title: how to get variable values when there is per item observations
body: <p>I am new to Bayesian statistics and pymc3. In my problem there is workers and reviewers. workers are given a set of questions.Responses given by workers are reviewed by the reviewers.
  So review is the observable variable. Based on those observes I need to calculate the quality of response, ability of worker and bias of reviewer.
  reviews are binary correct(Boolean 1) and incorrect(Boolean 0)
  I created following model using pymc3 and used find_map function to calculate the wanted variables..</p>
  <pre><code>##function
  def predict(ob):
      with pm3.Model() as last:
         quality_precision = pm3.Gamma('quality_precision', 2, 1)
         ability = pm3.Normal(name=&quot;ability&quot;, mu=0, sd=10)
         quality = pm3.Normal(name='quality', mu=ability, sd=1 / np.sqrt(quality_precision))
         reviewer_bias= pm3.Normal(name=&quot;reviewer_bias&quot;, mu=0, sd=5)
         iscorrect = pm3.Binomial('iscorrect',n=1, p=sigmoid(quality + reviewer_bias), observed=ob)
         start = pm3.find_MAP()
     return start
  
  
  
  ##function call
     print(predict([0,1,1,1,1]))
  </code></pre>
  <p>Model
  <a href="https://i.stack.imgur.com/qGIFJ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/qGIFJ.png" alt="enter image description here" /></a></p>
  <p>When I give observations for a particular response it is calculating the quality of that response, workers ability. It also gives a values for reviewer bias. But if the observations are like [0,1,1,1,1] that is from several reviewers. How can I calculate each reviewers bias separately?.</p>
  <p>Again if I have observations of 2 responses. how can I proceed? how to get quality for those responses separately? I can give an observation set a time.. But ability will be calculated only for that response's observations. But ability needed to be calculated for the all reviews given to that persons responses. Help me!</p>