Diffusive Nested Sampling: Brewer et. al.

Brendon et. al. has a newer version of nested sampling algorithm, they call it Diffusive Nested Sampling (DNS). As the name indicates, it principally differs from the "classic" nested sampling in presenting the hard constraint. It relaxes the hard evolving constraint and lets the samples to explore the mixture distribution of nested probability distributions, each successive distribution occupying e^-1 times the enclosed prior mass of the previously seen distributions. The mixture distribution is weighted at will (a hack :P) which is a clever trick of exploration. This reinforces the idea of "no peaks left behind" for multimodal problems.

On a test problem they claim that DNS "can achieve four times the accuracy of classic Nested Sampling, for the same computational effort; equivalent to a factor of 16 speedup".

I have not played with it yet. However, it seems worth trying. Just a note to myself.

PS:
What can grow out of side talks in a conference?
If you know the power of scrapping in the napkin paper, you would not be surprised.

The paper is available in arxiv:
http://arxiv.org/abs/0912.2380
The code is available at: http://lindor.physics.ucsb.edu/DNest/; comes with handy instructions.

---
Thanks are due to Dr. Brewer for indicating typos in the draft and suggestions + allowing to use the figures.
 The original nested sampling code is available in the book by sivia and skilling: Data Analysis: A Bayesian Tutorial
 

Edit: Sep 5, 2013 An illustrative animation of Diffusive Nested Sampling (www.github.com/eggplantbren/DNest3) sampling a multimodal posterior distribution. The size of the yellow circle indicates the importance weight. The method can travel between the modes because the target distribution includes the (uniform) prior as a mixture component.

Human Body as an Ecosystem and advent of Green Medicine

This sounds fascinating concept; equally impressive to grasp!

In an article published in scientific american, Humans Carry More Bacterial Cells than Human Ones, scientists claim human body to contain more bacterial cell than the human cell itself. So if you have 100 trillion cells in your body,  about the same number of bacteria are are paying you homage. Nice host. Moreover, it has also been reported that they have also contributed to human genes (http://en.wikipedia.org/wiki/Human_Genome_Project, http://www.ornl.gov/sci/techresources/Human_Genome/home.shtml). Strangely, other species seem to have less  connections with bacteria; or may be it is yet to be discovered.

By definition, Ecosystem is a functional unit consisting of living things in a given area, non-living chemical and physical factors of their environment, linked together through nutrient cycle and energy flow. Since they help to maintain various body processes, this makes human as a host and the body as an ecosystem.

We had already learnt that some bacteria were friendly and some were not. Identification of pathogenic bacteria and use of  antibiotic treatment has been hailed as one of the great success in medical history. The side effects of antibiotics are not so unfamiliar and reasoned as  killing off pathogenic as well as friendly bacteria. However, once we are able to understand the ecosystem of human body, curing "infectious" diseases should be just a treat load of another identified bacteria! Shall we call it Green Medicine?

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.