayesian data analysis, using, as an example, a linear mixed models analysis of data from a typical psycholinguistics experiment. We discuss hypothesis testing using the Bayes factor, and model selection using cross-validation. We close with some examples illustrating the flexibility of model specification in the Bayesian framework. Suggestions for further reading are also provided.

We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional dynamic system (the logistic map) containing an observational noise. A ``pure'' Maximum Likelihood (ML) method is suggested to estimate the structural parameter of the logistic map along with the initial value $x_1$ considered as an additional unknown parameter. Comparisons with previously proposed techniques on simulated numerical examples give favorable results (at least, for the investigated combinations of sample size $N$ and noise level). Besides, unlike some suggested techniques, our method does not require the a priori knowledge of the noise variance. We also clarify the nature of the inherent difficulties in the statistical analysis of deterministically chaotic time series and the status of previously proposed Bayesian approaches. We note the trade-off between the need of using a large number of data points in the ML analysis to decrease the bias (to guarantee consistency of the estimation) and the unstable nature of dynamical trajectories with exponentially fast loss of memory of the initial condition. The method of statistical moments for the estimation of the parameter of the logistic map is discussed. This method seems to be the unique method whose consistency for deterministically chaotic time series is proved so far theoretically (not only numerically).

We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional dynamic system (the logistic map) containing an observational noise. A ``pure'' Maximum Likelihood (ML) method is suggested to estimate the structural parameter of the logistic map along with the initial value $x_1$ considered as an additional unknown parameter. Comparisons with previously proposed techniques on simulated numerical examples give favorable results (at least, for the investigated combinations of sample size $N$ and noise level). Besides, unlike some suggested techniques, our method does not require the a priori knowledge of the noise variance. We also clarify the nature of the inherent difficulties in the statistical analysis of deterministically chaotic time series and the status of previously proposed Bayesian approaches. We note the trade-off between the need of using a large number of data points in the ML analysis to decrease the bias (to guarantee consistency of the estimation) and the unstable nature of dynamical trajectories with exponentially fast loss of memory of the initial condition. The method of statistical moments for the estimation of the parameter of the logistic map is discussed. This method seems to be the unique method whose consistency for deterministically chaotic time series is proved so far theoretically (not only numerically).

We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional dynamic system (the logistic map) containing an observational noise. A ``pure'' Maximum Likelihood (ML) method is suggested to estimate the structural parameter of the logistic map along with the initial value $x_1$ considered as an additional unknown parameter. Comparisons with previously proposed techniques on simulated numerical examples give favorable results (at least, for the investigated combinations of sample size $N$ and noise level). Besides, unlike some suggested techniques, our method does not require the a priori knowledge of the noise variance. We also clarify the nature of the inherent difficulties in the statistical analysis of deterministically chaotic time series and the status of previously proposed Bayesian approaches. We note the trade-off between the need of using a large number of data points in the ML analysis to decrease the bias (to guarantee consistency of the estimation) and the unstable nature of dynamical trajectories with exponentially fast loss of memory of the initial condition. The method of statistical moments for the estimation of the parameter of the logistic map is discussed. This method seems to be the unique method whose consistency for deterministically chaotic time series is proved so far theoretically (not only numerically).

This book is the outcome of teaching, for more than 30 years, a course titled  "statistical quality control" to B.S. students using many books especially   the book written by Dr Grant & Dr. Leavenworth and the one written by  Dr Kaoru Ishikawa on this subject.  The book is divided into 14 chapters.

This book is the outcome of teaching, for more than 30 years, a course titled  "statistical quality control" to B.S. students using many books especially   the book written by Dr Grant & Dr. Leavenworth and the one written by  Dr Kaoru Ishikawa on this subject.  The book is divided into 14 chapters.

This book is the outcome of teaching, for more than 30 years, a course titled  "statistical quality control" to B.S. students using many books especially   the book written by Dr Grant & Dr. Leavenworth and the one written by  Dr Kaoru Ishikawa on this subject.  The book is divided into 14 chapters.

This book is the outcome of teaching, for more than 30 years, a course titled  "statistical quality control" to B.S. students using many books especially   the book written by Dr Grant & Dr. Leavenworth and the one written by  Dr Kaoru Ishikawa on this subject.  The book is divided into 14 chapters.

College outline series, no. 27 published also under title an outline of statistical methods. Includes bibliographies

"Selected bibliography of works on the quantitative study of organisms": p. 40-42

"Selected bibliography of works on the quantitative study of organisms": p. 40-42

"Selected bibliography of works on the quantitative study of organisms": p. 40-42

"Selected bibliography of works on the quantitative study of organisms": p. 40-42