Confidence interval for poor Chi squared fit

[nicknock]

I have a set of data that consists of about ~1000 data points, each of which has two measurements. I have a series of models with two parameters that I have fit to this data to find the best fitting pair of parameters. There is quite a spread around the best-fitting model, because none of the models are perfect, but this isn't because of the measurement errors, which are known.

Anyway, because the fit is bad, the reduced chi-squared value is much greater than 1. This is ok, its well known that the models aren't perfect. But, is it still possible to calculate the, say 1 sigma, confidence interval on my best fit, and if so, what is the value of Delta Chi-squared I use to calculate this interval when I vary my parameters?

 

[Valkarie]

The answer to your question is yes, it is still possible to calculate the 1 sigma confidence interval on your best fit parameters. The value of Delta Chi-squared that you would use is still 1. It is generally accepted that for a chi-squared statistic with n degrees of freedom, the 1 sigma confidence interval is defined by a change in chi-squared of n. In your case, since you have two parameters, the number of degrees of freedom is two, and so the 1 sigma confidence interval is defined by a change in chi-squared of 2.