Custom Likelihood
While a Bayesian Reference type problem is for data that originate from a functional dependency, \(d = (x_j, y_j)_{j=1...N}\;\) with \(y_j = f(x_j) + \epsilon\), a Custom Likelihood model makes no such assumption.
With a Custom Likelihood, the function \(p(d|\vartheta)\) is given directly by a user-defined model of the form \(f:\; \mathbb{R}^N\rightarrow\mathbb{R}\), where \(N\) is the number of variables.
Likelihood Models
Additive Normal Likelihood
Whereas with an Additive Normal Likelihood, the computational model is assumed to be of the form \(f(x;\vartheta)\), where \(d\) is a set of M given data points. The output of the model represents the values of the function at the given points for which Korali can build a likelihood function \(p(d|\vartheta)\), and a prior probability density \(p(\vartheta)\).
Currently, Korali uses a Normal estimator for the error component of the likelihood calculation, using a statistical-type variable, sigma:
With a Custom Likelihood, the function \(p(d|\vartheta)\) is given directly by a user-defined model of the form \(f:\mathbb{R}^N\rightarrow\mathbb{R}\), where \(N\) is the number of variables.
Usage
e["Problem"]["Type"] = "Bayesian/Custom"
Variable-Specific Settings
These are settings required by this module that are added to each of the experiment’s variables when this module is selected.
- Prior Distribution
Usage: e[“Variables”][index][“Prior Distribution”] = string
Description: Indicates the name of the distribution to use as prior distribution.
- Distribution Index
Usage: e[“Variables”][index][“Distribution Index”] = unsigned integer
Description: Stores the the index number of the selected prior distribution.
- Name
Usage: e[“Variables”][index][“Name”] = string
Description: Defines the name of the variable.
Configuration
These are settings required by this module.
- Likelihood Model
Usage: e[“Problem”][“Likelihood Model”] = Computational Model
Description: Stores the user-defined likelihood model. It should return the value of the Log Likelihood of the given sample.
Variable Defaults
These following configuration will be assigned to each of the experiment variables by default. Any settings defined by the user will override the given settings specified in these defaults.
{ "Distribution Index": 0 }