We address the issue of unbiased model selection and propose a methodology based on Bayesian inference to extract physical information from kaon photoproduction $p(gamma,K^+)Lambda$ data. We use the single-channel Regge-plus-resonance (RPR) framework for $p(gamma,K^+)Lambda$ to illustrate the proposed strategy. The Bayesian evidence Z is a quantitative measure for the models fitness given the worlds data. We present a numerical method for performing the multidimensional integrals in the expression for the Bayesian evidence. We use the $p(gamma,K^+)Lambda$ data with an invariant energy W > 2.6 GeV in order to constrain the background contributions in the RPR framework with Bayesian inference. Next, the resonance information is extracted from the analysis of differential cross sections, single and double polarization observables. This background and resonance content constitutes the basis of a model which is coined RPR-2011. It is shown that RPR-2011 yields a comprehensive account of the kaon photoproduction data and provides reasonable predictions for $p(e,e K^+)Lambda$ observables.
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