AutoBayes: A System for Generating Data Analysis Programs from Statistical Models

Data analysis is an important scientific task which is required whenever information needs to be extracted from raw data. Statistical approaches to data analysis, which use methods from probability theory and numerical analysis, are well-founded but difficult to implement: the development of a statistical data analysis program for any given application is time-consuming and requires substantial knowledge and experience in several areas. In this paper, we describe AutoBayes, a program synthesis system for the generation of data analysis programs from statistical models. A statistical model specifies the properties for each problem variable (i.e., observation or parameter) and its dependencies in the form of a probability distribution. It is a fully declarative problem description, similar in spirit to a set of differential equations. From such a model, AutoBayes generates optimized and fully commented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Code is produced by a schema-guided deductive synthesis process. A schema consists of a code template and applicability constraints which are checked against the model during synthesis using theorem proving technology. AutoBayes augments schema-guided synthesis by symbolic-algebraic computation and can thus derive closed-form solutions for many problems. It is well-suited for tasks like estimating best-fitting model parameters for the given data. Here, we describe AutoBayes's system architecture, in particular the schema-guided synthesis kernel. Its capabilities are illustrated by a number of advanced textbook examples and benchmarks

From euclidean field theory to quantum field theory

In order to construct examples for interacting quantum field theory models, the methods of euclidean field theory turned out to be powerful tools since they make use of the techniques of classical statistical mechanics. Starting from an appropriate set of euclidean n-point functions (Schwinger distributions), a Wightman theory can be reconstructed by an application of the famous Osterwalder-Schrader reconstruction theorem. This procedure (Wick rotation), which relates classical statistical mechanics and quantum field theory, is, however, somewhat subtle. It relies on the analytic properties of the euclidean n-point functions. We shall present here a C*-algebraic version of the Osterwalder-Scharader reconstruction theorem. We shall see that, via our reconstruction scheme, a Haag-Kastler net of bounded operators can directly be reconstructed. Our considerations also include objects, like Wilson loop variables, which are not point-like localized objects like distributions. This point of view may also be helpful for constructing gauge theories.Comment: 35 page

A solution space for a system of null-state partial differential equations 1

In this first of four articles, we study a homogeneous system of $2N+3$ linear partial differential equations (PDEs) in $2N$ variables that arises in conformal field theory (CFT) and multiple Schramm-Lowner evolution (SLE). In CFT, these are null-state equations and conformal Ward identities. They govern partition functions for the continuum limit of a statistical cluster or loop model, such as percolation, or more generally the Potts models and O$(n)$ models, at the statistical mechanical critical point. (SLE partition functions also satisfy these equations.) For such a lattice model in a polygon $\mathcal{P}$ with its $2N$ sides exhibiting a free/fixed side-alternating boundary condition, this partition function is proportional to the CFT correlation function $\langle\psi_1^c(w_1)\psi_1^c(w_2)\dotsm\psi_1^c(w_{2N-1})\psi_1^c(w_{2N})\rangle^{\mathcal{P}}$ where the $w_i$ are the vertices of $\mathcal{P}$ and where $\psi_1^c$ is a one-leg corner operator. When conformally mapped onto the upper half-plane, methods of CFT show that this correlation function satisfies the system of PDEs that we consider. This article is the first of four that completely and rigorously characterize the space of all solutions for this system of PDEs that grow no faster than a power law. In this first article, we use methods of analysis to prove that the dimension of this solution space is no more than $C_N$, the $N$th Catalan number. This proof is contained entirely within this article, except for the proof of lemma 14, which constitutes the second article ("part II"). In the third article ("part III"), we use the results of this article to prove that the solution space of this system of PDEs has dimension $C_N$ and is spanned by solutions constructed with the CFT Coulomb gas (contour integral) formalism. In the fourth article ("part IV"), we prove further CFT-related properties about these solutions.Comment: Minor typos from v3 corrected, reference to Fig. 11 inserted into tex

Confidence intervals of prediction accuracy measures for multivariable prediction models based on the bootstrap-based optimism correction methods

In assessing prediction accuracy of multivariable prediction models, optimism corrections are essential for preventing biased results. However, in most published papers of clinical prediction models, the point estimates of the prediction accuracy measures are corrected by adequate bootstrap-based correction methods, but their confidence intervals are not corrected, e.g., the DeLong's confidence interval is usually used for assessing the C-statistic. These naive methods do not adjust for the optimism bias and do not account for statistical variability in the estimation of parameters in the prediction models. Therefore, their coverage probabilities of the true value of the prediction accuracy measure can be seriously below the nominal level (e.g., 95%). In this article, we provide two generic bootstrap methods, namely (1) location-shifted bootstrap confidence intervals and (2) two-stage bootstrap confidence intervals, that can be generally applied to the bootstrap-based optimism correction methods, i.e., the Harrell's bias correction, 0.632, and 0.632+ methods. In addition, they can be widely applied to various methods for prediction model development involving modern shrinkage methods such as the ridge and lasso regressions. Through numerical evaluations by simulations, the proposed confidence intervals showed favourable coverage performances. Besides, the current standard practices based on the optimism-uncorrected methods showed serious undercoverage properties. To avoid erroneous results, the optimism-uncorrected confidence intervals should not be used in practice, and the adjusted methods are recommended instead. We also developed the R package predboot for implementing these methods (https://github.com/nomahi/predboot). The effectiveness of the proposed methods are illustrated via applications to the GUSTO-I clinical trial

