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Position(s) Available: Assistant Professor of Mathematics (Tenure-track) in the Department of Mathematics and Computer Science. Responsibilities: Strong commitment for teaching undergraduate and graduate mathematics courses, and developing curricular material and pedagogies. Successful candidates must actively help the department to build its programs. Preference will be given for candidates with a credible research program in algebraic geometry or algebra. Qualifications: Applicants must have an earned doctorate in mathematics by 16 August 2012. The Department: The department offers a bachelor’s and a master’s degree in mathematics and computer science. The department also offers many service and developmental mathematics courses. Application Procedure: Applications should be made electronically at: https://chicagostate.peopleadmin.com/postings/4823 and should include a (1) cover letter (2) curriculum vita, (3) the research agenda, (4) the teaching philosophy and (5) three references. The letters of recommendation commenting on teaching and/or research and inquiries may be sent to: Dawit Getachew, Chair, Search Committee, Department of Mathematics and Computer Science, Chicago State University, 9501 S. King Dr., Chicago, IL 60628, or emailed to Rohan Attele, kattele@csu.edu. Application review begins on 07 March 2012 and will continue until the position is filled. All offers of employment are contingent upon verification of identity, work authorization in the United States, and budgetary approval. Chicago State University is an Equal Opportunity/Affirmative Action Employer. Women and members of groups underrepresented in academia are especially encouraged to apply.

UNIVERSITY OF CALIFORNIA, SANTA BARBARA

Mathematics Department

Temporary Lecturer Position, Inquiry Based Learning

JOB #MATH1201

Areas of Specialization: Algebra, Analysis, Applied Math, Geometry, Number Theory, PDE, Topology

Applications received before April 4, 2012 will be given full consideration.

The Department of Mathematics at University of California, Santa Barbara is seeking applications for a temporary Lecturer in Mathematics. The teaching load is three courses per term (nine courses total on a quarter system), and some teaching will include collaboration with faculty on inquiry-based learning. Candidates with a background in Inquiry Based teaching are sought. Previous post-doctoral experience is preferred, but new Ph.Ds will be also considered. The appointment is for one-year, renewable up to two additional years subject to satisfactory performance and availability of grant funds. Effective date July 1, 2012. Salary is dependent upon qualifications.

The Department is especially interested in candidates who can contribute to the diversity and excellence of the academic community through research, teaching and service.

To apply for this position, applicants should submit a curriculum vitae, statement of teaching philosophy, teaching evaluations (if available), and the American Mathematical Society cover sheet (available online at http://www.ams.org). They should also arrange for three letters of reference to be sent, at least two of which address teaching effectiveness. Materials should either be submitted electronically via http://www.mathjobs.org.

Terms and conditions of employment are subject to UC policy and appropriate bargaining agreements.

Information about the UCSB Mathematics Department is available through the Department's Home Page: http://www.math.ucsb.edu/index.

UCSB is an Equal Opportunity/Affirmative Action Employer.

This is one of my favorite papers:

In applications, statistical models are often restricted to what produces reasonable estimates based on the data at hand. In many cases, however, the principles that allow a model to be restricted can be derived theoretically, in the absence of any data and with minimal applied context. We illustrate this point with three well-known theoretical examples from spatial statistics and time series. First, we show that an autoregressive model for local averages violates a principle of invariance under scaling. Second, we show how the Bayesian estimate of a strictly-increasing time series, using a uniform prior distribution, depends on the scale of estimation. Third, we interpret local smoothing of spatial lattice data as Bayesian estimation and show why uniform local smoothing does not make sense. In various forms, the results presented here have been derived in previous work; our contribution is to draw out some principles that can be derived theoretically, even though in the past they may have been presented in detail in the context of specific examples.

I just love this paper. But it’s only been cited 17 times (and four of those were by me), so I must have done something wrong. In retrospect I think it would’ve made more sense to write it as three separate papers; then each might have had its own impact. In any case, I hope the article provides some enjoyment and insight to those of you who click through.

