Bayesian Inference Lecture Slides.
The notebook for the lab class can be downloaded from here.
To obtain the lab class in ipython notebook, first open the ipython notebook. Then paste the following code into the ipython notebook
import urllib urllib.urlretrieve('https://github.com/SheffieldML/notebook/blob/master/lab_classes/machine_learning/MLAI_lab4.ipynb', 'MLAI_lab4.ipynb')
You should now be able to find the lab class by clicking
the ipython notebook menu.
There is a YouTube video available of me giving this material at the Gaussian Process Road Show in Uganda.
GPRS Uganda Video
Second half overlaps with the material from this week’s lectures.
Video from 2011 on Gaussian Densities and Bayesian Inference
- Rogers and Girolami Chapter 3: Bayesian Methods Section 3.1-3.3 (pg 95-117)
- Sections 1.2.3 (pg 21-24) of Bishop
- Sections 1.2.6 (start from just past equ 1.64, pg 30-32) of Bishop
- Section 2.3 of Bishop up to top of pg 85 (multivariate Gaussians).
- Section 3.3 of Bishop up to pg 159 (pg 152-159). (Bayesian linear regression)
- Sections 3.7-3.8 of Rogers and Girolami (pg 122-133).
- Section 3.4 of Bishop (pg 161-165).
Univariate Bayesian Inference
Multivariate Bayesian Inference
Bayesian Polynomials on Olympics Data
Learning Outcomes Week 5
- Understand the principal of integrating parameters and how to use Bayes rule to do so.
- Understand the role of the prior distribution.
- In multivariate and univariate Gaussian examples, be able to combine the prior with the likelihood to form a posterior distribution..
- Recognise the role of the marginal likelihood and know its form for Bayesian regression under Gaussian priors.
- Be able to compute the expected output of the model and its covariance using the posterior distribution and the formula for the function.
- Understand the effect of model averaging and its advantages when
making predictions including:
- Error bars
- Regularized prediction (reduces variance)