Bayesian multinomial logit: Theory and route choice example

Statisticians along with other scientists have made significant computational advances that enable the estimation of formerly complex statistical models. The Bayesian inference framework combined with Markov chain Monte Carlo estimation methods such as the Gibbs sampler enable the estimation of discrete choice models such as the multinomial logit (MNL) model. MNL models are frequently applied in transportation research to model choice outcomes such as mode, destination, or route choices or to model categorical outcomes such as crash outcomes. Recent developments allow for the modification of the potentially limiting assumptions of MNL such as the independence from irrelevant alternatives (IIA) property. However, relatively little transportation-related research has focused on Bayesian MNL models, the tractability of which is of great value to researchers and practitioners alike. This paper addresses MNL model specification issues in the Bayesian framework, such as the value of including prior information on parameters, allowing for nonlinear covariate effects, and extensions to random parameter models, so changing the usual limiting IIA assumption. This paper also provides an example that demonstrates, using route-choice data, the considerable potential of the Bayesian MNL approach with many transportation applications. This paper then concludes with a discussion of the pros and cons of this Bayesian approach and identifies when its application is worthwhile

Modelling attribute non-attendance in choice experiments for rural landscape valuation

Non-market effects of agriculture are often estimated using discrete choice models from stated preference surveys. In this context we propose two ways of modelling attribute non-attendance. The first involves constraining coefficients to zero in a latent class framework, whereas the second is based on stochastic attribute selection and grounded in Bayesian estimation. Their implications are explored in the context of a stated preference survey designed to value landscapes in Ireland. Taking account of attribute non-attendance with these data improves fit and tends to involve two attributes one of which is likely to be cost, thereby leading to substantive changes in derived welfare estimates.

Utility in Willingness to Pay Space: A Tool to Address Confounding Random Scale Effects in Destination Choice to the Alps

We compare two approaches for estimating the distribution of consumers' willingness to pay (WTP) in discrete choice models. The usual procedure is to estimate the distribution of the utility coefficients and then derive the distribution of WTP, which is the ratio of coefficients. The alternative is to estimate the distribution of WTP directly. We apply both approaches to data on site choice in the Alps. We find that the alternative approach fits the data better, reduces the incidence of exceedingly large estimated WTP values, and provides the analyst with greater control in specifying and testing the distribution of WTP. © 2008 Agricultural and Applied Economics Association.

Algorithms for Hidden Markov Models With Imprecisely Specified Parameters

Hidden Markov models (HMMs) are widely used models for sequential data. As with other probabilistic graphical models, they require the specification of precise probability values, which can be too restrictive for some domains, especially when data are scarce or costly to acquire. We present a generalized version of HMMs, whose quantification can be done by sets of, instead of single, probability distributions. Our models have the ability to suspend judgment when there is not enough statistical evidence, and can serve as a sensitivity analysis tool for standard non-stationary HMMs. Efficient inference algorithms are developed to address standard HMM usage such as the computation of likelihoods and most probable explanations. Experiments with real data show that the use of imprecise probabilities leads to more reliable inferences without compromising efficiency.

