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### 4.2 Options for p-value Computations

The methods calc_nested_lrt_pvalue and calc_lrt_pvalue use the Dvegas library to compute p-values by numerical Monte Carlo integration. The details of the numerical integration and other operations related to the computation of p-values can be configured with the following Fitter methods:

double inner_region_fraction()
void inner_region_fraction(double f)
These methods return or set the initial fraction of sample points that are thrown in the “inner region” of the integral, where no non-zero contributions are expected (within some approximation). For details see the discussion in [arXiv:1207.1446]. The default setting is 0.1.
double inner_region_power()
void inner_region_power(double alpha)
These methods return or set the exponent \alpha appearing in the probability density function for the inner region. For details see the discussion in [arXiv:1207.1446]. The default setting is 1.
int dvegas_verbosity()
void dvegas_verbosity(int n)
These methods return or set the verbosity level of the numerical integration. If set to 0, no output is produced. Values of 1 to 3 print increasing amounts of information on std::cout. The default setting is 0.
int dvegas_nbins()
void dvegas_nbins(int n)
These methods return or set the number of bins used in the VEGAS adaptation. More information can be found in the Dvegas documentation. The default setting is 50.
int dvegas_nfirstshots()
void dvegas_nfirstshots(int n)
These methods return or set the number of sample points (shots) for the first iteration of the VEGAS algorithm. The default setting is 1000.
int dvegas_nshots()
void dvegas_nshots(int n)
These methods return or set the number of sample points (shots) for all subsequent iterations of the VEGAS algorithm. The default setting is 500.
int dvegas_niterations()
void dvegas_niterations(int n)
These methods return or set the maximum number of VEGAS iterations which are performed before terminating the calculation and returning the result. The default setting is 20.
double dvegas_precision()
void dvegas_precision(double p)
These methods return or set the desired relative precision of the p-value computation. If this relative precision is reached the integration is terminated and the result is returned. The default setting is 0.01.
double orthogonalization_tolerance()
void orthogonalization_tolerance(double t)
To construct the model hyperplane (see [arXiv:1207.1446]) from the derivatives of the observables with respect to the parameters, the Fitter class uses the Gram Schmidt orthogonalisation algorithm. These methods return or set the tolerance for the orthogonalisation, i.e. the minimum length of a vector for which it is considered unequal to zero. Remeber that, internally, all derivatives are multiplied with the scale of the corresponding parameter. The default setting is 10^-6.