diff --git a/python/likelihoods/likelihood_function.py b/python/likelihoods/likelihood_function.py index fd19675b..5d4e51ce 100644 --- a/python/likelihoods/likelihood_function.py +++ b/python/likelihoods/likelihood_function.py @@ -5,6 +5,9 @@ class student_t(GPy.likelihoods.likelihood_function): """Student t likelihood distribution For nomanclature see Bayesian Data Analysis 2003 p576 + $$\ln(\frac{\Gamma(\frac{(v+1)}{2})}{\Gamma(\sqrt(v \pi \Gamma(\frac{v}{2}))})+ \ln(1+\frac{(y_i-f_i)^2}{\sigma v})^{-\frac{(v+1)}{2}}$$ + TODO:Double check this + Laplace: Needs functions to calculate ln p(yi|fi) @@ -17,6 +20,8 @@ class student_t(GPy.likelihoods.likelihood_function): def link_function(self, y_i, f_i): """link_function $\ln p(y_i|f_i)$ + $$\ln \Gamma(\frac{v+1}{2}) - \ln \Gamma(\frac{v}{2}) - \ln \frac{v \pi \sigma}{2} - \frac{v+1}{2}\ln (1 + \frac{(y_{i} - f_{i})^{2}}{v\sigma})$$ + TODO: Double check this :y_i: datum number i :f_i: latent variable f_i @@ -24,11 +29,15 @@ class student_t(GPy.likelihoods.likelihood_function): """ e = y_i - f_i - return gammaln((v+1)*0.5) - gammaln(v*0.5) - np.ln(v*np.pi*sigma)*0.5 - (v+1)*0.5*np.ln(1 + ((e/sigma)**2)/v) + return gammaln((v+1)*0.5) - gammaln(v*0.5) - np.ln(v*np.pi*sigma)*0.5 - (v+1)*0.5*np.ln(1 + ((e/sigma)**2)/v) #Check the /v! def link_grad(self, y_i, f_i): """gradient of the link function at y_i, given f_i w.r.t f_i + derivative of log((gamma((v+1)/2)/gamma(sqrt(v*pi*gamma(v/2))))*(1+(t^2)/(a*v))^((-(v+1))/2)) with respect to t + $$\frac{(y_i - f_i)(v + 1)}{\sigma v (y_{i} - f_{i})^{2}}$$ + TODO: Double check this + :y_i: datum number i :f_i: latent variable f_i :returns: float(gradient of likelihood evaluated at this point) @@ -40,6 +49,8 @@ class student_t(GPy.likelihoods.likelihood_function): """hessian at this point (the hessian will be 0 unless i == j) i.e. second derivative w.r.t f_i and f_j + second derivative of + :y_i: @todo :f_i: @todo :f_j: @todo