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Asking questions of the posterior predictive distribution

Add examples of questions that can be asked of the posterior predictive distribution for the hierarchal negative binomial distribution. such as:

  • what is the probability I will respond to David in less than 20 seconds
  • Who are the most likely people I will respond to
  • etc

varnames

For the current pymc3 in pm.traceplot it should be varnames=, not vars=.

Section II Check2: Bayes Factor fails

Running win 10x64, anaconda, python3.5, theano 0.9.0dev4, pymc3 3.0rc4 updated 10-dec-2106.
Have confirmed
pm.switch(tau........
not found.
Perhaps an alternative syntax is used.
Code section and error output follows.
franc

with pm.Model() as model:

# Index to true model
prior_model_prob = 0.5
#tau = pm.DiscreteUniform('tau', lower=0, upper=1)
tau = pm.Bernoulli('tau', prior_model_prob)

# Poisson parameters
mu_p = pm.Uniform('mu_p', 0, 60)

# Negative Binomial parameters
alpha = pm.Exponential('alpha', lam=0.2)
mu_nb = pm.Uniform('mu_nb', lower=0, upper=60)

y_like = pm.DensityDist('y_like',
         lambda value: pm.switch(tau, 
             pm.Poisson.dist(mu_p).logp(value),
             pm.NegativeBinomial.dist(mu_nb, alpha).logp(value)
         ),
         observed=messages['time_delay_seconds'].values)

start = pm.find_MAP()
step1 = pm.Metropolis([mu_p, alpha, mu_nb])
step2 = pm.ElemwiseCategorical(vars=[tau], values=[0,1])
trace = pm.sample(200000, step=[step1, step2], start=start)

_ = pm.traceplot(trace[burnin:], varnames=['tau'])

AttributeError Traceback (most recent call last)
in ()
18 pm.NegativeBinomial.dist(mu_nb, alpha).logp(value)
19 ),
---> 20 observed=messages['time_delay_seconds'].values)
21
22 start = pm.find_MAP()

C:\Anaconda3\lib\site-packages\pymc3\distributions\distribution.py in new(cls, name, *args, **kwargs)
29 data = kwargs.pop('observed', None)
30 dist = cls.dist(*args, **kwargs)
---> 31 return model.Var(name, dist, data)
32 else:
33 raise TypeError("Name needs to be a string but got: %s" % name)

C:\Anaconda3\lib\site-packages\pymc3\model.py in Var(self, name, dist, data)
301 else:
302 var = ObservedRV(name=name, data=data,
--> 303 distribution=dist, model=self)
304 self.observed_RVs.append(var)
305 if var.missing_values:

C:\Anaconda3\lib\site-packages\pymc3\model.py in init(self, type, owner, index, name, data, distribution, model)
584 self.missing_values = data.missing_values
585
--> 586 self.logp_elemwiset = distribution.logp(data)
587 self.model = model
588 self.distribution = distribution

in (value)
14
15 y_like = pm.DensityDist('y_like',
---> 16 lambda value: pm.switch(tau,
17 pm.Poisson.dist(mu_p).logp(value),
18 pm.NegativeBinomial.dist(mu_nb, alpha).logp(value)

AttributeError: module 'pymc3' has no attribute 'switch'

Add poisson regression example

Add poisson regression to the tutorial with covariates such as: day of week, time of day, number of people in conversation etc.

Section 2 fails when trying to sample the model

I am using pymc3 version 3.0 together with anaconda 4.0.0 & python 2.7 and theano 0.8.2.
In the section 2 notebook:

with pm.Model() as model:
    mu = pm.Uniform('mu', lower=0, upper=100)
    y_est = pm.Poisson('y_est', mu=mu, observed=messages['time_delay_seconds'].values)

    y_pred = pm.Poisson('y_pred', mu=mu)

    start = pm.find_MAP()
    step = pm.Metropolis()
    trace = pm.sample(50000, step, start=start, progressbar=True)

Leaving out the y_ptred = ... statement removes the crash but also removes the purpose of the example...