Publication year: 2012
Source: Computational Statistics & Data Analysis, Available online 4 February 2012

Min Wang, Xiaoqian Sun

We study the problems of hypothesis testing and point estimation for the correlation coefficient between the disturbances in the system of two seemingly unrelated regression equations. An objective Bayesian solution to each problem is proposed based on combined use of the invariant loss function and the objective prior distribution for the unknown model parameters. It is shown that this new solution possesses an invariance property under monotonic reparameterization of the quantity of interest. The performance of the proposed solution is examined through a simulation study. Furthermore, the solution is illustrated by an application to the real annual data for analyzing the investment model.

Some recent blog discussion revealed some confusion that I’ll try to resolve here.

I wrote that I’m not a big fan of subjective priors. Various commenters had difficulty with this point, and I think the issue was most clearly stated by Bill Jeffreys, who wrote:

It seems to me that your prior has to reflect your subjective information before you look at the data. How can it not?

But this does not mean that the (subjective) prior that you choose is irrefutable; Surely a prior that reflects prior information just does not have to be inconsistent with that information. But that still leaves a range of priors that are consistent with it, the sort of priors that one would use in a sensitivity analysis, for example.

I think I see what Bill is getting at. A prior represents your subjective belief, or some approximation to your subjective belief, even if it’s not perfect. That sounds reasonable but I don’t think it works. Or, at least, it often doesn’t work.

Let’s start with a simple example. You hop on a scale that gives unbiased measurements with errors that have a standard deviation of 0.1 kg. To do Bayesian analysis, you assign a N(0,10000^2) prior on your true weight. That doesn’t represent your subjective belief! It’s not even an approximation. No problem—it works fine for most purposes—but it’s not subjective.

More generally, think of all the linear and logistic regressions we use. Instead of thinking of these as subjective beliefs, I prefer to think of the joint probability distribution as a model, reflecting a set of assumptions. In some settings these assumptions represent subjective beliefs, in other settings they don’t.

This article from 2002 might help. If I could go back and alter it, I’d add something on weakly informative priors, but I still agree with the general approach discussed there.

P.S. Just to give an example of what I mean by prior information: The analyses in Red State Blue State all use noninformative prior distributions. But a lot of prior information comes in, in the selection of what questions to study, what models to consider, and what variables to include in the model. For example, as state-level predictors we include region of the country, Republican vote in the previous presidential election, and average state income. Prior information goes into the choice and construction of all these predictors. But the prior distribution is a particular probability distribution that in this case is flat and does not reflect prior knowledge.

One way to think about informative prior distributions is as a form of smoothing: when setting the parameters of a probability distribution based on prior knowledge, we are imposing some time smoothness on the parameters. I think that’s probably a good idea and that the Red State Blue State analyses (among others) would be better for it. I didn’t set up this prior structure because I wasn’t easily equipped to do so and it seemed like too much effort, but perhaps at some future time this sort of structuring will be as commonplace as hierarchical modeling is today.

Jimmy sends in this.

Steps include “Make whimsical sparkles by drawing an ellipse using the Ellipse Tool,” “Rotate the sparkles . . . Give some sparkles less Opacity by using the Transparency Palette,” and “Add a haze around each sparkle by drawing a white ellipse using the Ellipse Tool.”

The punchline:

Now, the next time you need to include a boring graph in one of your designs you’ll be able to add some extra emphasis and get people to really pay attention to those numbers!

P.S. to all the commenters: Yeah, yeah, do your contrarian best and tell me why chartjunk is actually a good thing, how I’m just a snob, etc etc.

de: Research Position [3+ y; PhD in the field of stochastics or Financial Math advantage; profound knowledge of Stat, Financial Math, Monte Carlo simulations and of stochastic differential equations; TvoeD scale; expected to cooperate in applied research projects] / Weierstrass Institute for Applied Analysis and Stochastics; Berlin / deadline February 29