If a model does not overload BCModel::LogAPrioriProbability, then its prior is the product of the individual priors for each of its parameters. We call these the factorized priors. To set a parameter's prior call

BCParameter::SetPrior(BCPrior* const prior);

You can call factorized priors within your overloaded LogAPrioriProbability by querying the log of the prior of a particular parameter with

BCParameter::GetLogPrior(double x)

The prior you set for a parameter need only inherit from BCPrior. BAT has several built in prior classes, such as BCConstantPrior and BCGaussianPrior. You can implement new factorized priors by inheriting from the BCPrior class. To illustrate how to do this, we will work through the construction of the Gaussian prior:

class BCGaussianPrior : public BCPrior

BCPrior is a pure-virtual class with three methods that must be overloaded:

double GetLogPrior(double x);
BCPrior* clone() const;
bool IsValid() const;

The first one contains the meat of our new prior:

double GetLogPrior(double x)
{
  return -0.5 * (x - fMean) * (x - fMean) / fSigma / fSigma - log(fSigma) - 0.5 * log(2 * M_PI);
}

This is, naturally, the log of a Guassian prior. The second one should simply return a copy of the prior:

BCPrior* clone() const
{
  return new BCGaussianPrior(*this);
}

The last function is required for checking that everything that is needed by the prior is properly set. You'll notice that our example calls on two member variables in its GetLogPrior: fMean and fSigma. So we must check whether they have been properly set:

bool IsValid() const
{
  return std::isfinite(fMean) and std::isfinite(fSigma) and fSigma > 0;
}

This checks that the mean and standard deviation are both finite and that the standard deviation is positive semi-definite, as it need be.

Naturally to be of use, we also create a constructor that allows us to set the mean and standard deviation at creation; and getters and setters that allow us to access them. (See the source code of BCGaussianPrior for their implementation.)

This is all that is required to create a new prior. BCPrior has several methods for getting properties of the prior: the mode; the integral over a range; the \(n\)'th raw, central, and standardized moments; the mean; the variance; the standard deviation; the skewness; and the kurtosis. These functions make their own internal calculations and need not be overloaded. If you wish to speed them up, or provide exact results, you may overload them. But take care that you overload them to give back proper results! For example, the mode of the Gaussian distribution is not simply fMean, since this presumes the range over which we query contains fMean. The more proper implementation is

double GetMode(double xmin, double xmax)
{
  if (fMean < xmin)
    return xmin;
  if (fMean > xmax)
    return xmax;
  return fMean;
}