Nested Sampling Algorithm (John Skilling)

Nested Sampling was developed by John Skilling (http://www.inference.phy.cam.ac.uk/bayesys/box/nested.pdf // http://ba.stat.cmu.edu/journal/2006/vol01/issue04/skilling.pdf).

Nested Sampling is a modified Markov Chain Monte Carlo algorithm which can be used to explore the posterior probability for the given model. The power of Nested Sampling algorithm lies in the fact that it is designed to compute both the mean posterior probability as well as the Evidence. The algorithm is initialized by randomly taking samples from the prior. The algorithm contracts the distribution of samples around high likelihood regions by discarding the sample with the least likelihood, Lworst.
To keep the number of samples constant, another sample is chosen at random and duplicated. This sample is then randomized by taking Markov chain Monte Carlo steps subject to a hard constraint so that its move is accepted only if the new likelihood is greater than the new threshold, L > Lworst. This ensures that the distribution of samples remains uniformly distributed and that new samples have likelihoods greater than the current likelihood threshold. This process is iterated until the convergence. The logarithm of the evidence is given by the area of the sorted log likelihood as a function of prior mass. When the algorithm has converged one can compute the mean parameter values as well as the log evidence.

For a nice description of Nested Sampling, the book by Sivia and Skilling is highly recommended: Data Analysis: A Bayesian Tutorial.
The  codes in C/python/R with an example of light house problem is available at:
http://www.inference.phy.cam.ac.uk/bayesys/
The paper is available at:
http://www.inference.phy.cam.ac.uk/bayesys/nest.ps.gz

Teaching and Learning: On the Board

How do you learn?
As a student, I have always been inspired by the class environment for teaching and learning.
One of the best way that I could point out is the fact that students learn by the looking at what the teacher is doing to solve the problem. For example, when my teacher was teaching the anatomy of an earthworm, just by looking at the picture, the way he drew it, I mastered it as soon as he finished drawing. Segment by segment, organ by organ. That was one of the amazing experience of biology class with me. By drawing the figure along with hearing the description worked at that time. Similarly, I had a full body size human skeleton system drawn on my wall.  It just worked straight out of board into brain.
So, when people talk about the interactive display of pictures in the biology classes, I feel what if I was in that class. What if my teacher had decided to bring a poster of earthworm instead of drawing it in the borad? could I learn it the same way?
Different students have different ways of learning. That was just one of the several case with me. Some people better learn by looking at the picture while being described. We all learn differently.
There are basic three kinds pointed in literatues:

• kinesthetic
• visual
• auditory

 In the classroom environments with bunch of students with different learning tendencies mixed together, is just like a puzzle spread around the room. An effective teacher is the one who has an art of touching everyone's style. Putting a video from MIT opencourse ware can be fun, but putting a video on the screen might not always be the best way to go.
Being innovative is rewarding because here is the tricky part: they are going to teach your kids some day.
:P