| Conference on Statistical Theory and Practice (25th) Held at the University of Wisconsin-Madison on 29-31 May 1985 |
85 |
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| Authors:
George E. P. Box; Richard A. Johnson; WISCONSIN UNIV-MADISON DEPT OF STATISTICS
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 | The formal program consisted of seven invited paper sessions: Bayesian Inference, Inference, Biostatistics, Time Series, Quality and Reliability, Experimental Design, and Modelling and Data Analysis. There were three contributed paper sessions, a panel discussion on 'The Future of Statistics in Industry and Government' and a banquet speech. The twenty-three distinguished speakers at the invited paper sessions all gave first rate presentations incorporating their latest findings within the framework of recent ... |
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| Anatomy of Some Time Series Models |
JUN 1983 |
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| Authors:
George E. P. Box; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| Most naturally occurring data are serial in space or time. With randomized designs, analysis which ignores the serial structure is possible. When the ordering of the data is not at our disposal adequate models must take specific account of serial structure and allow for error dependence, possible non-stationarity, time trend removal, dynamic relationships between variables, feedback between variables, and choice of dependent and independent variables. Stochastic difference equations supply a ... |
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| Constrained Nonlinear Least Squares |
JUN 1983 |
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| Authors:
George E. P. Box; Hiromitsu Kanemasu; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| The method of least squares is widely used for the fitting of data of functions containing unknown parameters. When these functions are non-linear in the parameters an iterative approach using successive local linearizations was suggested by Gauss. To encourage convergence various modifications and alternatives have been suggested. It has been proposed that, at the early stages, use of the method of steepest descent might speed convergence. A method might be ... |
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| The Importance of Practice in the Development of Statistics |
JAN 1983 |
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| Authors:
George E. P. Box; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| The paper shows how application and consideratio of the scientific context in which Statistics is used can initiate important advances such as least squares, ratio estimators, correlation, contingency tables, studentization, experimental design, the analysis of variance, randomisation, fractional replication, variance component analysis, bioassay, limits for a ratio, quality control, sampling inspection, non-parametric tests, cumulative sum charts, data analysis plotting techniques, and a resolution of the Bayes - frequentist controversy. It ... |
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| Choice of Response Surface Design and Alphabetic Optimality |
FEB 1982 |
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| Authors:
George E. P. Box; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| It is argued that the specification of problem of experimental design (and in particular, of response surface design) should depend on scientific context. The specification for a widely developed theory of 'alphabetic optimality' for response surface applications is analyzed and found to be unduly limiting. Ways in which designs might be chosen to satisfy a set of criteria of greater scientific relevance are suggested. Detailed consideration is given to regions ... |
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| Estimating Current Trend and Growth Rates in Seasonal Time Series |
MAY 1981 |
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| Authors:
George E. P. Box; David A. Pierce; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| The importance of appropriate stochastic models in choosing efficient methods of statistical analysis is discussed. The fitting to data of Seasonal Autoregressive Moving Average models is described and it is shown how trend may be estimated in an appropriate class of models of this kind. The procedure is illustrated for a model fitted to a money supply series published by the Federal Reserve Board. Error limits are calculated. In a ... |
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| Measures of Lack of Fit for Response Surface Designs and Predictor Variable Transformations |
APR 1981 |
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| Authors:
George E. P. Box; N. R. Draper; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| Some first and second order response surface designs are discussed from the point of view of their ability to detect certain likely kinds of lack of fit. This leads to consideration of conditions for representational adequacy of first and second order models in transformed predictor variables. (Author) |
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| Sampling and Bayes' Inference in Scientific Modeling and Robustness. |
DEC 1980 |
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| Authors:
George E. P. Box; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| Scientific learning is an iterative process employing Criticism and Estimation. Correspondingly the formulated model factors into two complimentary parts - a predictive part allowing model criticism, and a Bayes posterior part allowing estimation. Implications for significance tests, the theory of precise measurement, and for ridge estimates are considered. Predictive checking functions for transformation, serial correlation, bad values, and their relation with Bayesian options are considered. Robustness is seen from a ... |
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| The Duality of Diagnostic Checking and Robustification in Model Building: Some Considerations and Examples. |
JUN 1980 |
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| Authors:
