What is the conjugate of HCl?
Table of acids and their conjugate bases
| Acid | Conjugate base |
|---|---|
| HCl Hydrochloric acid | Cl− Chloride ion |
| H2SO4 Sulfuric acid | HSO − 4 Hydrogen sulfate ion |
| HNO3 Nitric acid | NO − 3 Nitrate ion |
| H3O+ Hydronium ion | H2O Water |
How to compute the posterior of a conjugate prior?
It means during the modeling phase, we already know the posterior will also be a beta distribution. Therefore, after carrying out more experiments, you can compute the posterior simply by adding the number of acceptances and rejections to the existing parameters α, β respectively, instead of multiplying the likelihood with the prior distribution.
How are conjugate priors useful in machine learning?
Concept of conjugate prior is extremely useful because, conjugate priors reduce the Bayesian updating to only modifying some parameters in the prior distribution. They are also necessary to learn and understand Machine Learning from Bayesian approach. Jupyter notebook used for this post can be found in my GitHub (link below).
When to skip posterior = likelihood * prior computation?
When you know that your prior is a conjugate prior, you can skip the posterior = likelihood * prior computation. Furthermore, if your prior distribution has a closed-form form expression, you already know what the maximum posterior is going to be. In the example above, the beta distribution is a conjugate prior to the binomial likelihood.
Why is a prior conjugate to the likelihood function computationally convenient?
For practical applications, we commonly pick a prior that is computationally convenient. A prior conjugate to the likelihood function is computationally convenient because it is of the same form as the posterior. To understand why this is helpful, let’s deal with the second question.