Tarification logit dans un réseau

Le problème de tarification qui nous intéresse ici consiste à maximiser le revenu généré par les usagers d'un réseau de transport. Pour se rendre à leurs destinations, les usagers font un choix de route et utilisent des arcs sur lesquels nous imposons des tarifs. Chaque route est caractérisée (aux yeux de l'usager) par sa "désutilité", une mesure de longueur généralisée tenant compte à la fois des tarifs et des autres coûts associés à son utilisation. Ce problème a surtout été abordé sous une modélisation déterministe de la demande selon laquelle seules des routes de désutilité minimale se voient attribuer une mesure positive de flot. Le modèle déterministe se prête bien à une résolution globale, mais pèche par manque de réalisme. Nous considérons ici une extension probabiliste de ce modèle, selon laquelle les usagers d'un réseau sont alloués aux routes d'après un modèle de choix discret logit. Bien que le problème de tarification qui en résulte est non linéaire et non convexe, il conserve néanmoins une forte composante combinatoire que nous exploitons à des fins algorithmiques. Notre contribution se répartit en trois articles. Dans le premier, nous abordons le problème d'un point de vue théorique pour le cas avec une paire origine-destination. Nous développons une analyse de premier ordre qui exploite les propriétés analytiques de l'affectation logit et démontrons la validité de règles de simplification de la topologie du réseau qui permettent de réduire la dimension du problème sans en modifier la solution. Nous établissons ensuite l'unimodalité du problème pour une vaste gamme de topologies et nous généralisons certains de nos résultats au problème de la tarification d'une ligne de produits. Dans le deuxième article, nous abordons le problème d'un point de vue numérique pour le cas avec plusieurs paires origine-destination. Nous développons des algorithmes qui exploitent l'information locale et la parenté des formulations probabilistes et déterministes. Un des résultats de notre analyse est l'obtention de bornes sur l'erreur commise par les modèles combinatoires dans l'approximation du revenu logit. Nos essais numériques montrent qu'une approximation combinatoire rudimentaire permet souvent d'identifier des solutions quasi-optimales. Dans le troisième article, nous considérons l'extension du problème à une demande hétérogène. L'affectation de la demande y est donnée par un modèle de choix discret logit mixte où la sensibilité au prix d'un usager est aléatoire. Sous cette modélisation, l'expression du revenu n'est pas analytique et ne peut être évaluée de façon exacte. Cependant, nous démontrons que l'utilisation d'approximations non linéaires et combinatoires permet d'identifier des solutions quasi-optimales. Finalement, nous en profitons pour illustrer la richesse du modèle, par le biais d'une interprétation économique, et examinons plus particulièrement la contribution au revenu des différents groupes d'usagers.

Detecting recombination in 4-taxa DNA sequence alignments with Bayesian hidden Markov models and Markov chain Monte Carlo

This article presents a statistical method for detecting recombination in DNA sequence alignments, which is based on combining two probabilistic graphical models: (1) a taxon graph (phylogenetic tree) representing the relationship between the taxa, and (2) a site graph (hidden Markov model) representing interactions between different sites in the DNA sequence alignments. We adopt a Bayesian approach and sample the parameters of the model from the posterior distribution with Markov chain Monte Carlo, using a Metropolis-Hastings and Gibbs-within-Gibbs scheme. The proposed method is tested on various synthetic and real-world DNA sequence alignments, and we compare its performance with the established detection methods RECPARS, PLATO, and TOPAL, as well as with two alternative parameter estimation schemes.

Contrasting probabilistic scoring rules

There are several scoring rules that one can choose from in order to score probabilistic forecasting models or estimate model parameters. Whilst it is generally agreed that proper scoring rules are preferable, there is no clear criterion for preferring one proper scoring rule above another. This manuscript compares and contrasts some commonly used proper scoring rules and provides guidance on scoring rule selection. In particular, it is shown that the logarithmic scoring rule prefers erring with more uncertainty, the spherical scoring rule prefers erring with lower uncertainty, whereas the other scoring rules are indifferent to either option.

Marginal and Interaction Effects in Ordered Response Models

In discrete choice models the marginal effect of a variable of interest that is interacted with another variable differs from the marginal effect of a variable that is not interacted with any variable. The magnitude of the interaction effect is also not equal to the marginal effect of the interaction term. I present consistent estimators of both marginal and interaction effects in ordered response models. This procedure is general and can easily be extended to other discrete choice models.