Steven P. Bailey; George E. P. Box; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| Consideration is given to the means by which appropriate diagnostic checking functions of the data can be developed to guard against feared model discrepancies. A formal basis for the selection of a function is given for situations where the feared inadequacy can be characterized by a discrepancy parameter beta which takes a (possible inappropriate) value of beta sub zero in the model. The relationship of this checking function with the ... |
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| Modeling the Nature and Frequency of Outliers. |
MAY 1980 |
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| Authors:
Steven P. Bailey; George E. P. Box; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| Bayesian techniques are applied to the problem of dealing with the possible occurrence of outlying observations. Since most experimental data are liable to occasional discrepancies, a robustification approach is taken whereby this experimental 'fact of life' is taken into account in the model. Special consideration is given to the way in which both the nature and the frequency of the outlying observations are modeled. In this regard, the Bayesian outlier ... |
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| Some Aspects of Model Estimation and Model Criticism. |
MAY 1980 |
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| Authors:
Steven P. Bailey; George E. P. Box; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| The recently advanced philosophy of model building is developed further. It is stressed how Bayesian inferences based on the posterior distribution of the model parameters are appropriate only after sampling theory inferences based on the predictive distribution of the data fail to discredit the model. An example involving the normal distribution is discussed in detail. Diagnostic checking functions are developed which can be applied in an intuitive sequential manner. Careful ... |
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| Sampling and Bayes' Inference in Scientific Modelling and Robustness, |
1980 |
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| Authors:
George E. P. Box; WISCONSIN UNIV-MADISON
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| A Study of Real Data. |
OCT 1979 |
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| Authors:
Gina Chen; George E. P. Box; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| Nine sets of real data are analyzed. The distributions within the contaminated exponential power family which best describe these data sets are obtained by maximum likelihood. It appears that heavy tailed distributions are often produced by secular inhomogeneity in mean and variance. A specific robust estimator would behave well if, in the real world, data occurred of the kind which favored it. In this paper more classical sets of data ... |
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| Further Study of Robustification via A Bayesian Approach. |
SEP 1979 |
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| Authors:
Gina Chen; George E. P. Box; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| A Bayesian model has been proposed which describes the generation of an observation by a process whereby with prior probability 1-alpha the usually assumed statistical structure is correct but with small probability alpha it is incorrect (for example, the observation has a very large variance). For a simple location estimate the nature of the down weighting of outlying observations produced by this model is studied and is compared with that ... |
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| Implied Assumptions for some Proposed Robust Estimators. |
SEP 1979 |
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| Authors:
Gina Chen; George E. P. Box; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| Assumptions which could motivate various L-estimators M-estimators are discussed. In particular, for samples of size ten a distribution in the contaminated expontential power family is found whose posterior mean approximates each of a number of proposed L-estimators. Also distributions in this family are found whose posterior modes approximate suggested M-estimators. (Author) |
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| Analysis of Variance with Autocorrelated Observations, |
JUN 1979 |
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| Authors:
Greta M. Ljung; George E. P. Box; WISCONSIN UNIV-MADISON
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| Sampling and Bayes' Inference in the Advancement of Learning. |
JUN 1979 |
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| Authors:
George E. P. Box; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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| Sampling theory inference (e.g. inference based on sampling distributions of statistics and in particular on significance tests) and Bayesian inference are usually thought of as rivals and much effort has been spent in propounding their relative merits. In this paper it is argued that both kinds of inference are needed in the scientific iteration whereby knowledge is acquired. This iteration employs a directed alternation between induction and deduction which uses ... |
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| Statistical Models for Time Series and Life Testing with Applications in Engineering Systems. |
1978 |
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| Authors:
George E. P. Box; G. K. Bhattacharyya; Richard A. Johnson; Grace Wahba; WISCONSIN UNIV-MADISON DEPT OF STATISTICS
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| Over the period of this grant 5 papers have been accepted for publication, 1 paper has been published, 5 technical reports have been written, and 4 theses have been completed. Over the period 1 April 1972 to June, 1978 35 papers have been published, 9 papers have been accepted for publication, 41 technical reports have been written, one book has been written and another revised, all of these have received ... |
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| Topics in Time Series Analysis. III. ARIMA Time Series Models with Non-Normal Shocks. |
JAN 1976 |
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| Authors:
