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Bob Jansen
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Chapter2_MorePyMC/MorePyMC.ipynb

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"`some_variable = mc.DiscreteUniform(\"discrete_uni_var\", 0, 4)`\n",
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"where 0,4 are the `DiscreteUniform`-specific upper and lower bound on the random variable. The [PyMC docs](http://pymc-devs.github.com/pymc/distributions.html) contain the specific parameters for stochastic variables. (Or use `??` if you are using IPython!)\n",
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"where 0, 4 are the `DiscreteUniform`-specific upper and lower bound on the random variable. The [PyMC docs](http://pymc-devs.github.com/pymc/distributions.html) contain the specific parameters for stochastic variables. (Or use `??` if you are using IPython!)\n",
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"\n",
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"The `name` attribute is used to retrieve the posterior distribution later in the analysis, so it is best to use a descriptive name. Typically, I use the Python variable's name as the name.\n",
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"source": [
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"Clearly, if $\\tau, \\lambda_1$ and $\\lambda_2$ are known, then $\\lambda$ is known completely, hence it is a deterministic variable. \n",
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"Inside the deterministic decorator, the `Stochastic` variables passed in behave like scalars or Numpy arrays ( if multivariable), and *not* like `Stochastic` variables. For example, running the following:\n",
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"Inside the deterministic decorator, the `Stochastic` variables passed in behave like scalars or Numpy arrays (if multivariable), and *not* like `Stochastic` variables. For example, running the following:\n",
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" @mc.deterministic\n",
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" def some_deterministic(stoch=some_stochastic_var):\n",
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"The *observed frequency* is then the frequency we observe: say rolling the die 100 times you may observe 20 rolls of 1. The observed frequency, 0.2, differs from the true frequency, $\\frac{1}{6}$. We can use Bayesian statistics to infer probable values of the true frequency using an appropriate prior and observed data.\n",
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"With respect to our A/B example, we are interested in using what we know, $N$ (the total trials adminsitered) and $n$ (the number of conversions), to estimate what $p_A$, the true frequency of buyers, might be. \n",
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"With respect to our A/B example, we are interested in using what we know, $N$ (the total trials administered) and $n$ (the number of conversions), to estimate what $p_A$, the true frequency of buyers, might be. \n",
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"To setup a Bayesian model, we need to assign prior distrbutions to our unknown quantities. *A priori*, what do we think $p_A$ might be? For this example, we have no strong conviction about $p_A$, so for now, let's assume $p_A$ is uniform over [0,1]:"
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