4. Using EPIC

You can use standard MCMC and Parallel-Tempering MCMC with this program. Besides, there is one experimental adaptive feature to each method that adjusts the covariance of the proposal multivariate Gaussian probability density for optimal efficiency, aiming at an acceptance rate around 0.234. In the PT-MCMC, the adaptation also adjusts the temperature levels of the chains and reduces the number of necessary chains if possible.

In the following sections I guide the user through the two approaches, with typical examples for demonstration.

• 4.1. Before starting
  • Changing the default working directory
  • The parameters names
  • The structure of the .ini file
• 4.2. The datasets
  • Type Ia supernovae
  • CMB distance priors
  • BAO data
  • \(H(z)\) data
  • \(f\sigma_8\) data
  • Including other data
• 4.3. The cosmological models
  • The \(\Lambda\text{CDM}\) model
  • The \(w\text{CDM}\) model
  • Interacting Dark Energy models
    • Proportional to \(\rho_d\)
    • Interacting dark energy in the dark \(SU(2)_R\) model
  • Fast-varying dark energy equation-of-state models
    • Model 1
    • Model 2
    • Model 3
  • Including a new model
• 4.4. Running MCMC
  • Initializing the chains
  • Sampling the posterior distribution
  • Adaptation (beta)
  • Analyzing the chains
    • Additional options
  • Making the triangle plots
    • Additional options
    • Combining two or more simulations in one plot
    • Visualizing chain sequences and convergence
• 4.5. Running PT-MCMC
  • Initializing the chains
  • Sampling the posterior distribution
  • Analyzing the chains
  • Adaptation (beta)