10.3 Quadratic method

The quadratic approximation, also known as the Laplace method or the normal approximation, consists of approximating the posterior with a Gaussian distribution. To do this, we first find the model of the posterior distribution; numerically, we can do this with an optimization method. Then we compute the Hessian matrix, from which we can then estimate the standard deviation. If you are wondering, the Hessian matrix is a square matrix of second-order partial derivatives. For what we care we can use it to obtain the standard deviation of in general a covariance matrix.

Bambi can solve Bayesian models using the quadratic method for us. In the following code block, we first define a model for the coin-flipping problem, the same one we already defined for the grid method, and then we fit it using the quadratic method, called laplace in Bambi:

Code 10.2

data = pd.DataFrame(data, columns=["w"]) 
priors = {"Intercept": bmb.Prior("Uniform...