Modelling three biased coins from generated data

Questions
1

Here is an experiment I ran to better understand pymc3. I have three biased coins and I perform the below experiment:

    1. Toss Coin1. If head choose Coin2 else choose Coin3
    2. Randomly choose a number n (between 1 and 10) that implies coin tosses to perform
    3. Toss Coin2/3 (as per 1. above) n times and observe number of heads.
    4. Perform 1,2,3 above multiple times

The ask is given data from above experiment, can we model the three coins ?

Code:
Data Generator:

coin1 = 0.4
coin2 = 0.9
coin3 = 0.1
numberOfDataPoints = 20000
maxTosses = 10
percentOfmaxTosses = 0.65

headTosses = []
totalTosses = []
for i in range(numberOfDataPoints):
    heads = 0
    total = 0
    isCoint2 = random() < coin1
    for rater in range(maxTosses):
        if random() <= percentOfmaxTosses:
            total = total + 1
            if isCoint2:
                if random() < coin2:
                    heads += 1
            else:
                if random() < coin3:
                    heads += 1
    if total > 5:
        headTosses.append(heads)
        totalTosses.append(total)

Model Code:

with pm.Model() as coins:
    coin1 = pm.Beta('coin1',2,2)
    coin2 = pm.Beta('coin2',5,2)
    coin3 = pm.Beta('coin3',2,5)
    first_toss = pm.Bernoulli('first_toss', coin1)
    p = pm.math.switch(first_toss > 0.5, coin2, coin3)
    output = pm.Binomial('output', n=totalTosses, p=p,observed=headTosses)
    exp = pm.sample(10000, tune = 5000)

Results:

* coin1 is found to be decently well modelled
* coin2 seems to be near to the original value
* coin3 is far off

Doubts:

  • Is there anything wrong in the above experiment?
  • Are there better ways to model this experiment?