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rate_model.py
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rate_model.py
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""" Several rate models"""
import pylab as pl
import pymc as mc
def binom(name, pi, p, n):
""" Generate PyMC objects for a binomial model
:Parameters:
- `name` : str
- `pi` : pymc.Node, expected values of rates
- `p` : array, observed values of rates
- `n` : array, effective sample sizes of rates
:Results:
- Returns dict of PyMC objects, including 'p_obs' and 'p_pred' the observed stochastic likelihood and data predicted stochastic
"""
assert pl.all(p >= 0), 'observed values must be non-negative'
assert pl.all(n >= 0), 'effective sample size must non-negative'
@mc.observed(name='p_obs_%s'%name)
def p_obs(value=p, pi=pi, n=n):
return mc.binomial_like(value*n, n, pi+1.e-9)
# for any observation with n=0, make predictions for n=1.e6, to use for predictive validity
n_nonzero = pl.array(n.copy(), dtype=int)
n_nonzero[n==0] = 1.e6
@mc.deterministic(name='p_pred_%s'%name)
def p_pred(pi=pi, n=n_nonzero):
return mc.rbinomial(n, pi+1.e-9) / (1.*n)
return dict(p_obs=p_obs, p_pred=p_pred)
def beta_binom(name, pi, p, n):
""" Generate PyMC objects for a beta-binomial model
:Parameters:
- `name` : str
- `pi` : pymc.Node, expected values of rates
- `p` : array, observed values of rates
- `n` : array, effective sample sizes of rates
:Results:
- Returns dict of PyMC objects, including 'p_obs' and 'p_pred' the observed stochastic likelihood and data predicted stochastic
"""
assert pl.all(p >= 0), 'observed values must be non-negative'
assert pl.all(n >= 0), 'effective sample size must non-negative'
p_n = mc.Uniform('p_n_%s'%name, lower=1.e4, upper=1.e9, value=1.e4) # convergence requires getting these bounds right
pi_latent = [mc.Beta('pi_latent_%s_%d'%(name,i), pi[i]*p_n, (1-pi[i])*p_n, value=pi_i) for i, pi_i in enumerate(pi.value)]
i_nonzero = (n!=0.)
@mc.observed(name='p_obs_%s'%name)
def p_obs(value=p, pi=pi_latent, n=n):
pi_flat = pl.array(pi)
return mc.binomial_like((value*n)[i_nonzero], n[i_nonzero], pi_flat[i_nonzero])
# for any observation with n=0, make predictions for n=1.e6, to use for predictive validity
n_nonzero = pl.array(n.copy(), dtype=int)
n_nonzero[n==0] = 1.e6
@mc.deterministic(name='p_pred_%s'%name)
def p_pred(pi=pi_latent, n=n_nonzero):
return mc.rbinomial(n, pi) / (1.*n)
return dict(p_n=p_n, pi_latent=pi_latent, p_obs=p_obs, p_pred=p_pred)
def poisson(name, pi, p, n):
""" Generate PyMC objects for a poisson model
:Parameters:
- `name` : str
- `pi` : pymc.Node, expected values of rates
- `p` : array, observed values of rates
- `n` : array, effective sample sizes of rates
:Results:
- Returns dict of PyMC objects, including 'p_obs' and 'p_pred' the observed stochastic likelihood and data predicted stochastic
"""
assert pl.all(p >= 0), 'observed values must be non-negative'
assert pl.all(n >= 0), 'effective sample size must non-negative'
i_nonzero = (n!=0.)
@mc.observed(name='p_obs_%s'%name)
def p_obs(value=p, pi=pi, n=n):
return mc.poisson_like((value*n)[i_nonzero], (pi*n)[i_nonzero])
# for any observation with n=0, make predictions for n=1.e6, to use for predictive validity
n_nonzero = pl.array(n.copy(), dtype=float)
n_nonzero[n==0.] = 1.e6
@mc.deterministic(name='p_pred_%s'%name)
def p_pred(pi=pi, n=n_nonzero):
return mc.rpoisson((pi*n).clip(1.e-9, pl.inf)) / (1.*n)
return dict(p_obs=p_obs, p_pred=p_pred)
def neg_binom(name, pi, delta, p, n):
""" Generate PyMC objects for a negative binomial model
:Parameters:
- `name` : str
- `pi` : pymc.Node, expected values of rates
- `delta` : pymc.Node, dispersion parameters of rates
- `p` : array, observed values of rates
- `n` : array, effective sample sizes of rates
:Results:
- Returns dict of PyMC objects, including 'p_obs' and 'p_pred' the observed stochastic likelihood and data predicted stochastic
"""
assert pl.all(p >= 0), 'observed values must be non-negative'
assert pl.all(n >= 0), 'effective sample size must non-negative'
i_zero = (n==0.)
