A Simple Approach to Maximum Intractable Likelihood Estimation

Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits maximum-likelihood (or maximum-a-posteriori) inference to be conducted, approximately, using essentially the same techniques. An elementary approach to this problem which simply obtains a nonparametric approximation of the likelihood surface which is then used as a smooth proxy for the likelihood in a subsequent maximisation step is developed here and the convergence of this class of algorithms is characterised theoretically. The use of non-sufficient summary statistics in this context is considered. Applying the proposed method to four problems demonstrates good performance. The proposed approach provides an alternative for approximating the maximum likelihood estimator (MLE) in complex scenarios

How do foreclosures exacerbate housing downturns?

This article uses a structural model to show that foreclosures played a crucial role in exacerbating the recent housing bust and to analyse foreclosure mitigation policy. We consider a dynamic search model in which foreclosures freeze the market for non-foreclosures and reduce price and sales volume by eroding lender equity, destroying the credit of potential buyers, and making buyers more selective. These effects cause price-default spirals that amplify an initial shock and help the model fit both national and cross-sectional moments better than a model without foreclosure. When calibrated to the recent bust, the model reveals that the amplification generated by foreclosures is significant: ruined credit and choosey buyers account for 25.4% of the total decline in non-distressed prices and lender losses account for an additional 22.6%. For policy, we find that principal reduction is less cost-effective than lender equity injections or introducing a single seller that holds foreclosures off the market until demand rebounds. We also show that policies that slow down the pace of foreclosures can be counterproductive.Accepted manuscrip

About the holographic pseudo-Goldstone boson

Pseudo-Goldstone bosons in 4D strongly coupled theories have a dual description in terms of 5D gauge theories in warped backgrounds. We introduce systematic methods of computing the pseudo-Goldstone potential for an arbitrary warp factor in 5D. When applied to electroweak symmetry breaking, our approach clarifies the relation of physical observables to geometrical quantities in five dimensions.Comment: 16 page

Millisecond single-molecule localization microscopy combined with convolution analysis and automated image segmentation to determine protein concentrations in complexly structured, functional cells, one cell at a time

We present a single-molecule tool called the CoPro (Concentration of Proteins) method that uses millisecond imaging with convolution analysis, automated image segmentation and super-resolution localization microscopy to generate robust estimates for protein concentration in different compartments of single living cells, validated using realistic simulations of complex multiple compartment cell types. We demonstrates its utility experimentally on model Escherichia coli bacteria and Saccharomyces cerevisiae budding yeast cells, and use it to address the biological question of how signals are transduced in cells. Cells in all domains of life dynamically sense their environment through signal transduction mechanisms, many involving gene regulation. The glucose sensing mechanism of S. cerevisiae is a model system for studying gene regulatory signal transduction. It uses the multi-copy expression inhibitor of the GAL gene family, Mig1, to repress unwanted genes in the presence of elevated extracellular glucose concentrations. We fluorescently labelled Mig1 molecules with green fluorescent protein (GFP) via chromosomal integration at physiological expression levels in living S. cerevisiae cells, in addition to the RNA polymerase protein Nrd1 with the fluorescent protein reporter mCherry. Using CoPro we make quantitative estimates of Mig1 and Nrd1 protein concentrations in the cytoplasm and nucleus compartments on a cell-by-cell basis under physiological conditions. These estimates indicate a 4-fold shift towards higher values in concentration of diffusive Mig1 in the nucleus if the external glucose concentration is raised, whereas equivalent levels in the cytoplasm shift to smaller values with a relative change an order of magnitude smaller. This compares with Nrd1 which is not involved directly in glucose sensing, which is almost exclusively localized in the nucleus under high and..

Determinantal equations for secant varieties and the Eisenbud-Koh-Stillman conjecture

We address special cases of a question of Eisenbud on the ideals of secant varieties of Veronese re-embeddings of arbitrary varieties. Eisenbud's question generalizes a conjecture of Eisenbud, Koh and Stillman (EKS) for curves. We prove that set-theoretic equations of small secant varieties to a high degree Veronese re-embedding of a smooth variety are determined by equations of the ambient Veronese variety and linear equations. However this is false for singular varieties, and we give explicit counter-examples to the EKS conjecture for singular curves. The techniques we use also allow us to prove a gap and uniqueness theorem for symmetric tensor rank. We put Eisenbud's question in a more general context about the behaviour of border rank under specialisation to a linear subspace, and provide an overview of conjectures coming from signal processing and complexity theory in this context.Comment: 21 pages; presentation improved as suggested by the referees; To appear in Journal of London Mathematical Societ