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Have been analyzed the latest experimental data for $\gamma + p \to K^{+} +\Lambda$ reaction of $C_{x'}$ and $C_{z'}$ double polarizations. In theoreticalcalculation, all of these observables can be classified into four Legendreclasses and represented by associated Legendre polynomial function itself\cite{fasano92}. In this analysis we attempt to determine the best data modelfor both observables. We use the bayesian technique to select the best model bycalculating the posterior probabilities and comparing the posterior among themodels. The posteriors probabilities for each data model are computed using aNested sampling integration. From this analysis we concluded that $C_{x'}$ and$C_{z'}$ double polarizations require two and three order of associatedLegendre polynomials respectively to describe the data well. The extractedcoefficients of each observable will also be presented. It shows the structureof baryon resonances qualitatively

Bayesian Analysis of $C_{x'}$ and $C_{z'}$ Double Polarizations in Kaon Photoproduction