A categorical foundation for Bayesian probability

Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \rightarrow D$, there is a corresponding inference map $I: D \rightarrow H$ which is unique up to a set of measure zero. Thus, given a data measurement $\mu: 1 \rightarrow D$, a posterior probability $\widehat{P_H}= I \circ \mu$ can be computed. This procedure is iterative: with each updated probability $P_H$, we obtain a new joint distribution which in turn yields a new inference map $I$ and the process repeats with each additional measurement. The main result uses an existence theorem for regular conditional probabilities by Faden, which holds in more generality than the setting of Polish spaces. This less stringent setting then allows for non-trivial decision rules (Eilenberg--Moore algebras) on finite (as well as non finite) spaces, and also provides for a common framework for decision theory and Bayesian probability.Comment: 15 pages; revised setting to more clearly explain how to incorporate perfect measures and the Giry monad; to appear in Applied Categorical Structure

Computations in non-commutative Iwasawa theory

We study special values of L-functions of elliptic curves over Q twisted by Artin representations that factor through a false Tate curve extension $Q(\mu_p^\infty,\sqrt[p^\infty]{m})/Q$. In this setting, we explain how to compute L-functions and the corresponding Iwasawa-theoretic invariants of non-abelian twists of elliptic curves. Our results provide both theoretical and computational evidence for the main conjecture of non-commutative Iwasawa theory.Comment: 60 pages; with appendix by John Coates and Ramdorai Sujath

Bayes and health care research.

Bayes’ rule shows how one might rationally change one’s beliefs in the light of evidence. It is the foundation of a statistical method called Bayesianism. In health care research, Bayesianism has its advocates but the dominant statistical method is frequentism. There are at least two important philosophical differences between these methods. First, Bayesianism takes a subjectivist view of probability (i.e. that probability scores are statements of subjective belief, not objective fact) whilst frequentism takes an objectivist view. Second, Bayesianism is explicitly inductive (i.e. it shows how we may induce views about the world based on partial data from it) whereas frequentism is at least compatible with non-inductive views of scientific method, particularly the critical realism of Popper. Popper and others detail significant problems with induction. Frequentism’s apparent ability to avoid these, plus its ability to give a seemingly more scientific and objective take on probability, lies behind its philosophical appeal to health care researchers. However, there are also significant problems with frequentism, particularly its inability to assign probability scores to single events. Popper thus proposed an alternative objectivist view of probability, called propensity theory, which he allies to a theory of corroboration; but this too has significant problems, in particular, it may not successfully avoid induction. If this is so then Bayesianism might be philosophically the strongest of the statistical approaches. The article sets out a number of its philosophical and methodological attractions. Finally, it outlines a way in which critical realism and Bayesianism might work together. </p

Evaluation of two lyophilized molecular assays to rapidly detect foot-and-mouth disease virus directly from clinical samples in field settings

Accurate, timely diagnosis is essential for the control, monitoring and eradication of foot‐and‐mouth disease (FMD). Clinical samples from suspect cases are normally tested at reference laboratories. However, transport of samples to these centralized facilities can be a lengthy process that can impose delays on critical decision making. These concerns have motivated work to evaluate simple‐to‐use technologies, including molecular‐based diagnostic platforms, that can be deployed closer to suspect cases of FMD. In this context, FMD virus (FMDV)‐specific reverse transcription loop‐mediated isothermal amplification (RT‐LAMP) and real‐time RT‐PCR (rRT‐PCR) assays, compatible with simple sample preparation methods and in situ visualization, have been developed which share equivalent analytical sensitivity with laboratory‐based rRT‐PCR. However, the lack of robust ‘ready‐to‐use kits’ that utilize stabilized reagents limits the deployment of these tests into field settings. To address this gap, this study describes the performance of lyophilized rRT‐PCR and RT‐LAMP assays to detect FMDV. Both of these assays are compatible with the use of fluorescence to monitor amplification in real‐time, and for the RT‐LAMP assays end point detection could also be achieved using molecular lateral flow devices. Lyophilization of reagents did not adversely affect the performance of the assays. Importantly, when these assays were deployed into challenging laboratory and field settings within East Africa they proved to be reliable in their ability to detect FMDV in a range of clinical samples from acutely infected as well as convalescent cattle. These data support the use of highly sensitive molecular assays into field settings for simple and rapid detection of FMDV

