[MUSIC] In this video, we will see another approach to avoid computing the evidence. It is called the conjugate distributions. Here's our Bayes formula again. Note that a likelihood is fixed by our model, and the evidence is fixed by our data. What we can vary though is a prior, and it is our own choice. So let's select it in the way, let's prove it easier to compute the procedure. The prior is said to be conjugate to the likelihood. If the prior and the posterior lie in the same family of distributions. For example, if the prior was normal parameterized by some parameters mu and sigma, we'd expect the posterior to be also normal but with some other mean end variance. Here's an example. Our likelihood is normal since with around theta with suffix squared and sigma squared. What would be the conjugate prior? Well, what if we choose a normal distribution? Here, I have two normal distributions. What will happen if I multiply them and renormalize in the way that they were integrate to one? Actually, we'll get again a normal distribution. Why does it happen so? The normal distribution is actually a constant times the exponent in the power of some parabola. And when we multiply two long distributions, those two parabolas sum up. And, again, we get another parabola. So the solution to this problem would be a normal distribution. To be a normal of theta, parameterized by some mean m and variance sigma s squared. And the posterior would be also normal, parameterized by some mu mean a and variance b squared. So let's see how it works on a numerical example. Imagine that the likelihood is a normal centered around theta with variance 1, and the prior is a standard normal. That is the mean is 0 and the variance is 1. We can drop all the constants and get the following form. So we have the product of two exponents. You will rearrange the terms, we will get the exponent from which we can easily find out the mean and the variance. The mean will be x squared x half, and the variance would be also half. [MUSIC]