The Poisson transform for unnormalised statistical models

Contrary to standard statistical models, unnormalised statistical models only specify the likelihood function up to a constant. While such models are natural and popular, the lack of normalisation makes inference much more difficult. Here we show that inferring the parameters of a unnormalised model on a space $\Omega$ can be mapped onto an equivalent problem of estimating the intensity of a Poisson point process on $\Omega$. The unnormalised statistical model now specifies an intensity function that does not need to be normalised. Effectively, the normalisation constant may now be inferred as just another parameter, at no loss of information. The result can be extended to cover non-IID models, which includes for example unnormalised models for sequences of graphs (dynamical graphs), or for sequences of binary vectors. As a consequence, we prove that unnormalised parameteric inference in non-IID models can be turned into a semi-parametric estimation problem. Moreover, we show that the noise-contrastive divergence of Gutmann & Hyv\"arinen (2012) can be understood as an approximation of the Poisson transform, and extended to non-IID settings. We use our results to fit spatial Markov chain models of eye movements, where the Poisson transform allows us to turn a highly non-standard model into vanilla semi-parametric logistic regression

Organic farm incomes in England and Wales 2009/10 (OF 0373)

This report presents results of research on the financial performance of organic farms in 2008/09 and 2009/10 financial years. Carried out for the Department for Environment, Food and Rural Affairs (Defra), this research continues project OF0373 and builds on previous work on the economics of organic farming carried out at Aberystwyth University (Projects OF0190, covering 1995/96 to 1998/99 and OF0189, covering 1999/00 to 2004/05)1. This report utilises data collected through the Farm Business Survey in England and Wales. An analysis of the FBS/Defra Data Archive for 2009/10 found a total of 241 businesses with some organic land, and of these holdings, 189 met the criterion for inclusion within this study by having greater than 70% fully organic certified land. In total, data from 185 organic farms were suitable for inclusion in the analysis. The organic holdings were matched with clusters containing a total of 785 comparable conventional holdings. It was not possible to identify comparable conventional businesses for four organic farms, though the gross margin results from one of these businesses could be utilised. Comparable conventional farms (CCF) were clustered to each organic farm to ensure that the comparison between farming types is based on a similar resource base e.g. similar land area, farm type, region and other factors. This enabled each organic farm to be matched to the average for a conventional farm cluster that comprised data from at least three comparable conventional holdings. The full sample analysis utilised data from 185 organic farms and provides the best comparison of organic and comparable conventional farm income data in 2009/10 (2008/09 data is provided for a non-identical comparison). The profitability (Farm Business Income) of most organic farm types was higher than that of comparable conventional farms. Organic lowland dairy and cropping farm types were considerably more profitable than their conventional comparisons, however, the organic LFA dairy and horticulture (not shown) farm types did not perform as well as conventional systems, mainly as a result of high feed and other livestock costs in LFA dairying and the specialisation/intensity of the comparable conventional horticulture systems, but both farm types had small organic samples which may also have affected the results. Data were also analysed using identical samples and gross margins

Organic farm incomes in England and Wales 2007/08 (OF 0373)

This report presents result of research on the financial performance of organic farms in 2006/07 and 2007/08, carried out for the Department for Environment, Food and Rural Affairs (Defra). This research builds on previous work on the economics of organic farming carried out at Aberystwyth University (Projects OF0190, covering 1995/96 to 1998/99 and OF0189, covering 1999/00 to 2004/05)1. Overall, identicla samples examined over a two year period 2006/07 to 2007/08 show that most organic sectors achieved higher net farm incomes in 2007/08 LFA cattle and sheep farm Net Farm Income (NFI) had the greatest increase,gaining by 46%, with strong gains in cropping and dairying. Organic mixed farming was the only sector to see reduced profitability, the identical sample falling back by 10%, while lowland cattle and sheep farming NFI increased by only 10%. When compared with comparable conventional farms, all organic farming sectors except poultry were above conventional profitability levels in 2007/08

Purification of single-photon entanglement with linear optics

We show that single-photon entangled states of the form |0>|1>+|1>|0> can be purified with a simple linear-optics based protocol, which is eminently feasible with current technology. Besides its conceptual interest, this result is relevant for attractive quantum repeater protocols.Comment: 4 pages, 3 figure

