Contract Adjustment under Uncertainty

Consider a contract over trade in continuous time between two players, according to which one player makes a payment to the other, in exchange for an exogenous service. At each point in time, either player may unilaterally require an adjustment of the contract payment, involving adjustment costs for both players. Players’ payoffs from trade under the contract, as well as from trade under an adjusted contract, are exogenous and stochastic. We consider players’ choice of whether and when to adjust the contract payment. It is argued that the optimal strategy for each player is to adjust the contract whenever the contract payment relative to the outcome of an adjustment passes a certain threshold, depending among other things of the adjustment costs. There is strategic substitutability in the choice of thresholds, so that if one player becomes more aggressive by choosing a threshold closer to unity, the other player becomes more passive. If players may invest in order to reduce the adjustment costs, there will be over-investment compared to the welfare maximizing levels.

Adaptive independent Metropolis--Hastings

We propose an adaptive independent Metropolis--Hastings algorithm with the ability to learn from all previous proposals in the chain except the current location. It is an extension of the independent Metropolis--Hastings algorithm. Convergence is proved provided a strong Doeblin condition is satisfied, which essentially requires that all the proposal functions have uniformly heavier tails than the stationary distribution. The proof also holds if proposals depending on the current state are used intermittently, provided the information from these iterations is not used for adaption. The algorithm gives samples from the exact distribution within a finite number of iterations with probability arbitrarily close to 1. The algorithm is particularly useful when a large number of samples from the same distribution is necessary, like in Bayesian estimation, and in CPU intensive applications like, for example, in inverse problems and optimization.Comment: Published in at http://dx.doi.org/10.1214/08-AAP545 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A class of N nonlinear hyperbolic conservation laws

AbstractThe Riemann problem for a class of nonlinear systems of first order hyperbolic conservation laws is studied. The class consists of systems where the derivative of the flux function is a lower triangular matrix. There are no assumptions on genuine nonlinearity and strict hyperbolicity. Existence and uniqueness are proved except in a set with measure zero in the phase space and a set with measure zero in the flux function space where there is a one-parameter family of solutions. Travelling waves are used as an entropy condition and examples show that the Lax or Liu entropy conditions are not sufficient. An example shows that the solution does not necessarily depend continuously on the data. The model may be used to describe three-phase and tracer flow and flow in a neighborhood of a heterogeneity in porous media

The Genomic HyperBrowser: inferential genomics at the sequence level

The immense increase in the generation of genomic scale data poses an unmet analytical challenge, due to a lack of established methodology with the required flexibility and power. We propose a first principled approach to statistical analysis of sequence-level genomic information. We provide a growing collection of generic biological investigations that query pairwise relations between tracks, represented as mathematical objects, along the genome. The Genomic HyperBrowser implements the approach and is available at http://hyperbrowser.uio.no

A new statistical method for curve group analysis of longitudinal gene expression data illustrated for breast cancer in the NOWAC postgenome cohort as a proof of principle

International audienceA new statistical method for curve group analysis of longitudinal gene expression data illustrated for breast cancer in the NOWAC postgenome cohort as a proof of principle Abstract Background: The understanding of changes in temporal processes related to human carcinogenesis is limited. One approach for prospective functional genomic studies is to compile trajectories of differential expression of genes, based on measurements from many case-control pairs. We propose a new statistical method that does not assume any parametric shape for the gene trajectories. Methods: The trajectory of a gene is defined as the curve representing the changes in gene expression levels in the blood as a function of time to cancer diagnosis. In a nested case–control design it consists of differences in gene expression levels between cases and controls. Genes can be grouped into curve groups, each curve group corresponding to genes with a similar development over time. The proposed new statistical approach is based on a set of hypothesis testing that can determine whether or not there is development in gene expression levels over time, and whether this development varies among different strata. Curve group analysis may reveal significant differences in gene expression levels over time among the different strata considered. This new method was applied as a " proof of concept " to breast cancer in the Norwegian Women and Cancer (NOWAC) postgenome cohort, using blood samples collected prospectively that were specifically preserved for transcriptomic analyses (PAX tube). Cohort members diagnosed with invasive breast cancer through 2009 were identified through linkage to the Cancer Registry of Norway, and for each case a random control from the postgenome cohort was also selected, matched by birth year and time of blood sampling, to create a case-control pair. After exclusions, 441 case-control pairs were available for analyses, in which we considered strata of lymph node status at time of diagnosis and time of diagnosis with respect to breast cancer screening visits. Results: The development of gene expression levels in the NOWAC postgenome cohort varied in the last years before breast cancer diagnosis, and this development differed by lymph node status and participation in the Norwegian Breast Cancer Screening Program. The differences among the investigated strata appeared larger in the year before breast cancer diagnosis compared to earlier years.ConclusionsThis approach shows good properties in term of statistical power and type 1 error under minimal assumptions. When applied to a real data set it was able to discriminate between groups of genes with non-linear similar patterns before diagnosis