Evaluated site-specific rate constants for the reactions of isobutane with CH3 and H were determined in a combined analysis of new shock tube experiments and existing literature data. In our shock tube experiments, CH3 radicals, produced from the pyrolysis of di-tert-butylperoxide, and H atoms, produced from the pyrolysis of C2H5I, were reacted with dilute mixtures of isobutane in argon at 870-1130 K and 140-360 kPa, usually with a radical chain inhibitor. Propene and isobutene, measured with GC/FID and MS, were quantified as characteristic of H-abstraction from the primary and tertiary carbons, respectively. Using the method of uncertainty minimization using polynomial chaos expansions (MUM-PCE), a comprehensive Cantera kinetics model based on JetSurF 2.0 was optimized to our experiments and available literature data spanning ambient temperatures to 1327 K. Based on Bayes' theorem, MUM-PCE constrains the kinetics model to the experimental data. The isobutane literature data used for optimization included both raw experimental data and reported branching and total rate measurements. Data for ethane were also included to better define the absolute rate constant for abstraction of H from primary carbons. For both H and CH3, the optimization increased the relative rate of tertiary to primary H-abstraction compared with existing estimates, especially at higher temperatures. We combine the present data for primary and tertiary sites with previous results from our group on 1-butane to derive site-specific rate constants for the reaction of H and CH3 with generic primary, secondary, and tertiary carbons suitable for a wide range of temperatures.