The development and calibration of a generic dynamic absorption chiller model

Although absorption cooling has been available for many years, the technology has typically been viewed as a poorly performing alternative to vapour compression refrigeration. Rising energy prices and the requirement to improve energy efficiency is however driving renewed interest in the technology, particularly within the context of combined cooling, heat and power systems (CCHP) for buildings. In order to understand the performance of absorption cooling, numerous models are available in the literature. However, the complexities involved in the thermodynamics of absorption chillers have so far restricted researchers to creating steady state or dynamic models reliant on data measurements of the internal chiller state, which require difficult-to-obtain, intrusive measurements. The pragmatic, yet fully-dynamic model described in this paper is designed to be easily calibrated using data obtained from the measurements of inflows and outflows to a chiller, without resorting to intrusive measurements. The model comprises a series of linked control volumes featuring both performance maps and lumped mass volumes, which reflect the underlying physical structure of the device. The model was developed for the ESP-r building simulation tool. This paper describes the modelling approach, theory and limitations, along with its calibration and the application of the model to a specific example

Quantum experiments with human eyes as detectors based on cloning via stimulated emission

We show theoretically that the multi-photon states obtained by cloning single-photon qubits via stimulated emission can be distinguished with the naked human eye with high efficiency and fidelity. Focusing on the "micro-macro" situation realized in a recent experiment [F. De Martini, F. Sciarrino, and C. Vitelli, Phys. Rev. Lett. 100, 253601 (2008)], where one photon from an original entangled pair is detected directly, whereas the other one is greatly amplified, we show that performing a Bell experiment with human-eye detectors for the amplified photon appears realistic, even when losses are taken into account. The great robustness of these results under photon loss leads to an apparent paradox, which we resolve by noting that the Bell violation proves the existence of entanglement before the amplification process. However, we also prove that there is genuine micro-macro entanglement even for high loss.Comment: 5 pages, 3 figure

Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening

We present a detailed analysis of a quantum memory for photons based on controlled and reversible inhomogeneous broadening (CRIB). The explicit solution of the equations of motion is obtained in the weak excitation regime, making it possible to gain insight into the dependence of the memory efficiency on the optical depth, and on the width and shape of the atomic spectral distributions. We also study a simplified memory protocol which does not require any optical control fields.Comment: 9 pages, 4 figures (Accepted for publication in Phys. Rev. A

Divide and conquer in ABC: Expectation-Progagation algorithms for likelihood-free inference

ABC algorithms are notoriously expensive in computing time, as they require simulating many complete artificial datasets from the model. We advocate in this paper a "divide and conquer" approach to ABC, where we split the likelihood into n factors, and combine in some way n "local" ABC approximations of each factor. This has two advantages: (a) such an approach is typically much faster than standard ABC and (b) it makes it possible to use local summary statistics (i.e. summary statistics that depend only on the data-points that correspond to a single factor), rather than global summary statistics (that depend on the complete dataset). This greatly alleviates the bias introduced by summary statistics, and even removes it entirely in situations where local summary statistics are simply the identity function. We focus on EP (Expectation-Propagation), a convenient and powerful way to combine n local approximations into a global approximation. Compared to the EP- ABC approach of Barthelm\'e and Chopin (2014), we present two variations, one based on the parallel EP algorithm of Cseke and Heskes (2011), which has the advantage of being implementable on a parallel architecture, and one version which bridges the gap between standard EP and parallel EP. We illustrate our approach with an expensive application of ABC, namely inference on spatial extremes.Comment: To appear in the forthcoming Handbook of Approximate Bayesian Computation (ABC), edited by S. Sisson, L. Fan, and M. Beaumon

Spin-singlet Gaffnian wave function for fractional quantum Hall systems

We characterize in detail a wave function conceivable in fractional quantum Hall systems where a spin or equivalent degree of freedom is present. This wave function combines the properties of two previously proposed quantum Hall wave functions, namely the non-Abelian spin-singlet state and the nonunitary Gaffnian wave function. This is a spin-singlet generalization of the spin-polarized Gaffnian, which we call the "spin-singlet Gaffnian" (SSG). In this paper we present evidence demonstrating that the SSG corresponds to the ground state of a certain local Hamiltonian, which we explicitly construct, and, further, we provide a relatively simple analytic expression for the unique ground-state wave functions, which we define as the zero energy eigenstates of that local Hamiltonian. In addition, we have determined a certain nonunitary, rational conformal field theory which provides an underlying description of the SSG and we thus conclude that the SSG is ungapped in the thermodynamic limit. In order to verify our construction, we implement two recently proposed techniques for the analysis of fractional quantum Hall trial states: The "spin dressed squeezing algorithm", and the "generalized Pauli principle".Comment: 15 pages, 2 figures. Version 3 fixes a typographical error in the Hamiltonian, Eq 3. Version 2 incorporates referee and editorial suggestions. The original title "Putting a Spin on the Gaffnian" was deemed to be too inappropriate for PR