Johannes Ledolter; George E. P. Box; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| In this paper the parent distribution of the shocks a sub t in ARIMA models is extended to the family of symmetric exponential power distributions, which covers the Normal as well as particular forms of symmetric leptokurtic and playkurtic distributions. The inference robustness of the parameters of ARIMA models and the effect of non Normality of the shocks on the forecasts is studied. (Author) |
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| Topics in Time Series Analysis. II. When are Exponential Smoothing Forecast Procedures Optimal. |
DEC 1975 |
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| Authors:
Johannes Ledolter; George E. P. Box; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| This paper shows that exponential smoothing forecast procedures, in particular those recommended by Brown, will provide optimal (MMSE) forecasts only if the underlying process is a member of a particular restricted class of ARIMA models. Actual study of time series, however, does not give any empirical support to this restricted class of models. (Author) |
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| Topics in Time Series Analysis. I. Review of Time Series Models and Their Forecasts. |
DEC 1975 |
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| Authors:
Johannes Ledolter; George E. P. Box; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| This paper provides a summary of the literature concerned with time series analysis and forecasting. We discuss the probabilistic foundations of time series analysis, the linear prediction theory, the general linear process, its parsimonious versions and their prediction. Furthermore, the philosophy of iterative model building and exponential smoothing techniques are discussed. (Author) |
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| Robust Designs. |
APR 1974 |
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| Authors:
George E. P. Box; Norman R. Draper; WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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| An experimental design for fitting the regression model Y = X beta + epsilon can be judged good by various criteria, fourteen of which are enumerated. One of these is that the design should be insensitive to wild observations. This situation is discussed from the points of view of parameter estimation and response estimation. It is shown that a suitable measure of design sensitivity to wild observations can be defined ... |
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| Statistical Models for Control, Optimization, Reliability, and Life Testing. |
31 MAY 1973 |
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| Authors:
George E. P. Box; Grace Wahba; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| The areas of research include topics of stochastic systems (especially with discrete control), statistical model building, the state variable approach, the effects of constraints on the degree of possible manipulation of a system, appropriate algorithms for optimal feed forward control, closed loop operations, discrete control and estimation, maximum likelihood estimation for the parameters of a dynamic model, estimation of the parameters in a stationary linear dynamic model, statistical analysis of ... |
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| Criteria for Judging Adequacy of Estimation by an Approximating Response Function. |
MAR 1973 |
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| Authors:
George E. P. Box; John Wetz; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| In response surface methodology the true functional form f(x) is usually not known and the response must be approximated by means of a graduating function g(x) (for example, by a polynomial in x) over the region of interest. The relationship between an observation y and the graduating function g(x) is therefore y = g(x) + beta + epsilon, where beta = f(x) - g(x). In the report, a measure (gamma ... |
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| Bayesian Inference in Statistical Analysis, |
1973 |
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| Authors:
George E. P. Box; George C. Tiao; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| The object of this book is to explore the use and relevance of Bayes' theorem to problems such as arise in scientific investigation in which inferences must be made concerning parameter values about which little is known a priori. A number of standard problems concerned with comparison of location and scale parameters are studied from a Bayesian viewpoint. (Author) |
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| Some Recent Advances in Forecasting and Control. Part II. |
AUG 1972 |
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| Authors:
George E. P. Box; Gwilym M. Jenkins; John F. MacGregor; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| The paper outlines an approach to discrete stochastic control which uses these models to typify the dynamic and stochastic characteristics of the system. This description of the system together with the type of cost function involved is shown to lead to appropriate optimal control schemes. Feedforward and feedback control schemes are worked out for situations typical of those occurring in the chemical and other process industries. A control problem more ... |
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| Statistical Models for Control and Optimization Techniques. |
AUG 1972 |
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| Authors:
George E. P. Box; Grace Wahba; Irwin Guttman; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| The main thrust of the research has been to continue the development of univariate and multivariate time series and dynamic model-building techniques. Important problems are associated with estimation of parameters which appear non-linearly. This has been tackled by use of Bayes' methods. Investigations have been made into lagged variable forecasting techniques, behavior of sample autocorrelation functions for non-stationary series, distribution theory of partial autocorrelation functions, new methods for estimation of ... |
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| Topics in Control. 3. Feedforward Control. |
JUL 1972 |
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| Authors:
