1 \documentclass{article
}
3 \title{CLS: an approach for a new statistical system
}
11 \section{Introduction
}
14 Statisticians who use a computer for data analysis invariably take one
15 of two approaches (considered in the extremes here for illustration):
17 \item the
\emph{FORTRAN
} approach of coding numerical and algorithmic
18 information into the computer program code used for the data
20 \item the
\emph{GUI
} approach, via Microsoft Excel, SPSS, Minitab, and
21 similar approaches, where tasks are facilitated, sometimes with
22 accompanying workflow support.
24 Both approaches have co-existed since the early
80s, with the FORTRAN
25 approach dating back to the dawn of the computing era.
27 \section{Components of a procedure
}
28 \label{sec:components
}
30 Statistics consists of a range of procedures that can be applied to
31 make decisions. However, the range of procedures and resulting
32 interpretation makes it difficult to actually drive a cook-book style
33 approach. But it remains that there is a
color-palette of procedures
34 which can be used to support decision making from collected
37 define a statistical procedure as a decision-making approach which
38 entails the intertwining of formal and informal structure.
40 Components, first pass
42 \item \label{statproc-decision
} Decision to make
43 \item \label{statproc-assessment
} Assessment approach to use (some are
44 inherently different, others just look different): example, T-test
45 is a simplified ANOVA, so look different. Or ML-based (with a
46 hill-climb) vs. ML with a LS fit (look different) vs. bayesian
47 Linear regression (inherently different).
48 \item \label{statproc-normalization
} Normalization of the problem for
49 assessment/comparison with other reference behaviours or
50 probabilistic processes.
51 \item \label{conclusion
} Type of conclusion desired, and instance of
52 that conclusion (when data is present)
55 This forms an
\textit{abstract class
} of a procedure, which can be
56 represented by a real class, which can then be instantiated through
57 the application of data.
59 Components from Gelman:
61 \item design or analysis state (
0th order)
64 \item ??normalization??
66 to characterize the application of a statistical procedure.
69 \label{sec:components:decision
}
71 By example, consider the t-test as an instance of a procedure,
72 representing the general class of testing hypotheses surrounding
2
73 means. Related would be formal likelihood tests with distributions,
74 the superspace/classes from regression and ANOVA.
77 \item are the
2 means the same?
78 \item what is the difference?
79 \item what is the strength of the difference?
82 One component (from Gelman's dicotomy) -- comparison. And decision
83 could equal ( comparsion, extremeness from expectation ).
86 \subsection{Core Assessment
}
87 \label{sec:components:assessment
}
89 This is the construction of the model and parameters that would be
90 used to form the term used to make the assessment. Here, we could
93 \label{eq:assess:ex:
1}
94 \hat{E
}[Y|G=
1] -
\hat{E
}[Y|G=
0]
96 as the fundamental quantity to compare. This can arise from many
97 sources such as regression models
99 \label{eq:assess:ex:
2}
100 Y =
\mu +
\beta G +
\epsilon \\
105 \label{eq:assess:ex:
2}
106 E
[Y|G
] =
\mu +
\beta G
109 \subsection{Normalized Behavior
}
110 \label{sec:components:normbeh
}
111 Let $X=(Y,G)$ from above, the whole data.
113 empirical adjustment:
116 \frac{ \hat\mu_1 -
\hat\mu_0}%
117 {\hat{SE
}(
\hat\mu_1 -
\hat\mu_0)
}
119 or regression-model-based:
123 {\hat{SE
}(
\hat\beta)
}
125 or likelihood-model-based: (FIXME!)
128 -
2 \log \frac{ L(
\hat\beta|X)
}%
131 or score-model-based:
134 \cal{I
}^
{-
1}(
\beta=
0,X) S(
\beta=
0,X)
137 \subsection{Conclusion Desired
}
138 \label{sec:component:conclusion
}
140 Value or Range on the Target Scale (existing parameter describing
141 data-oriented substantive model)
143 Translation of Value/Range on the Decision Scale (what to do, what to
144 decide about the problem, i.e. in a testing framework).
146 \section{Class Implementation
}