Since I'm trying to learn pymc3 I currently have no idea where to start.
Something goes wrong in theano (strack-trace):

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-12-76dad9c91fda> in <module>()
      7     start = pm.find_MAP()
      8     step = pm.Metropolis()
----> 9     trace = pm.sample(50000, step, start=start, progressbar=True)

C:\Users\egbert\AppData\Local\Continuum\Anaconda\py27_64\lib\site-packages\pymc3\sampling.pyc in sample(draws, step, start, trace, chain, njobs, tune, progressbar, model, random_seed)
    148         sample_func = _sample
    149 
--> 150     return sample_func(**sample_args)
    151 
    152 

C:\Users\egbert\AppData\Local\Continuum\Anaconda\py27_64\lib\site-packages\pymc3\sampling.pyc in _sample(draws, step, start, trace, chain, tune, progressbar, model, random_seed)
    157     progress = progress_bar(draws)
    158     try:
--> 159         for i, strace in enumerate(sampling):
    160             if progressbar:
    161                 progress.update(i)

C:\Users\egbert\AppData\Local\Continuum\Anaconda\py27_64\lib\site-packages\pymc3\sampling.pyc in _iter_sample(draws, step, start, trace, chain, tune, model, random_seed)
    239         if i == tune:
    240             step = stop_tuning(step)
--> 241         point = step.step(point)
    242         strace.record(point)
    243         yield strace

C:\Users\egbert\AppData\Local\Continuum\Anaconda\py27_64\lib\site-packages\pymc3\step_methods\compound.pyc in step(self, point)
     12     def step(self, point):
     13         for method in self.methods:
---> 14             point = method.step(point)
     15         return point

C:\Users\egbert\AppData\Local\Continuum\Anaconda\py27_64\lib\site-packages\pymc3\step_methods\arraystep.pyc in step(self, point)
    116         bij = DictToArrayBijection(self.ordering, point)
    117 
--> 118         apoint = self.astep(bij.map(point))
    119         return bij.rmap(apoint)
    120 

C:\Users\egbert\AppData\Local\Continuum\Anaconda\py27_64\lib\site-packages\pymc3\step_methods\metropolis.pyc in astep(self, q0)
    123             q = q0 + delta
    124 
--> 125         q_new = metrop_select(self.delta_logp(q, q0), q, q0)
    126 
    127         if q_new is q:

C:\Users\egbert\AppData\Local\Continuum\Anaconda\py27_64\lib\site-packages\theano\compile\function_module.pyc in __call__(self, *args, **kwargs)
    869                     node=self.fn.nodes[self.fn.position_of_error],
    870                     thunk=thunk,
--> 871                     storage_map=getattr(self.fn, 'storage_map', None))
    872             else:
    873                 # old-style linkers raise their own exceptions

C:\Users\egbert\AppData\Local\Continuum\Anaconda\py27_64\lib\site-packages\theano\gof\link.pyc in raise_with_op(node, thunk, exc_info, storage_map)
    312         # extra long error message in that case.
    313         pass
--> 314     reraise(exc_type, exc_value, exc_trace)
    315 
    316 

C:\Users\egbert\AppData\Local\Continuum\Anaconda\py27_64\lib\site-packages\theano\compile\function_module.pyc in __call__(self, *args, **kwargs)
    857         t0_fn = time.time()
    858         try:
--> 859             outputs = self.fn()
    860         except Exception:
    861             if hasattr(self.fn, 'position_of_error'):

Section 2 pymc3 error

Section 2 - Model Check II - Bayes Factor

Model fails

14 
  15     y_like = pm.DensityDist('y_like',
---> 16              lambda value: pm.switch(tau, 
  17                  pm.Poisson.dist(mu_p).logp(value),
  18                  pm.NegativeBinomial.dist(mu_nb, alpha).logp(value)

AttributeError: module 'pymc3' has no attribute 'switch'

Found a fix suggested by Cameron Davidson-Pilson which looks like it was intended to be merged into your code (but seems it wasn't?). The suggested revision to lambda works fine.

  y_like = pm.DensityDist('y_like',
               lambda value: pm.math.switch(tau, 
                   pm.Poisson.dist(mu_p).logp(value),
                   pm.NegativeBinomial.dist(mu_nb, alpha).logp(value)
               ),
               observed=messages['time_delay_seconds'].values)

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