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P.E. Freeman, V. Kashyap, A. Siemiginowska (CfA)
Many astronomers use programs in standard packages to fit parametrized models to their data and to estimate the errors for each model parameter value. But how does one determine if a chosen error-estimation method will yield statistically valid results? In this talk, we review error-estimation techniques, and discuss the conditions that must be met for each to be used properly. We begin with standard frequentist methods currently available to users of Sherpa, the fitting and modeling program of the CIAO software package: {\tt uncertainty} (varying one parameter's value with all other parameter values fixed); {\tt projection} (varying one parameter's value with all other parameter values allowed to float to new best-fit values); and {\tt covariance} (estimating errors using the covariance matrix). We then examine other methods that we plan to incorporate into future versions of CIAO. These include likelihood-based, non-parametric techniques that deal with censored data (survival analysis), as well as Bayesian-based methods such as marginalization (the integration of the likelihood surface in parameter space) and Markov-Chain Monte Carlo (MCMC), the latter of which is especially suitable for complex problems that do not lend themselves to analytic solutions.
The author(s) of this abstract have provided an email address for comments about the abstract: pfreeman@head-cfa.harvard.edu