The Priors Module

class mogp_emulator.Priors.Prior

Generic Prior Object

d2logpdtheta2(x)

Computes second derivative of log probability at a given value

dlogpdtheta(x)

Computes derivative of log probability at a given value

logp(x)

Computes log probability at a given value

class mogp_emulator.Priors.NormalPrior(mean, std)

Normal Distribution Prior object

Admits input values from -inf/+inf, and no transformations are assumed. Thus, for mean function hyperparameters this produces a normal distribution with given mean and variance, and for covariance/nugget hyperparameters this produces a lognormal distribution with given log mean and variance.

Take two parameters: mean and std. mean can take any numeric value, while std must be positive.

d2logpdtheta2(x)

Computes second derivative of log probability at a given value

dlogpdtheta(x)

Computes derivative of log probability at a given value

logp(x)

Computes log probability at a given value

class mogp_emulator.Priors.GammaPrior(shape, scale)

Gamma Distribution Prior object

Admits input values from -inf/+inf assumed on a logarithmic scale, and transforms by taking the exponential of the input. Thus, this is assumed to be appropriate for covariance hyperparameters where such transformations are assumed when computing the covariance function.

Take two parameters: shape \({\alpha}\) and scale \({\beta}\). Both must be positive, and they are defined such that

\({p(x) = \frac{\beta^{-\alpha}x^{\beta - 1}}{\Gamma(/alpha)} \exp(-x/\beta)}\)

d2logpdtheta2(x)

Computes second derivative of log probability at a given value

dlogpdtheta(x)

Computes derivative of log probability at a given value

logp(x)

Computes log probability at a given value

class mogp_emulator.Priors.InvGammaPrior(shape, scale)

Inverse Gamma Distribution Prior object

Admits input values from -inf/+inf assumed on a logarithmic scale, and transforms by taking the exponential of the input. Thus, this is assumed to be appropriate for covariance hyperparameters where such transformations are assumed when computing the covariance function.

Take two parameters: shape \({\alpha}\) and scale \({\beta}\). Both must be positive, and they are defined such that

\({p(x) = \frac{\beta^{\alpha}x^{-\beta - 1}}{\Gamma(/alpha)} \exp(-\beta/x)}\)

d2logpdtheta2(x)

Computes second derivative of log probability at a given value

dlogpdtheta(x)

Computes derivative of log probability at a given value

logp(x)

Computes log probability at a given value