A probabilistic analysis of argument cogency

This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align

The three-dimensional Anderson model of localization with binary random potential

We study the three-dimensional two-band Anderson model of localization and compare our results to experimental results for amorphous metallic alloys (AMA). Using the transfer-matrix method, we identify and characterize the metal-insulator transitions as functions of Fermi level position, band broadening due to disorder and concentration of alloy composition. The appropriate phase diagrams of regions of extended and localized electronic states are studied and qualitative agreement with AMA such as Ti-Ni and Ti-Cu metallic glasses is found. We estimate the critical exponents nu_W, nu_E and nu_x when either disorder W, energy E or concentration x is varied, respectively. All our results are compatible with the universal value nu ~ 1.6 obtained in the single-band Anderson model.Comment: 9 RevTeX4 pages with 11 .eps figures included, submitted to PR

Race and sex: teachers' views on who gets ahead in schools?

The research reported here was part of a large study of the impact of age, disability, race and sex on the teaching profession in England. The basic question asked in this research was how do these factors interact with career aspirations and achievements of classteachers, promoted teachers and headteachers? There were three different data sources: a large postal survey drawn from diverse geographic regions across England with over 2000 respondents; face‐to‐face individual interviews with over 100 teachers in 18 case study schools from across all of the main regions of England; discussions with special interest groups of teachers. Not surprisingly, the answer to the above question was complex. Nonetheless, the paper's conclusion highlights some of the noteworthy themes across this broad sample of teachers from primary, secondary and special schools

Direct detection and characterization of foot-and-mouth disease virus in East Africa using a field-ready real-time PCR platform

Effective control and monitoring of foot-and-mouth disease (FMD) relies upon rapid and accurate disease confirmation. Currently, clinical samples are usually tested in reference laboratories using standardized assays recommended by The World Organisation for Animal Health (OIE). However, the requirements for prompt and serotype-specific diagnosis during FMD outbreaks, and the need to establish robust laboratory testing capacity in FMD-endemic countries have motivated the development of simple diagnostic platforms to support local decision-making. Using a portable thermocycler, the T-COR™ 8, this study describes the laboratory and field evaluation of a commercially available, lyophilized pan-serotype-specific real-time RT-PCR (rRT-PCR) assay and a newly available FMD virus (FMDV) typing assay (East Africa-specific for serotypes: O, A, Southern African Territories [SAT] 1 and 2). Analytical sensitivity, diagnostic sensitivity and specificity of the pan-serotype-specific lyophilized assay were comparable to that of an OIE-recommended laboratory-based rRT-PCR (determined using a panel of 57 FMDV-positive samples and six non-FMDV vesicular disease samples for differential diagnosis). The FMDV-typing assay was able to correctly identify the serotype of 33/36 FMDV-positive samples (no cross-reactivity between serotypes was evident). Furthermore, the assays were able to accurately detect and type FMDV RNA in multiple sample types, including epithelial tissue suspensions, serum, oesophageal–pharyngeal (OP) fluid and oral swabs, both with and without the use of nucleic acid extraction. When deployed in laboratory and field settings in Tanzania, Kenya and Ethiopia, both assays reliably detected and serotyped FMDV RNA in samples (n = 144) collected from pre-clinical, clinical and clinically recovered cattle. These data support the use of field-ready rRT-PCR platforms in endemic settings for simple, highly sensitive and rapid detection and/or characterization of FMDV

Critical Dynamics of a Vortex Loop Model for the Superconducting Transition

We calculate analytically the dynamic critical exponent $z_{MC}$ measured in Monte Carlo simulations for a vortex loop model of the superconducting transition, and account for the simulation results. In the weak screening limit, where magnetic fluctuations are neglected, the dynamic exponent is found to be $z_{MC} = 3/2$. In the perfect screening limit, $z_{MC} = 5/2$. We relate $z_{MC}$ to the actual value of $z$ observable in experiments and find that $z \sim 2$, consistent with some experimental results

Facts, Values and Quanta

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.Comment: 30 pages, AMS Late