Entrance hall of the ICMSMCMC and particle methods: sampling, inference and stochastic approximation

In September 2016, ICMS hosted a workshop on MCMC and particle methods: sampling, inference and stochastic approximation

The increasing popularity of MCMC algorithms and the need to tackle problems of growing complexity have brought high demands on the efficiency of this class of sampling methods, which are often undeniably costly. The answer to such demands has produced both a higher level of sophistication in the design of MCMC algorithms and the introduction of alternative approaches. In particular, the sampling and stochastic approximation landscape has been noticeably enriched by the introduction of Sequential Monte Carlo (SMC) algorithms and (stochastic) Cubature Methods (CM), both of them most often practically implemented in conjunction with the by now renowned particle methods (and with MCMC as well). 

Delegates at the MCMC and particle methods: sampling, inference and stochastic approximation workshop, 2016

 

It was a very busy week with mini-courses and a range of talks as part of the workshop.  During the week Gareth Roberts, (University of Warwick) gave a sold-out public lecture entitled, From tea to infinity: a story of randomised algorithms.  The talk included details of Lady Ottoline’s tea preference (tea first, and then milk) and the 1982 World Cup draw! 

 

Gareth Roberts discusses the thorny issue of tea first, then milk OR milk first, then tea


 

Whilst the workshop was on, we took the opportunity to speak the delegates in a bit more detail.

Antonietta Mira, Università della Svizzera Italiana, Switzerland and Università dell’Insubria, Italy

 

Tell me about today's event and your role in it

I was an invited speaker this morning. I also chaired the afternoon session. The topic of the ICMS workshop is very much in line with my research interests. This is not my first time at ICMS!

What brought you to this area of research?

I have 3 principal advisors and mentors to whom I owe very much. They are the main drivers of me being in this fascinating research area.

Pietro Muliere: I owe him being a statistician. His passion, motivation and insight have been really valuable to me and I hope to be able to transmit these values to my own students. He guided me with patience from my undergraduate studies in economics all the way to my Italian doctorate in statistics and I still enjoy discussing with him interesting problems that he brings to my attention.

Luke Tierney and Charlie Geyer from University of Minnesota-Minneapolis where I got my PhD focusing on computational statistics. Prof Tierney has since moved to the University of Iowa

Other than exploring maths, what are the benefits of taking part?

Collaborating with co-authors who are also here. Getting to know other researcher. Networking and discussing.

What will you take back to your [day job/research/studies]?

New friends and colleagues. New research ideas and insight.  Old friends and old ideas revived and revisited.

Have you met interesting people, and if so, what connections have you made?

Many interesting people. I have invited them to give seminars at my institution and have received invitations to visit them. During the coffee break today I will meet a magician, friend of a colleague, whom I met here for the first time. We will have a magic jam session!

Do you have any advice for first-time ICMS attendees?

Attend all lectures, also the ones that might seem distant from your core research interests to get a multidisciplinary insight. Talk to people and create connections. Do not be afraid to share ideas, ask questions and participate to discussions: your point of view is important!

Have you been to many other conferences? How does ICMS differ?

It helps building a community thanks to the nice and friendly environment and the events (public lectures, receptions, dinner, long breaks) it organizes. The one week format is a good one. This differs from many other workshop conferences that are typically restricted to 3 days. The 2 longer tutorials at this workshop are also useful. Having people staying in the same/close hotels is also a good idea to help creating connections – you meet them for breakfast and you walk back to the hotel together continuing the conversations initiated during the day.

I very much value the support ICMS offers, it is important especially for the early career researchers (but appreciated also for the more established professors).

If you could solve one maths problem, what would it be?

I have a trio of problems relevant for the Data Science revolution that we are bringing forward:

  • Multi- resolution inference,
  • Multi-phase inference,
  • Multi- source inference.

See this article by Prof. Xiao-Li Meng, Department of Statistics, Harvard University. Like all his papers it is really very insightful! Thanks Xiao-Li for feeding our minds.

http://www.stat.harvard.edu/Faculty_Content/meng/COPSS_50.pdf

Do you have any thoughts regarding how we can raise the profile of maths?

I think the profile of math is already raised in the past few years. Many books, events, exhibits. What we should work at is at increasing the profile of probability, statistics, data science. Here is my attempt to achieve this: www.diamoinumeri.ch

Do you have any thought on how diversity in mathematics can be improved?

