This article is reporting the implementation of integrated energy constrained stochastic inversion to Group F Malay Basin reservoir. The technique involved Bayesian seismic inversion which use frequency domain seismic attribute as a constraint instead of time domain seismic amplitude. Maximum Amplitude Weighed Integrated Energy Spectra is proposed energy spectral attribute to be used to constrain the stochastic process. The new attribute is obtained by multiplying integrated energy spectra with maximum amplitude of accordingly seismic trace. It is found that Maximum Amplitude Weighed Integrated Energy Spectra provides a more separable signature in responding bed thickness changes than time domain seismic signature. Therefore, Maximum Amplitude Weighed Integrated Energy Spectra is supposed to be better in detecting seismically thin-bed structure. Its low degree of ambiguity in sensing thin-bed seismic is a potential to increase the vertical resolution and reduce of thin bed interpretation uncertainty. This article incorporates the maximum amplitude weighed integrated energy spectra with a Bayesian seismic inversion by using it to control the degree of match (likelihood) between seismic model and data. It insures that thin-bed structure can be accessed and sufficient resolution result can be attained. An inversion of near and far stack of a Malay Basin's seismic confirm that AVO attribute is better mapped after the seismic are inverted to reflection coefficient or relative acoustic impedance volume rather than from original amplitude. The gas sand penetrated by an appraisal well is detected by reflectivity coefficient AVO cross-plot while it does not appear in the same cross-plot from amplitude.