if (isinstance(delta, mc.Node) and pl.shape(delta.value) == ()) \
or (not isinstance(delta, mc.Node) and pl.shape(delta) == ()): # delta is a scalar
@mc.observed(name='p_obs_%s'%name)
def p_obs(value=p, pi=pi, delta=delta, n=n):
return mc.negative_binomial_like(value[~i_zero]*n[~i_zero], pi[~i_zero]*n[~i_zero]+1.e-9, delta)
else:
@mc.observed(name='p_obs_%s'%name)
def p_obs(value=p, pi=pi, delta=delta, n=n):
return mc.negative_binomial_like(value[~i_zero]*n[~i_zero], pi[~i_zero]*n[~i_zero]+1.e-9, delta[~i_zero])
# for any observation with n=0, make predictions for n=1.e9, to use for predictive validity
n_nonzero = n.copy()
n_nonzero[i_zero] = 1.e9
@mc.deterministic(name='p_pred_%s'%name)
def p_pred(pi=pi, delta=delta, n=n_nonzero):
return mc.rnegative_binomial(pi*n+1.e-9, delta) / pl.array(n+1.e-9, dtype=float)
return dict(p_obs=p_obs, p_pred=p_pred)
# TODO: remove this legacy-named method
neg_binom_model = neg_binom
def neg_binom_lower_bound_model(name, pi, delta, p, n):
""" Generate PyMC objects for a negative binomial lower bound model
:Parameters:
- `name` : str
- `pi` : pymc.Node, expected values of rates
- `delta` : pymc.Node, dispersion parameters of rates
- `p` : array, observed values of rates
- `n` : array, effective sample sizes of rates
:Results:
- Returns dict of PyMC objects, including 'p_obs' the observed stochastic
"""
assert pl.all(p >= 0), 'observed values must be non-negative'
assert pl.all(n > 0), 'effective sample size must be positive'
@mc.observed(name='p_obs_%s'%name)
def p_obs(value=p, pi=pi, delta=delta, n=n):
return mc.negative_binomial_like(pl.maximum(value*n, pi*n), pi*n+1.e-9, delta)
return dict(p_obs=p_obs)
def normal_model(name, pi, sigma, p, s):
""" Generate PyMC objects for a normal model
:Parameters:
- `name` : str
- `pi` : pymc.Node, expected values of rates
- `sigma` : pymc.Node, dispersion parameters of rates
- `p` : array, observed values of rates
- `s` : array, standard error of rates
:Results:
- Returns dict of PyMC objects, including 'p_obs' and 'p_pred' the observed stochastic likelihood and data predicted stochastic
"""
assert pl.all(s >= 0), 'standard error must be non-negative'
i_inf = pl.isinf(s)
@mc.observed(name='p_obs_%s'%name)
def p_obs(value=p, pi=pi, sigma=sigma, s=s):
return mc.normal_like(value[~i_inf], pi[~i_inf], 1./(sigma**2. + s[~i_inf]**2.))
s_noninf = s.copy()
s_noninf[i_inf] = 0.
@mc.deterministic(name='p_pred_%s'%name)
def p_pred(pi=pi, sigma=sigma, s=s_noninf):
return mc.rnormal(pi, 1./(sigma**2. + s**2.))
return dict(p_obs=p_obs, p_pred=p_pred)
# FIXME: negative ESS
def log_normal_model(name, pi, sigma, p, s):
""" Generate PyMC objects for a lognormal model
:Parameters:
- `name` : str
- `pi` : pymc.Node, expected values of rates
- `sigma` : pymc.Node, dispersion parameters of rates
- `p` : array, observed values of rates
- `s` : array, standard error sizes of rates
:Results:
- Returns dict of PyMC objects, including 'p_obs' and 'p_pred' the observed stochastic likelihood and data predicted stochastic
"""
assert pl.all(p > 0), 'observed values must be positive'
assert pl.all(s >= 0), 'standard error must be non-negative'
i_inf = pl.isinf(s)
@mc.observed(name='p_obs_%s'%name)
def p_obs(value=p, pi=pi, sigma=sigma, s=s):
return mc.normal_like(pl.log(value[~i_inf]), pl.log(pi[~i_inf]+1.e-9),
1./(sigma**2. + (s[~i_inf]/value[~i_inf])**2.))
s_noninf = s.copy()
s_noninf[i_inf] = 0.
@mc.deterministic(name='p_pred_%s'%name)
def p_pred(pi=pi, sigma=sigma, s=s_noninf):
return pl.exp(mc.rnormal(pl.log(pi+1.e-9), 1./(sigma**2. + (s/(pi+1.e-9))**2)))
return dict(p_obs=p_obs, p_pred=p_pred)
def offset_log_normal(name, pi, sigma, p, s):
""" Generate PyMC objects for an offset log-normal model
:Parameters:
- `name` : str
- `pi` : pymc.Node, expected values of rates
- `sigma` : pymc.Node, dispersion parameters of rates
- `p` : array, observed values of rates
- `s` : array, standard error sizes of rates
:Results:
- Returns dict of PyMC objects, including 'p_obs' and 'p_pred' the observed stochastic likelihood and data predicted stochastic
"""
assert pl.all(p >= 0), 'observed values must be non-negative'
assert pl.all(s >= 0), 'standard error must be non-negative'
p_zeta = mc.Uniform('p_zeta_%s'%name, 1.e-9, 10., value=1.e-6)
i_inf = pl.isinf(s)
@mc.observed(name='p_obs_%s'%name)
def p_obs(value=p, pi=pi, sigma=sigma, s=s, p_zeta=p_zeta):
return mc.normal_like(pl.log(value[~i_inf]+p_zeta), pl.log(pi[~i_inf]+p_zeta),
1./(sigma**2. + (s/(value+p_zeta))[~i_inf]**2.))
s_noninf = s.copy()
s_noninf[i_inf] = 0.
@mc.deterministic(name='p_pred_%s'%name)
def p_pred(pi=pi, sigma=sigma, s=s_noninf, p_zeta=p_zeta):
return pl.exp(mc.rnormal(pl.log(pi+p_zeta), 1./(sigma**2. + (s/(pi+p_zeta))**2.))) - p_zeta
return dict(p_zeta=p_zeta, p_obs=p_obs, p_pred=p_pred)