A multi-epoch VLBI survey of the kinematics of CFJ sources

Context. This is the second in a series of papers presenting VLBI observations of the 293 Caltech-Jodrell Bank Flat-spectrum (hereafter CJF) sources and their analysis. Aims. We obtain a consistent motion dataset large enough to allow the systematic properties of the population to be studied. Methods. We present detailed kinematic analysis of the complete flux-density limited CJF survey. We computed 2D kinematic models based on the optimal model-fitting parameters of multi-epoch VLBA observations. This allows us to calculate not only radial, but also orthogonal motions, and thus to study curvature and acceleration. Statistical tests of the motions measured and their reliability were performed. A correlation analysis between the derived apparent motions, luminosities, spectral indices, and core dominance and the resulting consequences is described. Results. With at least one velocity in each of the 237 sources, this sample is much larger than any available before, so it allows a meaningful statistical investigation of apparent motions and any possible correlations with other parameters in AGN jets. The main results to emerge are as follows: - In general motions are not consistent with a single uniform velocity applicable to all components along a jet. - We find a slight trend towards a positive outward acceleration and also adduce some evidence for greater acceleration in the innermost regions. - We find a lack of fast components at physical distances less than a few pc from the reference feature. - Only ~4% of the components from galaxies and <2% of those from quasars undergo large bends i.e. within 15° of ± 90°. - The distribution of radial velocities shows a broad distribution of velocities (apparent velocities up to 30 c). Fifteen percent of the best-sampled jet components exhibit low velocities that may need to be explained in a different manner to the fast motions. - Some negative superluminal motions are seen, and in 15 cases (6%) these are definitely significant. - We find a strong correlation between the 5 GHz luminosity and the apparent velocity. - The CJF galaxies, on average, show slower apparent jet-component velocities than the quasars. - The mean velocity in the VLBA 2 cm survey (Kellermann et al. 2004, ApJ, 609, 539) is substantially higher than in the CJF survey, the ratio could be roughly a factor of 1.5-2. This supports the observed trend toward increasing apparent velocity with increasing observing frequency. Conclusions. This AGN survey provides the basis for any statistical analysis of jet and jet-component properties

Generating realistic scaled complex networks

Research on generative models is a central project in the emerging field of network science, and it studies how statistical patterns found in real networks could be generated by formal rules. Output from these generative models is then the basis for designing and evaluating computational methods on networks, and for verification and simulation studies. During the last two decades, a variety of models has been proposed with an ultimate goal of achieving comprehensive realism for the generated networks. In this study, we (a) introduce a new generator, termed ReCoN; (b) explore how ReCoN and some existing models can be fitted to an original network to produce a structurally similar replica, (c) use ReCoN to produce networks much larger than the original exemplar, and finally (d) discuss open problems and promising research directions. In a comparative experimental study, we find that ReCoN is often superior to many other state-of-the-art network generation methods. We argue that ReCoN is a scalable and effective tool for modeling a given network while preserving important properties at both micro- and macroscopic scales, and for scaling the exemplar data by orders of magnitude in size.Comment: 26 pages, 13 figures, extended version, a preliminary version of the paper was presented at the 5th International Workshop on Complex Networks and their Application

The Effect of Water Storage on the Bending Properties of Esthetic, Fiber-Reinforced Composite Orthodontic Archwires

Objective: To study the effect of water storage on the bending properties of fiber-reinforced composite archwires and compare it to nickel-titanium (NiTi), stainless steel (SS), and beta-titanium archwires. Materials and Methods: Align A, B, and C and TorQ A and B composite wires from BioMers Products, 0.014-, 0.016, and 0.018-inch, and 0.019 × 0.025-inch NiTi, 0.016-inch SS, and 0.019 × 0.025-inch beta-titanium archwires were tested (n  =  10/type/size/condition). A 20-mm segment was cut from each end of the archwire; one end was then stored in water at 37°C for 30 days, while the other was stored dry. The segments were tested using three-point bending to a maximum deflection of 3.1 mm with force monitored during loading (activation) and unloading (deactivation). Statistical analysis was completed via two-way analysis of variance with wire and condition (dry and water-stored) as factors. Results: In terms of stiffness and force delivery during activation, in general: beta-titanium was \u3e TorQ B \u3e TorQ A \u3e 0.019 × 0.025-inch NiTi and 0.016-inch SS \u3e Align C \u3e 0.018-inch NiTi \u3e Align B \u3e 0.016-inch NiTi \u3e Align A \u3e 0.014-inch NiTi. Water exposure was detrimental to the larger translucent wires (Align B and C, TorQ A and B) because they were more likely to craze during bending, resulting in decreased forces applied at a given deflection. Align A and the alloy wires were not significantly (P\u3e .05) affected by water storage. Overall, the alloy wires possessed more consistent force values compared to the composite wires