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Change AR1 likelihood to have correct variance for first observation #3897

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Change AR1 likelihood to have correct variance for first observation #3897

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7 changes: 5 additions & 2 deletions pymc3/distributions/timeseries.py
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Original file line number Diff line number Diff line change
Expand Up @@ -73,9 +73,12 @@ def logp(self, x):

x_im1 = x[:-1]
x_i = x[1:]
boundary = Normal.dist(0., tau=tau_e).logp

innov_like = Normal.dist(k * x_im1, tau=tau_e).logp(x_i)
var_ar1 = 1 / ((1-k**2)*tau_e) #the variance of an AR(1) process
sd_ar1 = tt.sqrt(var_ar1) #the standard deviation of an AR(1) process
boundary = Normal.dist(0., sigma=sd_ar1).logp #likelihood of the first observation

innov_like = Normal.dist(k * x_im1, tau=tau_e).logp(x_i) #likelihood of all adjacent pairs of observations
return boundary(x[0]) + tt.sum(innov_like)

def _repr_latex_(self, name=None, dist=None):
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