Modeling Transport Mode Decisions Using Hierarchical Binary Spatial Regression Models with Cluster Effects

This work is motivated by a mobility study conducted in the city of Munich, Germany. The variable of interest is a binary response, which indicates whether public transport has been utilized or not. One of the central questions is to identify areas of low/high utilization of public transport after adjusting for explanatory factors such as trip, individual and household attributes. The goal is to develop flexible statistical models for a binary response with covariate, spatial and cluster effects. One approach for modeling spatial effects are Markov Random Fields (MRF). A modification of a class of MRF models with proper joint distributions introduced by Pettitt et al. (2002) is developed. This modification has the desirable property to contain the intrinsic MRF in the limit and still allows for efficient spatial parameter updates in Markov Chain Monte Carlo (MCMC) algorithms. In addition to spatial effects, cluster effects are taken into consideration. Group and individual approaches for modeling these effects are suggested. The first one models heterogeneity between clusters, while the second one models heterogeneity within clusters. A naive approach to include individual cluster effects results in an unidentifiable model. It is shown how an appropriate reparametrization gives identifiable parameters. This provides a new approach for modeling heterogeneity within clusters. For hierarchical spatial binary regression models with individual cluster effects two MCMC algorithms for parameter estimation are developed. The first one is based on a direct evaluation of the likelihood. The second one is based on the representation of binary responses with Gaussian latent variables through a threshold mechanism, which is particularly useful for probit models. Simulation results show a satisfactory behavior of the MCMC algorithms developed. Finally the proposed model classes are applied to the mobility study and results are interpreted

Evolutionary Approaches to Optimization Problems in Chimera Topologies

Chimera graphs define the topology of one of the first commercially available quantum computers. A variety of optimization problems have been mapped to this topology to evaluate the behavior of quantum enhanced optimization heuristics in relation to other optimizers, being able to efficiently solve problems classically to use them as benchmarks for quantum machines. In this paper we investigate for the first time the use of Evolutionary Algorithms (EAs) on Ising spin glass instances defined on the Chimera topology. Three genetic algorithms (GAs) and three estimation of distribution algorithms (EDAs) are evaluated over $1000$ hard instances of the Ising spin glass constructed from Sidon sets. We focus on determining whether the information about the topology of the graph can be used to improve the results of EAs and on identifying the characteristics of the Ising instances that influence the success rate of GAs and EDAs.Comment: 8 pages, 5 figures, 3 table

Massively Parallel Computation Using Graphics Processors with Application to Optimal Experimentation in Dynamic Control

The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability has lead to its adoption in many non-graphics applications, including wide variety of scientific computing fields. At the same time, a number of important dynamic optimal policy problems in economics are athirst of computing power to help overcome dual curses of complexity and dimensionality. We investigate if computational economics may benefit from new tools on a case study of imperfect information dynamic programming problem with learning and experimentation trade-off that is, a choice between controlling the policy target and learning system parameters. Specifically, we use a model of active learning and control of linear autoregression with unknown slope that appeared in a variety of macroeconomic policy and other contexts. The endogeneity of posterior beliefs makes the problem difficult in that the value function need not be convex and policy function need not be continuous. This complication makes the problem a suitable target for massively-parallel computation using graphics processors. Our findings are cautiously optimistic in that new tools let us easily achieve a factor of 15 performance gain relative to an implementation targeting single-core processors and thus establish a better reference point on the computational speed vs. coding complexity trade-off frontier. While further gains and wider applicability may lie behind steep learning barrier, we argue that the future of many computations belong to parallel algorithms anyway.Graphics Processing Units, CUDA programming, Dynamic programming, Learning, Experimentation

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

A flexible approach to parametric inference in nonlinear time series models

Many structural break and regime-switching models have been used with macroeconomic and …nancial data. In this paper, we develop an extremely flexible parametric model which can accommodate virtually any of these speci…cations and does so in a simple way which allows for straightforward Bayesian inference. The basic idea underlying our model is that it adds two simple concepts to a standard state space framework. These ideas are ordering and distance. By ordering the data in various ways, we can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. By allowing the state equation variances to depend on the distance between observations, the parameters can evolve in a wide variety of ways, allowing for everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). We show how our model will (approximately) nest virtually every popular model in the regime-switching and structural break literatures. Bayesian econometric methods for inference in this model are developed. Because we stay within a state space framework, these methods are relatively straightforward, drawing on the existing literature. We use arti…cial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth

A flexible approach to parametric inference in nonlinear and time varying time series models

Many structural break and regime-switching models have been used with macroeconomic and …nancial data. In this paper, we develop an extremely flexible parametric model which can accommodate virtually any of these speci…cations and does so in a simple way which allows for straightforward Bayesian inference. The basic idea underlying our model is that it adds two simple concepts to a standard state space framework. These ideas are ordering and distance. By ordering the data in various ways, we can accommodate a wide variety of nonlinear time series models, including those with regime-switching and structural breaks. By allowing the state equation variances to depend on the distance between observations, the parameters can evolve in a wide variety of ways, allowing for everything from models exhibiting abrupt change (e.g. threshold autoregressive models or standard structural break models) to those which allow for a gradual evolution of parameters (e.g. smooth transition autoregressive models or time varying parameter models). We show how our model will (approximately) nest virtually every popular model in the regime-switching and structural break literatures. Bayesian econometric methods for inference in this model are developed. Because we stay within a state space framework, these methods are relatively straightforward, drawing on the existing literature. We use arti…cial data to show the advantages of our approach, before providing two empirical illustrations involving the modeling of real GDP growth

Beta Spectrum Generator: High precision allowed β\beta spectrum shapes

Several searches for Beyond Standard Model physics rely on an accurate and highly precise theoretical description of the allowed $\beta$ spectrum. Following recent theoretical advances, a C++ implementation of an analytical description of the allowed beta spectrum shape was constructed. It implements all known corrections required to give a theoretical description accurate to a few parts in $10^4$. The remaining nuclear structure-sensitive input can optionally be calculated in an extreme single-particle approximation with a variety of nuclear potentials, or obtained through an interface with more state-of-the-art computations. Due to its relevance in modern neutrino physics, the corresponding (anti)neutrino spectra are readily available with appropriate radiative corrections. In the interest of user-friendliness, a graphical interface was developed in Python with a coupling to a variety of nuclear databases. We present several test cases and illustrate potential usage of the code. Our work can be used as the foundation for current and future high-precision experiments related to the beta decay process. Source code: https://github.com/leenderthayen/BSG Documentation: http://bsg.readthedocs.i