Priors

Background

Priors is shorthand for Prior Probability Distribution. In the Bayesian interpretation of probability, the prior is what you know about your model before you perform the experiment. For instance, you might only know that your rate constants/transition probabilities are faster than once per year and slower than once per femtosecond, but ignoring this in your analysis means you’re not properly handling probabilities.

Specific Priors

Because many of the Bayesian-based modeling methods are related to either a simple Gaussian mixture model (GMM) or a simple hidden Markov model (HMM), they have very similar parameterizations, and thus the same type of priors. In tMAVEN, this is reflected by the re-use of preference variables amongst some of the modeling methods. Generally, the preference variables are specified as modeler.<method name>.prior.<parameter name>.

GMM

These are the default prior values for a variational Bayes GMM. They are for a joint Normal-Gamma distribution and values are taken from the vbFRET emissions. Mixture coefficients are Dirichlet.

Parameter	Value
\(a\) (Gamma)	0.1
\(b\) (Gamma)	0.01
\(\beta\) (Normal)	0.25
\(\pi\) (Mixture)	1.0

HMM

These are thedefault prior values for ebhmm (i.e., ebFRET), vbconhmm (i.e., global vbFRET), and vbhmm (i.e., vbFRET). Emissions are Normal-Gamma, first data-point is Dirichlet, and transition probability for each state is Dirichlet.

Parameter	Value
\(a\) (Gamma)	0.1
\(b\) (Gamma)	0.01
\(\beta\) (Normal)	0.25
\(\alpha\) (Transition probability)	1.0
\(\pi\) (First datapoint)	1.0