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abstraction has all the behaviors of the concrete program and that none of these behaviors is unsafe. Since the abstract program is simpler, it is hopefully easier to analyze, but if it is too simple, it will have unsafe behaviors that the original program avoids. Instead of tracking precise variable values, the abstract program tracks only certain predicates of the variables. For example, instead of x, the program may only maintain the predicate x 0. Thus, if the original program branches on the test x 100, the abstract program cannot tell which way to go and must therefore explore both alternatives. For this reason, the abstract program is nondeterministic (i.e., has many possible executions), even though the original program is deterministic (i.e., has only one possible execution). Xia and Hook refer to other work for actually computing the abstract program. Their main contribution is a technique for encoding the abstraction using dependent types. This method appears to work well, since the annotations are small, and the abstraction is easy to extract and verify.

but this may not be enough Statistical software programs may differ in their syntax and in subtle but important details, such as the precedence of operators or the exact speci cation of parameters to statistical functions These idiosyncrasies may raise barriers against researchers who use software different from that of the original author Even if the same software is used in the veri cation, the syntax of the statistical programming language may change over time Mechanisms to allow a statistical software program to declare a legacy syntax and operate under it are rare3 We recommend that researchers who create a veri cation dataset provide the programs used to generate the research But as this may not be enough, we recommend that researchers explicitly write out the model being estimated, using parentheses and brackets where necessary to identify precedence clearly.

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Since syntax for variable transformation and case selection may be idiosyncratic to the version of the statistical software program, we recommend that researchers document these steps of their analysis 11142 Implementation There are often many ways to solve the same problem, and there is no guarantee that algorithms to solve a particular problem are the same across statistical software packages Nor do programs that implement the same algorithms necessarily implement them in an identical manner Methods for computing statistical distributions, generating random numbers, and nding the optima of nonlinear functions may vary across statistical packages and programming languages, and as a consequence may produce varied results (see 3) Many packages offer users a variety of options, and these options and their defaults will not generally be consistent across statistical packages Options may govern the choice of algorithm, implementation, or aspects of both.

oratory/diagnostic services, and hospital care, are often viewed in isolation, as if one sector of the health care economy can be optimized independent of the others (often referred to as the silo mentality) When cost containment is the primary economic objective, a short-term, risk-averse decision framework emerges The focus shifts from optimizing long-term population health outcomes to minimizing short-run medical expenditure for speci c services Such a short-term cost-minimization strategy may be myopic, because many of the advantages and cost savings of medical innovations are actually realized in the long term A recent study provided some evidence of the value of new medicines Lichtenberg used data from the 1996 Medical Expenditure Panel Survey (MEPS) to evaluate the relationship between the age of drugs and mortality, morbidity, and total medical expenditure (Lichtenberg, 2001) The results suggest that, despite higher prices, newer medicines are associated with lower overall medical care expenditures.

Even familiar procedures such as regression may offer implementation-speci c options; for example, the regress command in Stata (v 60) has four options for calculating the standard error of the coef cients Maximum likelihood algorithms have even more options There are over 400 different combinations of algorithmic options and over a dozen continuous parameters that can be used to control the behavior of the MLE solver in Gauss (v 40) Since these options can affect results, any option used in the estimation, even the default, should be noted in the documentation accompany the replication dataset Optimization search algorithms typically simply climb uphill until a maximum is found They are prone to stop when they nd a local optimum of.

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