Bayesian Estimation of Parameters

Joachim Köppen Strasbourg 2011

Short explanations:

• we compute the likelihood that an observed data set (a Gaussian curve of given height, width, and position of the centre, subjected to Gaussian noise with a RMS amplitude) is represented by model parameters (Analysis: RMS noise, height, width, center position). Each time, the Compute button is clicked, a new data set is generated. It is shown in the top panel, if onely one parameter is selected for Plot
• the results are shown as the distributions of the likelihood for the parameters which had been selected for plotting: hence it can be a curve in 1D or a false colour map in 2D.
• click on the lower left buttons to select what you want to do:
  • plot select for plotting. If more than 2 parameters are selected, only the first 2 are plotted, while the other ones are held fixed to the value currtly displayed in the field!
  • lock this parameter will have the same value as given as taken for the observed data, in the upper left section
  • enter (grey color) this parameter will be fixed to the value given in this field
  • integ. the likelihood is integrated over the entire range of values for this parameter. This parameter is treated as a "nuisance parameter". As this computation may take some time, the Compute button's magenta colour changes during execution.
• the likelihood densities are shown between the maximum value (normalized to 1) and a minimum value (Ymin givin in log10 value). The button toggles between several values for Ymin.