Why does statistics have two theories?

The public image of statistics is changing, and recently the changes have been mostly for the better, as we’ve all seen. But occasional court cases, a few conspicuous failures, and even appeals to personal feelings suggest that careful thought may be in order. Actually, statistics itself has more th...

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Bibliographic Details
Published inPast, Present, and Future of Statistical Science pp. 261 - 276
Format Book Chapter
LanguageEnglish
Published Chapman and Hall/CRC 2014
Subjects
CVT
Observed Likelihood Function
Simple Scalar Model
MCMC
Jeffreys Prior
Location Model
Data Dependent Priors
Regular Models
Violates
Pivotal Quantity
Observed Log Likelihood Function
Bayes Approach
Curved Parameters
Interest Parameter
Confidence Calculation
Canonical Parameter
Distribution Function
Transformation Parameter Models
Bootstrap Distribution
Bayes Inference
Log Likelihood Ratio
Linear Parameter
Home Town
Exponential Model
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DOI10.1201/b16720-29

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Summary:The public image of statistics is changing, and recently the changes have been mostly for the better, as we’ve all seen. But occasional court cases, a few conspicuous failures, and even appeals to personal feelings suggest that careful thought may be in order. Actually, statistics itself has more than one theory, and these approaches can give contradictory answers, with the discipline largely indifferent. Saying “we are just exploring!” or appealing to mysticism can’t really be appropriate, no matter the spin. In this paper for the COPSS 50th Anniversary Volume, I would like to examine three current approaches to central theory. As we will see, if continuity that is present in the model is also required for the methods, then the conflicts and contradictions resolve.
DOI:10.1201/b16720-29