Statistical Prediction Analysis

Aitchison, J.; Dunsmore, I. R.

doi:10.1017/cbo9780511569647

Cited by 731 publications

(330 citation statements)

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“…In contrast, much of classical inference relies on the ''plug-in principle" that in this case would lead us to predict pðs new jn new ¼ 5Þ solely based onĥ, the maximum likelihood estimate. Plug-in procedures ignore uncertainty in h, and hence lead to predictions that are overconfident, that is, predictions that are less variable than they should be (Aitchison & Dunsmore, 1975). 3 You are now presented with the new set of five questions.…”

Section: Bayesian Parameter Estimationmentioning

confidence: 99%

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

Wagenmakers

Lodewyckx

Kuriyal

et al. 2010

Cognitive Psychology

654

642

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a b s t r a c tIn the field of cognitive psychology, the p-value hypothesis test has established a stranglehold on statistical reporting. This is unfortunate, as the p-value provides at best a rough estimate of the evidence that the data provide for the presence of an experimental effect. An alternative and arguably more appropriate measure of evidence is conveyed by a Bayesian hypothesis test, which prefers the model with the highest average likelihood. One of the main problems with this Bayesian hypothesis test, however, is that it often requires relatively sophisticated numerical methods for its computation. Here we draw attention to the Savage-Dickey density ratio method, a method that can be used to compute the result of a Bayesian hypothesis test for nested models and under certain plausible restrictions on the parameter priors. Practical examples demonstrate the method's validity, generality, and flexibility.

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Section: Bayesian Parameter Estimationmentioning

confidence: 99%

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

Wagenmakers

Lodewyckx

Kuriyal

et al. 2010

Cognitive Psychology

654

642

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“…1-2. Light (la, 2a) and phase contrast (lb, 2b) micrographs of MO cells untreated (1) or treated with taxol (2) and stained with an antiserum against tubulin. Insets: optical diffractograms.…”

Section: Immunostainingmentioning

confidence: 99%

“…Scale bars = 50 pm. particular cell to one of the groups known, a prior statistical prediction analysis was performed (2). Dimensions of the structures or interstructural distances in absolute units contained in the diffractograms were calculated on the basis of the position of the peaks of the radial distribution of light intensity (13).…”

Section: Immunostainingmentioning

confidence: 99%

Numerical evaluation of changes in the cytoplasmic microtubule complex of C3H mouse cells by optical diffractometry and of changes in cell shape by fourier analysis

Mareel¹,

Bruyne²,

Ostrowski

et al. 1986

Cytometry

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MO mouse cells in culture on glass were treated with taxol, or nocodazole. or incubated at 4°C to alter their cytoplasmic microtubule complex (CMTC). From each treated group and from an untreated group, 30 cells stained with an antiserum against tubulin, were photographed under the photomicroscope, and negatives were analysed by optical diffractometry. Differences between groups of cells were tested by variance analysis. Phasecontrast micrographs of the same cells were used for Fourier analysis of cell shape. Both types of analyses provided numerical objective data about changes in the CMTC and in cell shape that were typical for the kind of treatment. We conclude that optical diffractometry of immunostained cells and Fourier analysis of cell shape are complementary to photomicroscopy for the study of the CMTC in cell populations cultured on an artificial substrate.Key terms: Cytoplasmic microtubule complex, optical diffractometry, Fourier analysis of cell shape, MO mouse cellsImmunocytochemistry is the method of choice to demonstrate the cytoplasmic microtubule complex (CMTC) (5) in cells spread on a n artificial substrate. In most cells immunocytochemistry has allowed at best a semiquantitative and interpretative evaluation of the CMTC (19). Optical diffractometry of morphological pictures allows a numerical evaluation that is objective and that permits statistical analysis.The diffraction pattern obtained by optical Fourier transform contains integrated information on the dimensions of structures, distances between them, and on their spatial arrangement. Since the diffraction pattern integrates the information from the whole analysed image, the signal-to-noise ratio may be higher than in the original image where regularities of the structure can be masked by random disorders. The radial distribution of light intensities contains information on the dimensions of structures and on distances between them; the angular distribution contains information on the predominant directions of structures.With a diffractometer coupled to a computer-based automatic detection system, a large number of pictures can be analysed and compared statistically. This method has been widely used in biology (18). Examples are screening of mitotic cells (ZO), automatic finding of metaphase chromosomes (13, cytology of cervical samples (22), analysis of cell structure (6), of collagen fibers in bone tissue (12,13), of the fine structure of arterial smooth muscle cells (211, and of myelin sheets (23).It is the purpose of the present investigation to see whether optical diffractometry can be used for quantitative and objective analysis of alterations of the CMTC in cells cultured on artificial substrate. Therefore, we have studied MO mouse cells from continuous cultures treated with agents that provoke known alterations of the CMTC, namely, taxol, nocodazole, and incubation at 4°C. Taxol leads to a n increased but unordered assembly 'Supported by the Kankerfonds van de Algemene Spa=-en Lijfrentekas, Brussels, Belgium and by the Polish Gover...

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“…The outcomes of the two experiments are connected through the same structure of the model and indexed by the same set of parameters. For details on the predictive inference methods and its wide range of applications readers may refer to Aitchison and Dunsmore (1975) and Geisser (1993). Predictive inference for a set of future responses of the model, conditional on the realized responses from the same model, has been derived by many authors including Aitchison and Scalthorpe (1965), Fraser and Haq (1969), and Haq and Khan (1990).…”

Section: Introductionmentioning

confidence: 99%

Predictive Distribution of Regression Vector and Residual Sum of Squares for Normal Multiple Regression Model

Khan

2005

Communications in Statistics - Theory and Methods

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This paper proposes predictive inference for the multiple regression model with independent normal errors. The distributions of the sample regression vector (SRV) and the residual sum of squares (RSS) for the model are derived by using invariant differentials. Also the predictive distributions of the future regression vector (FRV) and the future residual sum of squares (FRSS) for the future regression model are obtained. Conditional on the realized responses, the future regression vector is found to follow a multivariate Student-t distribution, and that of the residual sum of squares follows a scaled beta distribution. The new results have been applied to the market return and accounting rate data to illustrate its application.Keywords: Multiple regression model; regression vector and residual sum of squares; non-informative prior; future regression model; predictive inference; future regression vector; multivariate normal, Student-t, beta and gamma distributions.

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Statistical Prediction Analysis

Cited by 731 publications

References 0 publications

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

Numerical evaluation of changes in the cytoplasmic microtubule complex of C3H mouse cells by optical diffractometry and of changes in cell shape by fourier analysis

Predictive Distribution of Regression Vector and Residual Sum of Squares for Normal Multiple Regression Model

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