Probability, Statistics, And Decision Making In The Atmospheric Sciences

560 Pages·1985·33.996 MB·\560

by  Allan Murphy (Author), Richard W. Katz (Author)

Probability, Statistics, and
Decision Making in
the Atmospheric Sciences
Q Tay&l oFrr ancis
Tay&l Forra Gnrcoiusp
�-
http://taylorandfrancis.com
Probability, Statistics, and
Decision Making in
the Atmospheric Sciences
edited by Allan H. Murphy
and Richard W. Katz
~ ~ ~~o~;~;n~~;up
LONDON AND NEW YORK
Firpsutb li1s9h8be5yWd e stvPireeIwsn sc,.
Publi2s0h1be9yRd o utledge
52a nVdeArvbeinlNutee wY, o rkY,1 0N017
2P arSkq uaMriel,tP oanrA kb,i ngOdxoonOn,X 144R N
Routliaesnd i gmep roitfnh Ttea y&lF orra nGcriosau npi ,n fobrumsai ness
Copyri1g9h8Tt5a© y &lF orra ncis
Alrli grhetsse Nrovp eador.ftt h biosom ka bye r eproirnr teepdr oodruu tcieldii nas neyd
formr b oy alneyc tereocnhiacn,i cmal, oorw oktnhoewrn moera nhse,r enafter invented,
inclupdhiontgo caonprdye icnogro drii nan ngiy,n formatioonr srteotrraigeev al system,
withpoeurtm iisnws riiotfrnio nmtg h e publishers.
Notice:
Prodourcc otr ponraammteaesby e t radeomrra ergkiss ttreardeedma anardrk uess ,e d
onflyoi rd entiafniedcx aptliaownnia tthiioonunttt eo in ntf ringe.
LibroafrCo nyg esrs CataClaorNgdu mb8e4r-:5 2287
ISB1N39 :7 8-0-36(7h-b2k8)4 33-6
Contents
Preface. . . . . . . . . . . . . . . . . . • . . . • . . ix
1 EXPLORATORY ANALYSIS OF ATMOSPHERIC DATA, Thomas E.
Graedel and Beat Kleiner • ..•..•.••. 1
1. Introduction .............. . 1
2. Summarization and Exposure of Sets of One-
Dimensional Data ..... . 2
3. Analyzing Two Sets of Data ....... . 27
4. Comparing Several Sets of Data ..... . 31
5. Summary and Conclusions .....•.... 38
2 DEVELOPING EMPIRICAL MODELS WITH MULTIPLE REGRESSION:
BIASED ESTIMATION TECHNIQUES, Donald W. Marquardt and
Ronald D. Snee . •..•.••..• 45
1. Introduction .............•. 45
2. Theory and Illustrative Examples ..... 47
3. Use of Biased Estimation in Data Analysis. 77
3 EXPLORATORY MULTIVARIATE ANALYSIS OF A SINGLE BATCH
OF DATA, K. Ruben Gabriel . . . . . . . . . . . . . 101
1. Introduction . . . . . . . . . • . . . . . . . . 101
2. One Batch of Multivariate Data and Their Descriptive
Statistics . . . . . . . . . . . • . . . . . . . • 101
3. The Geometry and Display of a Batch of Multivariate
Data • . • • • . . . . . . . . • . • . • . . . 111
4. Data Analysis of the Variables' Configuration. • 123
5. Analyzing the Scatter of the Units . . . . . . . 133
6. Joint Analysis of Variables and Units--Modeling. 144
7. Other Literature . . . . . . . . . . • . . 150
4 MULTIVARIATE COMPARISONS OF DATA FROM SEVERAL
BATCHES, K. Ruben Gabriel ....... . 153
Comparing Several Batches of Observations 153
On Tests of Significance. . . ....• 183
v
vi
5 TIME SERIES ANALYSIS--FREQUENCY DOMAIN, RiahaPd H.
Jones . •.••• 189
1. Introduction. . . • . . 189
2. Termi no 1o gy . . . . . . 189
3. Periodic Mean Functions 191
4. Estimating the Spectral Density . . . . 195
5. Estimating via the Covariance Function. 202
6. Estimating the Covariance Function via Two Passes
of the FFT. . . . . . • 206
7. The Effects of Filtering. 208
8. Testing Hypotheses. . . . 211
9. Multivariate Time Series. 215
6 TIME SERIES ANALYSIS--TIME DOMAIN, RiahaPd H. Jones. 223
1. Introduction ..•..•....... 223
2. First-Order Autoregression ..•... 223
3. Higher-Order Autoregressions •.... 229
4. Order Selection .......... . 237
5. Autoregressive-Moving Average Models. 240
6. Hypothesis Tests .........• 244
7. Multivariate Time Series ..... . 246
8. State Space Recursive Estimation .. 251
7 PROBABILISTIC MODELS, RiahaPd W. Katz. 261
1. Introduction ..... 261
2. Examples ••.•... 262
3. Probability Theory •. 270
4. Statistical Inference 279
8 STATISTICAL WEATHER FORECASTING, HaPry R. Glahn. 289
1. Introduction ..... . 289
2. Methods of Application. 290
3. Histograms ..... . 294
4. Scatter Diagrams .. . 297
5. Regression ...••. 301
6. Discriminant Analysis 315
7. Canonical Correlation 320
8. Logit Model . . . 323
9. Map Typing •..... 324
10. Analogues ..... . 325
11. Present Status ... . 326
12. Future of Statistical Weather Forecasting 329
9. PROBABILISTIC WEATHER FORECASTING, Attan H. MUPphy 337
1. Introduction. . . . . . . . . . . . . . . . . . 337
2. Probability Forecasts: Definition, Interpretation,
and Motivation. . . . . . . • 338
3. Objective Probability Forecasts . . . • . . • . . . 339
vii
Subjective Probability Forecasts. . . . . . . .. . . . 352
Communication of Uncertainty in Weather Forecasts . • 367
10 FORECAST EVALUATION, Allan H. Mu..PJlhy and Hapald Daan. 379
1. Introduction • . . . . . . . . . • . • . . . . . . 379
2. Nature and Purposes of Evaluation. . . . . . • • . 380
