We perform a likelihood analysis of the minimal Anomaly-Mediated Supersymmetry Breaking (mAMSB) model using constraints from cosmology and accelerator experiments. We find that a wino-like or a Higgsino-like neutralino LSP, $m_{tilde chi^0_{1}}$, may provide the cold dark matter (DM) with similar likelihood. The upper limit on the DM density from Planck and other experiments enforces $m_{tilde chi^0_{1}} lesssim 3~TeV$ after the inclusion of Sommerfeld enhancement in its annihilations. If most of the cold DM density is provided by the $tilde chi_0^1$, the measured value of the Higgs mass favours a limited range of $tan beta sim 5$ (or for $mu > 0$, $tan beta sim 45$) but the scalar mass $m_0$ is poorly constrained. In the wino-LSP case, $m_{3/2}$ is constrained to about $900~TeV$ and ${m_{tilde chi^0_{1}}}$ to $2.9pm0.1~TeV$, whereas in the Higgsino-LSP case $m_{3/2}$ has just a lower limit $gtrsim 650TeV$ ($gtrsim 480TeV$) and $m_{tilde chi^0_{1}}$ is constrained to $1.12 ~(1.13) pm0.02~TeV$ in the $mu>0$ ($mu<0$) scenario. In neither case can the anomalous magnetic moment of the muon, ${(g-2)_mu}$, be improved significantly relative to its Standard Model (SM) value, nor do flavour measurements constrain the model significantly, and there are poor prospects for discovering supersymmetric particles at the LHC, {though there} are some prospects for direct DM detection. On the other hand, if the ${m_{tilde chi^0_{1}}}$ contributes only a fraction of the cold DM density, {future LHC $E_T$-based searches for gluinos, squarks and heavier chargino and neutralino states as well as disappearing track searches in the wino-like LSP region will be relevant}, and interference effects enable ${rm BR}(B_{s, d} to mu^+mu^-)$ to agree with the data better than in the SM in the case of wino-like DM with $mu > 0$.
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