With Bayesian statistics, constrained and phenomenological supersymmetric models are examined and compared with the strongest contemporary experimental results, including the Higgs discovery, Large Hadron Collider (LHC) searches for supersymmetry, dark matter relic density measurements, rare decays and electroweak precision tests. Preliminary introductions to relevant supersymmetry phenomenology, Bayesian statistics and algorithms, and comprehensive descriptions of likelihood functions for experimental results are provided. Likelihood functions for searches for supersymmetry at the LHC are built at the event-level from Monte-Carlo simulations, including CMS 35/pb, 1.1/fb and 4.4/fb searches. Five studies of different supersymmetric models, including the Constrained Minimal Supersymmetric Standard Model (CMSSM), the Non-Universal Higgs Model, the Non-Universal Gaugino Model and phenomenological MSSM models, and for different states of knowledge, including hypothetical benchmark scenarios, and pre- and post-Higgs discovery, are comprehensively presented. Credible regions for model parameters, Bayesian evidences, best-fit points and $p$-values are calculated in each study. We demonstrate that the CMSSM's soft-breaking masses could be determined from LHC searches with 100/fb at 14 TeV for a specific favourable choice of parameters consistent with all current constraints. The favoured soft-breaking scale in the CMSSM increases to $M_\text{SUSY} \approx 1$ TeV with stau-coannihilation and $M_\text{SUSY} \approx 3$ TeV with $A$-funnel annihilation. Agreement with the anomalous magnetic moment of the muon ($\delta a_\mu$) is difficult in the CMSSM, and, without $\delta a_\mu$, $\mu<0$ is insignificantly preferred. The CMSSM struggles to simultaneously agree with experimental results - its $p$-value is ostensibly significant. In our pMSSM model with nine free parameters, if the mass of the lightest neutralino is between 200 GeV and 500 GeV, agreement with and electroweakino searches at the LHC is possible.