Diversity is already high at the lower seniority levels: in some countries there are even more female as undergrad and graduate students in math/stat/prob. As we climb up the ladder the proportion changes. It could help to have more women at top/decision levels that would bring a different point of view in decision processes.   Shadowing and mentoring might also help.

Who is your favourite mathematician and why?

Like before, I have 3 favourite contemporary mathematician/statisticians:

  • David Spiegelhalter, aka Prof. Risk, for his effort in increasing public risk awareness. Uncertainty and risk are key (statistical) concepts in everybody’s every day life and people should be better aware of them and learn how to manage and deal with them. I recommend his book, Sex by Numbers: instructive, interesting and fun https://understandinguncertainty.org/sex-numbers
  • Adrian FM Smith, who shares his vision with me on where the world is moving and how (Bayesian) statistics/data science can help push it forward in the right directions trying to make sense out of complex data.
  • Prof. Persi Diaconis, who has fostered my passion for mathematical-magic, among other things.  I recommend his book,

Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks http://press.princeton.edu/titles/9510.html

If we got back in the past I would also mention,

  • Fra Luca Pacioli,  an Italian mathematician Franciscan friar dear friend and collaborator with Leonardo da Vinci. I studied one of his manuscripts: De Viribus Quantitatis ("the power of numbers" is my non-literary translation of the title) a treatise on mathematics and magic written between 1496 and 1508, it contains the first reference to card tricks as well as guidance on how to juggle, eat fire, and make coins dance.

http://www.aboca.com/it/azienda/comunicazione/news/mate-magicahttps://www.youtube.com/watch?v=pnV0Yb1g3s

 

 

Magnus Jamieson, University of Strathclyde.

Magnus is a PhD student at the University of Strathclyde

Tell me about today's event and your role in it

I attended the ICMS MCMC series of workshops as a PhD student looking to broaden my understanding of monte carlo methods with the aim of better using these techniques in my power systems research.

What brought you to this area of research?

Monte-Carlo based methods are widely used in power systems analysis and planning due to the stochastic processes involved and part of my work is going to involve using MCMC-based techniques to project fault rates due to factors such as weather. The MC methods used in power systems rarely are as advanced as the ones discussed over the last few days but it was good to get an understanding of some of the more novel techniques being used today.

Other than exploring maths, what are the benefits of taking part?

Getting to meet people from different disciplines whose skills overlap and seeing the intersections of different disciplines. For instance, comparing how epidemiology employs MCMC could offer my sector some interesting insights into how to model faults cascading throughout a power system.

What will you take back to your [day job/research/studies]? 

The talk on epidemiology's use of MCMC could offer interesting ways of interpreting and modelling faults in a distribution networks, so it's certainly provided food for thought in how I approach my own research.

Have you met interesting people, and if so, what connections have you made?

I attended with my PhD supervisor so spent much of my spare time discussing topics pertaining to that with him. I managed to have some interesting discussions with epidemiologists based at Edinburgh University about the aforementioned subjects!

Do you have any advice for first-time ICMS attendees?

Don't expect to 100% understand all of the mathematics, just try and grasp the concepts.

Have you been to many other conferences? How does ICMS differ?

I've been to a few power-sector conferences and they are often as much about hawking products as they are knowledge exchange, so it was refreshing to attend a conference overtly about dissemination of new knowledge.

If you could solve one maths problem, what would it be?

Cybersecurity is a major issue in the power sector with the increasing prevalence of communications technology in power systems, so solving p=np would help a lot of network engineers sleep a lot easier.

Do you have any thoughts regarding how we can raise the profile of maths?

Initiatives like STEM ambassadors are great for piquing people's interest in the area but I'm really not sure. So much is dependent on teachers' enthusiasm for the subject and how we communicate the "big-picture" but in my experience teaching was very hit-or-miss and people aren't going to engage with a subject they don't enjoy or don't see the relevance of.

Do you have any thought on how diversity in mathematics can be improved?

I'm probably not the best person to ask, to be honest! But one aspect would be to try and ensure people from all incomes and backgrounds are capable of pursuing the discipline, which means better support for working-class pupils and students, and which is as much a political problem as an educational one. Bursaries for students from such backgrounds (and making such students aware of such bursaries, I certainly never was) would be a good blunt-force measure.

Who is your favourite mathematician and why?

He's considered more of a physicist, but physics is essentially just applied mathematics so I would say he counts: I would say Erwin Schrodinger for providing the most accessible thought-experiment in quantum theory. There's an art to turning a convoluted and complex mathematical problem into an easily understood, pub-table friendly metaphor that captures the imagination.

 

 

 

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