title: Posterior from joint normal prior distribution
body: <p>I have some basic questions about gaussian inference.</p>
  
  <p>I have following data:</p>
  
  <pre><code>(Log) dose, Number of animals, Number of deaths
  -0.86, 5, 0
  -0.30, 5, 1
  -0.05, 5, 3
  0.73, 5, 5
  </code></pre>
  
  <p>EDIT: I'm assuming a simple regression model for the dose response logit(θ) = α + βx where logit(θ) = log(θ / (1-θ)). θ stands for a probability of death given dose x.</p>
  
  <p>I want to create a joint normal prior distribution on (α,β), with α ∼ N(0,22),β ∼ N(10,102), and corr(α,β) = 0.5 and then calculate the posterior density in a grid of points around the prior (α: 0 ± 4, β: 10 ± 20).</p>
  
  <p>First, I have created joint normal prior distribution following:</p>
  
  <pre><code>import numpy as np
  from scipy import stats
  x = np.array([-0.86, -0.30, -0.05, 0.73])
  n = np.array([5, 5, 5, 5])
  y = np.array([0, 1, 3, 5])
  prior = stats.multivariate_normal([0, 10], [[0.5, 0], [0, 0.5]])
  </code></pre>
  
  <p>Is this right?</p>
  
  <p>Second, how do I calculate posterior density in a grid?</p>