Austin rochford open source bayesian inference in python with pymc3

sure! here is an informative tutorial on using austin rochford's open-source bayesian inference library in python with pymc3.

### introduction to pymc3:
pymc3 is a python library for probabilistic programming that allows you to build and analyze bayesian statistical models. it provides a high-level interface for specifying and running bayesian models, making it easier to perform complex probabilistic inference tasks.

### installation:
you can install pymc3 using pip:

### example code:
here is a simple example demonstrating how to use pymc3 to perform bayesian inference on a synthetic dataset:

### explanation:
1. we first generate a synthetic dataset with a true slope of 2 and a true intercept of 5, adding some noise to the data.
2. we then define a bayesian linear regression model in pymc3, specifying priors for the slope, intercept, and noise level.
3. we use the observed data `y` to define the likelihood of the model.

### conclusion:
pymc3 provides a powerful and flexible framework for performing bayesian inference in python. it allows you to easily specify complex bayesian models and perform inference using advanced sampling algorithms. by using pymc3, you can leverage the power of bayesian statistics to make informed decisions based on your data.

i hope this tutorial helps you get started with using pymc3 for bayesian inference. let me know if you have any questions or need further clarification.

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