15,227 research outputs found
A Point Decision For Partially Identified Auction Models
This paper proposes a decision theoretic method to choose a single reserve price for partially identified auction models, such as Haile and Tamer, 2003, using data on transaction prices from English auctions. The paper employs Gilboa and Schmeidler, 1989 for inference that is robust with respect to the prior over unidentified parameters. It is optimal to interpret the transaction price as the highest value, and maximize the posterior mean of the seller’s revenue. The Monte Carlo study shows substantial gains relative to the average revenues of the Haile and Tamer interval.
Optimal pricing using online auction experiments: A P\'olya tree approach
We show how a retailer can estimate the optimal price of a new product using
observed transaction prices from online second-price auction experiments. For
this purpose we propose a Bayesian P\'olya tree approach which, given the
limited nature of the data, requires a specially tailored implementation.
Avoiding the need for a priori parametric assumptions, the P\'olya tree
approach allows for flexible inference of the valuation distribution, leading
to more robust estimation of optimal price than competing parametric
approaches. In collaboration with an online jewelry retailer, we illustrate how
our methodology can be combined with managerial prior knowledge to estimate the
profit maximizing price of a new jewelry product.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS503 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Maximum Weight Matching via Max-Product Belief Propagation
Max-product "belief propagation" is an iterative, local, message-passing
algorithm for finding the maximum a posteriori (MAP) assignment of a discrete
probability distribution specified by a graphical model. Despite the
spectacular success of the algorithm in many application areas such as
iterative decoding, computer vision and combinatorial optimization which
involve graphs with many cycles, theoretical results about both correctness and
convergence of the algorithm are known in few cases (Weiss-Freeman Wainwright,
Yeddidia-Weiss-Freeman, Richardson-Urbanke}.
In this paper we consider the problem of finding the Maximum Weight Matching
(MWM) in a weighted complete bipartite graph. We define a probability
distribution on the bipartite graph whose MAP assignment corresponds to the
MWM. We use the max-product algorithm for finding the MAP of this distribution
or equivalently, the MWM on the bipartite graph. Even though the underlying
bipartite graph has many short cycles, we find that surprisingly, the
max-product algorithm always converges to the correct MAP assignment as long as
the MAP assignment is unique. We provide a bound on the number of iterations
required by the algorithm and evaluate the computational cost of the algorithm.
We find that for a graph of size , the computational cost of the algorithm
scales as , which is the same as the computational cost of the best
known algorithm. Finally, we establish the precise relation between the
max-product algorithm and the celebrated {\em auction} algorithm proposed by
Bertsekas. This suggests possible connections between dual algorithm and
max-product algorithm for discrete optimization problems.Comment: In the proceedings of the 2005 IEEE International Symposium on
Information Theor
- …