## Pacific Northwest Statistics Seminar

- Date: 10/14/2011

University of Victoria

**Circular Distributions and Fisheries Models**

On Friday October 14, 2011, we are holding the Pacific Northwest Seminar in honour of Dr. Bill Reed who retired from the University of Victoria on July 1, 2011. The seminars will focus on two areas that Bill has worked in: assessing goodness-of-fit and applied statistics. Michael Stephens will offer a theoretical discussion of assessing the fit of circular distributions and emerging issues in this field. Jon Schnute will discuss applied fisheries models and will look at what further research is required in this area.

### Abstracts

**Dr. Jon Schnute,** *Adjunct Professor, UBC Fisheries Centre*

**Title:**

Mathematics and Ecology: Heavenly Marriage, Shotgun Wedding, or Impending Divorce?

**Abstract:**

Mathematics and ecology have a natural affinity through the concept of quantity. For example, the question “How many fish are alive in the sea right now?” has a quantitative answer that depends on precise definitions of “fish”, “alive”, “the sea”, and “right now”. If an ecologist tries to answer this question, she will probably solicit the help of a mathematician or statistician who knows something about sampling theory (a heavenly marriage). If she applies for funding and the proposal doesn’t include a mathematical component, she probably won’t get any money unless that component is added (a shotgun wedding). I can now reveal that, based on my definitions, the answer to this question is 12,288,052,987,972 fish. When she discovers that I’ve played a sneaky mathematical trick to give an utterly false sense of precision and accuracy, she will probably fire me (an impending divorce).

In this talk, I’ll trace the role of mathematics as a descriptor of the real world, quickly citing the work of famous scientists, including: Nicolaus Copernicus, Tycho Brahe, Galileo Galilei, Johannes Kepler, René Descartes, Isaac Newton, Leonhard Euler, Carl Friedrich Gauss, Florence Nightingale, Bernhard Riemann, Ludwig Boltzmann, Albert Einstein, Richard Feynman, and Steven Weinberg. From there, I’ll move to somewhat more familiar territory among the mathematical and ecological communities at the University of Victoria with a discussion of work by Carlo Cercignani, Marvin Shinbrot, Reinhard Illner, Buzz Holling, Carl Walters, Colin Clark, and the celebrated Bill Reed.

What has this generation of ecologically oriented mathematicians accomplished? What natural limits apply to mathematical descriptions of ecology? In what directions should students and future scientists focus their research? You might want to attend this lecture, if only to watch me self-destruct as I attempt to cover so much territory in a single lecture.

**Dr. Michael Stephens**, *Professor Emeritus, Department of Statistics and Actuarial Science, Simon Fraser University*

**Title:**

a) Rayleigh's Test: A discrete look at the drunken man, and b) Testing Benford's Law

**Abstract:**

An interesting correspondence between Karl Pearson and Lord Rayleigh took place in 1905 in the pages of Nature. Suppose a man takes successive steps with random orientation. Pearson wanted to know how far he would be from the starting point 0 after N steps. Suppose this distance is R. Lord Rayleigh gave a large-N solution, and the next year Kluyver gave a full mathematical solution. Pearson's question has become known as the problem of the drunken man. The size of R, for large N, is often used to test if directions are uniform around a circle. This is called Rayleigh's test. The distribution of R has importance in studying directional data, and the von Mises distribution.

Sometimes, in applied statistics, directions are grouped into cells of angular width, say, 10 or 20 degrees, and all the directions in the cell are regarded as placed at the midpoint. New results will be given on the distribution of R for such data. An interesting conjecture arises.

The second problem concerns testing fit for Benford's Law, which gives a discrete distribution for the nine possible first significant digits of sets of numbers. Work with Mary Lesperance and Bill Reed to test if data follows Benford's Law will be described.

**1:30-2:00pm**

**Registration and poster setup** in the common area outside of room A240 in the Human and Social Development building.

**Poster Session and Student Poster Competition:**

Posters can be put up for presentation in the common area outside of **HSD A240**. Along with the poster session we will host a student poster competition. A PIMS prize of $500.00 will be awarded to the winner. Please email Laura Cowen [lcowen at uvic.ca] if you would like to present a poster and indicate if you are a graduate student who would like to enter the competition.

**2:00-3:00pm**

**Dr. Jon Schnute**, Adjunct Professor, UBC Fisheries Centre

**3:00-4:00pm**

**Poster session and refreshments.**

**4:00-5:00pm**

**Dr. Michael Stephens**, Professor Emeritus, Department of Statistics and Actuarial Science, Simon Fraser University

**5:30-…**

**Reception and dinner** (covered by registration fee, no-host cash bar), Cadboro Commons building in the Village Greens cafeteria.

### Registration

For space and catering purposes please email Laura Cowen [lcowen at uvic.ca] by October 5th, 2011 if you plan to attend the meeting and dinner. The buffet dinner will include vegetarian dishes but if you have other dietary concerns please let us know and we will attempt to accommodate.

Registration cost is **$68.00 (US $68.00)** including HST or **$45.00 (US $45.00)** for graduate students which includes the buffet dinner at Cadboro Commons. **Receipts will be handed out at the meeting on October 14th. **

**Online registration is now available. To register as a Graduate Student, please follow this link. To register at the regular rate of $68 USD please use the registration module below by clicking "Sign Up".**

### Building Locations

**Conference site: HSD A240**

The Health and Social Development building is located within the ring road on the west side of campus (the nearest parking is lot 6, accessible from the Ring Road).

http://www.uvic.ca/buildings/hsd.html

**Cadboro Commons**

Cadboro Commons is located outside of the ring road on the east side of campus across from the library (the nearest parking is lot 5, close to the residences accessible from Sinclair Road).

http://www.uvic.ca/buildings/com.html

Maps for the campus are located at:

http://www.uvic.ca/students/undergraduate/explore/maps

### Accommodation

For those who will spend the evening in Victoria or wish to extend their stay to the weekend we have secured conference rates at the following hotels.

**Executive House Hotel**

http://www.executivehouse.com/

Toll Free 1-800-663-7001

Tel 250-388-5111

Fax 250-385-1323

Guestrooms for $79.00/night plus tax single occupancy, $89.00/night plus tax double occupancy. When making a registration tell them you are eligible for the government rate.

**Inn at Laurel Point**

680 Montreal Street

Victoria, BC

V8V 1Z8

250.386.8721 or 1.800.663.7667

Guestrooms for $99.00/night plus tax single or double occupancy in the Laurel Wing; $120.00/night in the deluxe wing. When making reservations identify yourself as being with the **Pacific Northwest Statistics Meeting**. This rate will be extended for 2 days. **The cutoff for obtaining this rate is Friday, September 23, 2011**.

### Bus transportation from downtown Victoria to UVic:

Bus numbers **14** (on Douglas at View, on Fort at Douglas) and **15** (on Fort at Blanshard on Fort at Douglas) run between downtown and UVic. For more information on schedules and routes look at:

http://www.bctransit.com/regions/vic/