This site generates 2 plots: one of the posterior plots for each parameter that the user defines...
... and another showing the distribution of all the best fit models that were drawn randomly from the posterior distribution.
While full instructions and explanations can be found here, the following video showing how to use the website might also be useful. In this case a basic linear model and a small data set were used for simplicity.
Instructions for using this page can be found below the input options.
Any results will be available for 15 days following completion.
They will then be deleted, so please download any results that you would like to keep for longer.
Firstly, you must input the model that you want to fit to your data. When inputting this model you can use the standard operators "+", "-", "*" (multiplication), "/" (division). Allowable functions (such as trigonometric functions) and constants are listed below. To raise a value to a given power use either "^" or "**".
When entering the model be careful to use parentheses to group the required parts of the equation. Click here to show an example input model.
2.2*sin(2.0*pi*f*t) + a*t^2 - (exp(2.3)/b)The webpage will parse this information and extract the parameters \(f\), \(t\), \(a\) and \(b\).
Once the model is submitted you can choose each parameter's type:
t(time) value could be such a parameter) that you can input directly or through file upload (uploaded files can be plain ascii text with whitespace or comma separated values). Currently only one parameter can be given as an independent variable, i.e. only one-dimensional models are allowed.
There are currently three prior probability distributions that you can choose for a variable:
Input the data that you would like to fit the model to. You can directly choose to input values directly in the form below (with whitespace or comma separated values), or upload a file containing the data (again with whitespace, or comma separated values). The number of input data points must be the same as the number of values input for the independent variable/abscissa parameter provided above.
There are currently two allowed likelihood functions:
The MCMC aims to draw samples (a chain of points) from the posterior probability distributions of the parameters. You need to tell it how many points to draw. There are three inputs required:
The MCMC algorithm is not guaranteed to produce sensible results every time, and your output may contain errors or look odd. Some information and trouble shooting can be found here.
If users really want to understand what is being done by this code I would advise learning about Bayesian analyses and Markov chain Monte Carlo methods. I would also advise learning python, or another programming language, and coding the analysis up themselves, particularly if you have a more complex problem. However, this site aims to be useful starting point.