def gaussian_logpdf(mu,sigma,x):
'''
Non-positive standar deviations will be clipped
'''
mu,sigma,x = map(np.float128,(mu,sigma,x))
x = (x-mu)/sigma
return -0.5*x*x - slog(sigma) - logsqrt2pi
def hmm_poisson_parameter_guess(X,Y,N):
'''
Based on a sequence of inferred states X, estimate the log of
the transition matrix A, the prior vector P, and the state
probability matrix B.
Parameters
----------
X : ndarary
1D integer array of hidden states with values in 0..N-1
Y : ndarary
1D integer array of observations
N : positive integer
Number of states
'''
# Estimate model parameters from best-guess X
p1 = np.mean(X)
p01 = np.sum(np.diff(X)== 1)/(1+np.sum(X==0))
p10 = np.sum(np.diff(X)==-1)/(1+np.sum(X==1))
mu0 = np.mean(Y[X==0])
mu1 = np.mean(Y[X==1])
params = (p1,p01,p10,mu0,mu1)
# Prior for state at first observation
logP = np.array([np.log1p(-p1),slog(p1)])
# State transition array
logA = np.array([
[np.log1p(-p01), slog(p01)],
[slog(p10), np.log1p(-p10)]],
dtype=np.float64)
# Poisson process rates
O = np.arange(N) # List of available states
logB = np.array([
poisson_logpdf(O, mu0),
poisson_logpdf(O, mu1)])
return logP,logA,logB,params
def poisson_logpdf(k,l):
k,l = map(np.float128,(k,l))
return k*slog(l)-l-np.array(map(log_factorial,k))