Prior Types of Lags

mica2 provides four types of lag (namely, Gaussian center) priors by specifying the option TypeLagPrior in the parameter file.

• Type 0

  The lags overall have a prior range of \((T_0, T_1)\), which are specified by LagLimitLow and LagLimitUpp options. They obey the restrict that \(T_0 < \tau_0 < \tau_1 < \tau_2 <... < T_1\).

  
  

• Type 1

  The lags have prior ranges as:

  \(T_0 + 0*W < \tau_0 < T_0 + 1*W\)

  \(T_0 + 1*W < \tau_1 < T_0 + 2*W\)

  …

  \(W = (T_1 - T_0)/K\), where \(K\) is the number of Gaussians.

  
  

• Type 2

  The lags are fixed at specific values and there is no limit on Guassian sigma.

  \(\tau_0 = T_0 + 0*\Delta T\)

  \(\tau_1 = T_0 + 1*\Delta T\)

  …

  \(\Delta T = (T_1 - T_0)/(K-1)\), where \(K\) is the number of Gaussians.

  
  

• Type 3

  The lags are fixed at specific values and Gaussian sigma ranges at \((\Delta T/2, \Delta T)\).

  \(\tau_0 = T_0 + 0*\Delta T\)

  \(\tau_1 = T_0 + 1*\Delta T\)

  …

  \(\Delta T = (T_1 - T_0)/(K-1)\), where \(K\) is the number of Gaussians.

  
  

• Type 4

  The lags ranges are specified in the option “StrLagPrior” with a format of [lag1_1:lag1_2:lag2_1:lag2_2…]. In this case, “LagLimitLow” and “LagLimitUpp” are no longer applicable.

  
  

For Types 2 and 3, it is better to use a relatively large number of Gaussians.

Note that for top-hat transfer function, the above types are generally similar (amplitude, center, and sigma of Gaussians correspond to amplitude, center, and width of top-hats, respectively), except for type 3, in which the top-hat widths are fixed to be \(\Delta T/2\).