Return of the Pyschowegians

06/15/2011 at 11:16 pm

In May of 2011, we took a family trip to Norway to learn about the land of our ancestors. The name Fostvedt is Norwegian and my Dad’s grandparents spoke Norwegian at home. So I, and my siblings, are not too far removed from our Norwegian roots. During the course of our trip we visited Oslo, Bergen, TrondheimBodø, Å (Lofoten Islands), Oopdal, Lillehammer, Kristiansand, and Fosstveit. It was the trip of a lifetime and some photos are below.

Asymptotic Results for Configuration Model Random Graphs with Arbitrary Degree Distributions (2010)

09/27/2010 at 10:38 pm

Luke Fostvedt, Dan Nordman, Alyson Wilson

Abstract: We consider a model for generating a random graph using the configuration model. In the configuration model, each node draws a degree independently from a marginal degreed distribution and endpoints pair randomly. We establish non-trivial bounds on the expected sizes of “buckets ” for large graphs. We define nodes i and j in a graph as neighbors if they share an edge, and we define the “bucket ” associated with node i as the set of nodes that are its neighbors and have degree greater than node i. We formalize this argument by providing an analysis for the expected number of items and pairs in a “bucket ” for arbitrarily specified degree distributions, which include power laws.

Paper: Technical Report

Fixed-cost vs. Fixed-risk post-election audits in Iowa

09/12/2010 at 10:31 pm

Jonathan Hobbs, Luke Fostvedt, Adam Pintar, David Rockoff, Eunice Kim, and Randy Griffiths

Electoral integrity has been a forefront issue during the past decade. Policy developments such as voter-verified paper records and post-election audits bolster transparency and voter confidence.

paper: pdf

JSM 2010: An Example of Performance Analysis for Network Community Detection

08/02/2010 at 9:08 pm

Abstract: Community detection algorithms have many applications ranging from search engines on the world wide web to the detection terrorist networks. While the computer scientists are trying to detect “clumpiness” in networks, as statisticians we are analyzing the performance of the algorithm. We pick a node and determine its expected number of neighbors with a degree greater than or equal to this chosen node. This is colloquially referred to the number of nodes in the chosen node’s “bucket”. We show that, for a multigraph with an arbitrary node degree distribution, both the number of nodes in the bucket and the number of pairs of nodes in the bucket are asymptotically finite. This is in contrast to an Erdos Renyi random graph where this quantity increases with O(n).

Poster: JSM 2010 Poster

Measure Theory and Probability Theory Study Guide

12/29/2009 at 9:24 am

Study Guide compiled by Cory Lanker and Luke Fostvedt, Iowa State University
Content includes: Sigma Algebras, Measurable Sets, Lebesgue Measures, Lebesgue Integration, General Lebesgue Integrals, Product Measures, Radon-Nikodym Theorem, Fubini and Tonelli’s theorems, Lebesgue Fundamental Theorem of Calculus, Inequalities, Independence, Borel-Cantelli Lemmas, Law of Large Numbers, Convergence in Probability, Convergence is Distribution, Kolmogorov Theorems, Continuous Mapping Theorem, Tightness, and Method of Moments.

Source: class notes by Dan Nordman, Fall 2009, STAT642, and “Real Analysis” by H. Royden and “Measure Theory” by P.R. Halmos. All references in this document are to Professor Dan Nordman’s class notes.
Content: This study guide is a good supplement to the Athreya Lahiri Text.

Study Guide: Measure Theory and Probability Theory Study Guide