John F. MacGregor; George E. P. Box; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| A general development is given for the feedforward control scheme which minimizes the mean square error of the output deviation from target using a general linear transfer function model to characterize the process dynamics and a general autoregressive-integrated-moving-average model to characterize the disturbance. It is then shown by way of an example how the state variable models and the optimal control theory of papers one and two in this series ... |
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| Topics in Control. 4. The Analysis of Closed-Loop Dynamic-Stochastic Systems. |
JUL 1972 |
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| Authors:
George E. P. Box; John F. MacGregor; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| Some of the problems involved in the identification, estimation, and diagnostic checking of univariate closed-loop systems are discussed. The procedure used in open-loop operation for identifying the process transfer function by cross-correlating the input and output sequences is shown to be invalid in closed-loop situations because the input and disturbance sequences are correlated. Under pure feedback where the input is calculated completely from the output this cross-correlation procedure is shown ... |
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| Forecasting Using Leading Indicators. |
JUN 1972 |
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| Authors:
George E. P. Box; Paul Newbold; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| It is frequently the case that forecasts of a discrete stochastic process (Y sub t) can be much improved by using information coming from some related process (X sub t) particularly if changes in Y tend to be anticipated by changes in X, in which case X is said to be a leading indicator for Y. The report shows information from leading indicators may be appropriately incorporated in computing forecasts. ... |
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| Time Series Analysis Forecasting and Control, |
1970 |
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| Authors:
George E. P. Box; Gwilym M. Jenkins; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| The book is concerned with the building of models for discrete time series and dynamic systems. It describes in detail how such models may be used to obtain optimal forecasts and optimal control action. All the techniques are illustrated with examples using economic and industrial data. In Part 1, models for stationary and nonstationary time series are introduced, and their use in forecasting is discussed and exemplified. Part II is ... |
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| STATISTICAL ANALYSIS AND DESIGN OF EXPERIMENTS. |
OCT 1969 |
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| Authors:
George E. P. Box; George C. Tiao; HARVARD UNIV BOSTON MASS GRADUATE SCHOOL OF BUSINESS ADMINISTRATION
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| Three books have been completed with the aid of the contract: Evolutionary Operation; Time Series Analysis, Forecasting and Control; and, Bayesian Inference. The report gives a brief discussion of the books. |
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| EVOLUTIONARY OPERATION: A METHOD FOR INCREASING INDUSTRIAL PRODUCTIVITY, |
APR 1969 |
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| Authors:
George E. P. Box; Norman R. Draper; HARVARD UNIV CAMBRIDGE MASS GRADUATE SCHOOL OF BUSINESS ADMINISTRATION
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| The book is about the philosophy and practice of evolutionary operation (EVOP), a simple but powerful statistical tool with wide application in industry. Experience has long shown that statistical methods, sometimes quite sophisticated in character, can be of great value in improving the efficiency of laboratory and pilot-plant investigations made by specially trained chemists and engineers. What originally motivated the introduction of EVOP, however, was the idea that the widespread ... |
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| MODELS FOR FORECASTING SEASONAL AND NON-SEASONAL TIME SERIES. |
JUN 1967 |
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| Authors:
George E. P. Box; Gwilym M. Jenkins; D. W. Bacon; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| The optimal forecasts of future values of a time series are determined by the nature of the stochastic model which describes that series. The main effort then in statistical analysis directed to forecasting must be in obtaining a suitable stochastic model for the series. The following paper outlines the approach which has been taken in a forthcoming book. Box, G. E. P. and Jenkins, G. M., Statistical Models for Forecasting ... |
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| BAYESIAN APPROACHES TO SOME BOTHERSOME PROBLEMS IN DATA ANALYSIS. |
OCT 1965 |
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| Authors:
George E. P. Box; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| A SIMPLE SYSTEM OF EVOLUTIONARY OPERATION SUBJECT TO EMPIRICAL FEEDBACK. |
OCT 1964 |
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| Authors:
George E. P. Box; WISCONSIN UNIV MADISON DEPT OF STATISTICS
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| Experimentation can lead to progress through empirical feedback or through scientific (technical) feedback; or more usually by some combination of both. Empirical feedback is typical of the 'try it and see' or Edisonian approach. Here information fed back from the experiment triggers a simple reaction like 'except a modification which increases yield.' By contrast scientific feedback occurs as an interaction between the data and the knowledge, experience, and imagination of ... |
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| A NOTE ON PARTIAL DUPLICATION OF DESIGNS. |
JAN 1964 |
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| Authors:
George E. P. Box; WISCONSIN UNIV MADISON
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| The object of the paper is to supply a simple and general procedure for estimating the effects and their variances and covariances for the augmented arrangements resulting from particular schemes of partial duplication. |
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Reports by Author
