Inferential, nonparametric statistics to assess the quality of probabilistic forecast systems

Maia, Aline de H. N. and Meinke, Holger and Lennox, Sarah and Stone, Roger (2007) Inferential, nonparametric statistics to assess the quality of probabilistic forecast systems. Monthly Weather Review, 135 (2). pp. 351-362. ISSN 0027-0644

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Many statistical forecast systems are available to interested users. To be useful for decision making, these systems must be based on evidence of underlying mechanisms. Once causal connections between the mechanism and its statistical manifestation have been firmly established, the forecasts must also provide some quantitative evidence of 'quality'. However, the quality of statistical climate forecast systems (forecast quality) is an ill-defined and frequently misunderstood property. Often, providers and users of such forecast systems are unclear about what quality entails and how to measure it, leading to confusion and misinformation. A generic framework is presented that quantifies aspects of forecast quality using an inferential approach to calculate nominal significance levels (p values), which can be obtained either by directly applying nonparametric statistical tests such as Kruskal–Wallis (KW) or Kolmogorov–Smirnov (KS) or by using Monte Carlo methods (in the case of forecast skill scores). Once converted to p values, these forecast quality measures provide a means to objectively evaluate and compare temporal and spatial patterns of forecast quality across datasets and forecast systems. The analysis demonstrates the importance of providing p values rather than adopting some arbitrarily chosen significance levels such as 0.05 or 0.01, which is still common practice. This is illustrated by applying nonparametric tests (such as KW and KS) and skill scoring methods [linear error in the probability space (LEPS) and ranked probability skill score (RPSS)] to the five-phase Southern Oscillation index classification system using historical rainfall data from Australia, South Africa, and India. The selection of quality measures is solely based on their common use and does not constitute endorsement. It is found that nonparametric statistical tests can be adequate proxies for skill measures such as LEPS or RPSS. The framework can be implemented anywhere, regardless of dataset, forecast system, or quality measure. Eventually such inferential evidence should be complemented by descriptive statistical methods in order to fully assist in operational risk management.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Author version not held.
Faculty/School / Institute/Centre: Historic - Faculty of Sciences - No Department (Up to 30 Jun 2013)
Faculty/School / Institute/Centre: Historic - Faculty of Sciences - No Department (Up to 30 Jun 2013)
Date Deposited: 02 Apr 2010 01:50
Last Modified: 14 Oct 2013 00:01
Uncontrolled Keywords: risk management; Monte Carlo method; numerical analysis; Southern Oscillation; nonparametric statistics; meteorology research
Fields of Research (2008): 01 Mathematical Sciences > 0104 Statistics > 010401 Applied Statistics
04 Earth Sciences > 0401 Atmospheric Sciences > 040105 Climatology (excl.Climate Change Processes)
15 Commerce, Management, Tourism and Services > 1503 Business and Management > 150313 Quality Management
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490501 Applied statistics
37 EARTH SCIENCES > 3702 Climate change science > 370202 Climatology
35 COMMERCE, MANAGEMENT, TOURISM AND SERVICES > 3507 Strategy, management and organisational behaviour > 350715 Quality management
Socio-Economic Objectives (2008): D Environment > 96 Environment > 9602 Atmosphere and Weather > 960299 Atmosphere and Weather not elsewhere classified
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