3. Predictands, Forecasts, and Attributes . . . . . . 381
4. Some Desirable Properties of Evaluation Measures • . 389
5. Some Inferential Measures for Categorical Forecasts. 394
6. Some Inferential Measures for Probability Forecasts. 412
7. Some Rela:ted Topics ..• ; . . • . . . • . . . . . . 428
11 DESIGN AND EVALUATION OF WEATHER MODIFICATION
EXPERIMENTS, Paul W. Mielke, Jr. 439
1. Introduction ...... . 439
2. Experimenta 1 Designs . . . 440
3. Evaluation Procedures ... 444
12 BAYESIAN INFERENCE, Robert L. Winkler 461
1. Introduction . . . . . . . 461
2. Bayes' Theorem . . . . . . . . . . . . . 462
3. Bayesian Inference with Discrete Prior Distributions 464
4. Bayesian Inference with Continuous Prior
Distributions. . . . . . . . . . . . • . . 467
5. Assessment of Likelihood Functions and Prior
Distributions. . . . . . . . . . . . . • . 475
6. Estimation, Hypothesis Testing, Prediction,
and Decision Making. . . . • • • . • • • . 481
7. Bayesian Inference in Meteorology. • . . . . 487
13 DECISION ANALYSIS, Robert L. Winkler and Allan H.
Murrphy. • • • • • • • • • • • • • 493
1. Introduction .••...... 493
2. Elements of Decision Analysis. 494
3. Decision Criteria .•.... 500
4. Assessment of Probabilities. 502
5. Assessment of Utilitie~ .. . 504
6. Value of Information ... . 508
7. Sequential Decisions .•.. 512
8. Sensitivity Analysis .••...... 517
9. Some Applications of Decision Analysis
in Meteorology .......... . 518
About the Contributors .......... . 525
Index ..•.......•.••...•.. 527
Other Titles of Interest from Westview Press 546
About the Book and Editors . . • . . . . . . 547
Q Tay&l oFrr ancis
Tay&l Forra Gnrcoiusp
�-
http://taylorandfrancis.com
Preface
Methodology drawn from the fields of probability. statistics. and
decision making plays an increasingly important role in the atmos-
pheric sciences. both in basic and applied research and in experi-
mental and operational studies. Applications of such methodology can
be found in almost every facet of the discipline. from the most theo-
retical and global (e.g •• atmospheric predictability. global climate
modeling) to the most practical and local (e.g •• crop-weather model-
ing. forecast evaluation). Almost every issue of the multitude of
journals published by the atmospheric sciences community now contains
one or more papers involving applications of concepts and/or method-
ology from the fields of probability and statistics. Despite the
increasingly pervashe nature of such applications. very few book-
length treatments of probabilistic and statistical topics of parti-
cular interest to atmospheric scientists have appeared (especially in
English) since the publication of the pioneering works of Brooks and
Carruthers (Handbook of Statistical Methods in Meteorology) in 1953
and Panofsky and Brier-(some Applications of:)tat;stics to Meteor-
~) in 1958. As a result. many relathify recent devifopments in
prooibility and statistics are not well known to atmospheric scien-
tists and recent work in active areas of meteorological research
involving significant applications of probabilistic and statistical
methods are not familiar to the meteorological community as a whole.
No single volume could be expected to cover completely the many
probabilistic. statistical. and decision-making topics and applica-
tions of interest and importance to atmospheric scientists. and this
book is no exception. It has been our intention here to place primary
emphasis on two types of contributions: (1) surveys of relatively new
developments in probability and statistics of potential interest to
atmospheric scientists; and (2) reviews of selected areas within the
atmospheric sciences. in which probability and statistics have played
and continue to play important roles. As in all volumes consisting of
contributions from many individuals. the scope and level of treatment
varies from chapter to chapter. However. we believe that the treat-
ment in the various chapters is generally appropriate for the intended
audience - students in atmospheric sciences who have taken at least
one course in probability and statistics and researchers and others in
meteorology familiar through their work with basic concepts and
methods in these fields. Moreover. some topics that undoubtedly will
be new to many readers (exploratory data analysis. decision analysis)
are treated at an introductory level. In all chapters. an effort has
been made to provide readers with extensive lists of references to the
relevant literature for more comprehensive treatments and/or real-
world applications. It is our hope that everyone who examines the
book will find at least one chapter that is of interest and useful.
ix