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

Great! you are selected for grad school, now what?

This is one of the post I am writing for the graduate students coming aboard.
First, my congratulations for being selected. Pursuing your dream in higher studies is going to be very important. It is important not only because you get into graduate school but also because it will define your career path for rest of your life.
Your question is regarding whether you wanna go the the university that offered you. If you had carefully selected and applied to the universities, you will have no problem in deciding once you get the offer letter But what if two very competent universities are calling you?
I have the following recommendations (and they apply equally to cases when one is preparing to apply for grad school):

• Visit the University website. Especially, the departmental website. 
• Visit Each faculty website, see the trends in the department research. Are the faculty actively involved in research?
• See if the research field particularly interests you.
• See if you can figure out the number of graduate student to faculty ratio. 
• If your support comes from doing the TA duties, see if you can figure out the number of undergraduate student to graduate student ratio.
• How about the weather? Location? Socialization?

These are the basic questions that you need before you start out your venture. They are important as it will guide your next five years (plus/minus 1) and ultimately your academic life.
Once you figure out such basic academic facts, you can then go for planning the (local) life style there. The best case scenario would be if you have any close friend living nearby. If you can contact the department secretary to learn about the housing, it will also make your life much better. Craiglist listing on apartments can also be equally illuminating.

Survival of the Fittest: Tricks allowed

Surviving in the wild is not easy, especially if you are born to survive in the wild. So, you come up with tricks to survive. You do whatever it takes to survive.
I found few videos, surprisingly awesome!

Cordyceps, a killer fungi, that invades the body of an insect to grow and diminish the insect population. This is one of the Fascinating animal and wildlife video from the BBC epic natural world masterpiece 'Planet Earth'. This video was brought to you by Sir David Attenborough and the Planet Earth team.


The next on is about the Zombie Snails. As written in its description:
... this parasite is called Leucochloridium paradoxum. There are many other "mind-controlling" parasites such as the Spinochordodes Tellinii which infect grasshoppers and forces them to drown themselves... (Where the worm reproduces). Oh and one of my favs is the Toxoplasma Gondii found in cats intestines. But I'll let yall look it up. Savor the knowledge my children.



Who is inside you?
JK!

Ask questions to Physics Nobel Laureate in YouTube

Have you ever wanted to ask a Nobel Laureate a question?
Now, here's your chance! Ask a Nobel Laureate is offering you a unique opportunity to communicate with some of the world´s most brilliant minds.
The current participating Nobel Laureate is Albert Fert, Nobel Prize in Physics 2007 "for the discovery of Giant Magnetoresistance", which forms the basis of the memory storage system found in your computer.

Albert Fert will answer a selection of your uploaded video questions.
Upload your video question no later than March, 19, 2010.
Vote for your favourite questions, and a selection of the most popular questions will be answered by Albert Fert. Video responses will be posted in early April.

From wikipedia:
Albert Fert (born 7 March 1938 in Carcassonne, Aude) is a French physicist and one of the discoverers of giant magnetoresistance which brought about a breakthrough in gigabyte hard disks. He is currently professor at Université Paris-Sud in Orsay and scientific director of a joint laboratory ('Unité mixte de recherche') between the Centre national de la recherche scientifique (National Scientific Research Centre) and Thales Group. Also, he is an Adjunct professor of physics at Michigan State University. He was awarded the 2007 Nobel Prize in Physics together with Peter Grünberg.
 
Head on to:
Ask a Nobel Laureate with Albert Fert
http://www.youtube.com/user/thenobelprize

NobelPrize.org page:
http://nobelprize.org/nobel_prizes/physics/laureates/2007/
Ask questions!!!

"The important thing is not to stop questioning. Curiosity has its own reason for existing."
-Albert Einstein