Graphical models and point set matching

Point pattern matching in Euclidean Spaces is one of the fundamental problems in Pattern Recognition, having applications ranging from Computer Vision to Computational Chemistry. Whenever two complex patterns are encoded by two sets of points identifying their key features, their comparison can be seen as a point pattern matching problem. This work proposes a single approach to both exact and inexact point set matching in Euclidean Spaces of arbitrary dimension. In the case of exact matching, it is assured to find an optimal solution. For inexact matching (when noise is involved), experimental results confirm the validity of the approach. We start by regarding point pattern matching as a weighted graph matching problem. We then formulate the weighted graph matching problem as one of Bayesian inference in a probabilistic graphical model. By exploiting the existence of fundamental constraints in patterns embedded in Euclidean Spaces, we prove that for exact point set matching a simple graphical model is equivalent to the full model. It is possible to show that exact probabilistic inference in this simple model has polynomial time complexity with respect to the number of elements in the patterns to be matched. This gives rise to a technique that for exact matching provably finds a global optimum in polynomial time for any dimensionality of the underlying Euclidean Space. Computational experiments comparing this technique with well-known probabilistic relaxation labeling show significant performance improvement for inexact matching. The proposed approach is significantly more robust under augmentation of the sizes of the involved patterns. In the absence of noise, the results are always perfect.

Improving the analysis of road pricing acceptability surveys by using hybrid models

Several international studies have analyzed the acceptability of road pricing schemes by means of an attitude survey in combination with the results of a stated choice experiment using both a descriptive analysis and a discrete-choice model with binary choice (?accept? or ?not accept? the toll). However, the use of hybrid discrete choice models constitutes an innovative alternative for integrating subjective attitudes and perceptions deriving from the survey of attitudes with the more objective variables from the stated choice experiment. This paper analyzes the results of applying these models to measure the acceptability of interurban road pricing among different groups of stakeholders (road freight and passenger operators, highway concessionaires, and associations of private car users) with qualitatively significant opinions on road pricing measures. Our results show that hybrid models are better suited to explaining the acceptability of a road pricing scheme by different groups of stakeholders than a separate analysis of the survey of attitudes and a discrete-choice model applied on a stated choice experiment. A particular finding was that the strong psycho-social latent variable of the perception of fairness explains the rejection or acceptance of a toll scheme by road stakeholders.

Hybrid choice model for propensity to travel and tour complexity

During the last years cities around the world have invested important quantities of money in measures for reducing congestion and car-trips. Investments which are nothing but potential solutions for the well-known urban sprawl phenomenon, also called the “development trap” that leads to further congestion and a higher proportion of our time spent in slow moving cars. Over the path of this searching for solutions, the complex relationship between urban environment and travel behaviour has been studied in a number of cases. The main question on discussion is, how to encourage multi-stop tours? Thus, the objective of this paper is to verify whether unobserved factors influence tour complexity. For this purpose, we use a data-base from a survey conducted in 2006-2007 in Madrid, a suitable case study for analyzing urban sprawl due to new urban developments and substantial changes in mobility patterns in the last years. A total of 943 individuals were interviewed from 3 selected neighbourhoods (CBD, urban and suburban). We study the effect of unobserved factors on trip frequency. This paper present the estimation of an hybrid model where the latent variable is called propensity to travel and the discrete choice model is composed by 5 alternatives of tour type. The results show that characteristics of the neighbourhoods in Madrid are important to explain trip frequency. The influence of land use variables on trip generation is clear and in particular the presence of commercial retails. Through estimation of elasticities and forecasting we determine to what extent land-use policy measures modify travel demand. Comparing aggregate elasticities with percentage variations, it can be seen that percentage variations could lead to inconsistent results. The result shows that hybrid models better explain travel behavior than traditional discrete choice models.

Wealth effects of mergers and acquisitions for US firms: using alternative pricing models

This empirical study employs a different methodology to examine the change in wealth associated with mergers and acquisitions (M&As) for US firms. Specifically, we employ the standard CAPM, the Fama-French three-factor model and the Carhart four-factor models within the OLS and GJR-GARCH estimation methods to test the behaviour of the cumulative abnormal returns (CARs). Whilst the standard CAPM captures the variability of stock returns with the overall market, the Fama-French factors capture the risk factors that are important to investors. Additionally, augmenting the Fama-French three-factor model with the Carhart momentum factor to generate the four-factor captures additional pricing elements that may affect stock returns. Traditionally, estimates of abnormal returns (ARs) in M&As situations rely on the standard OLS estimation method. However, the standard OLS will provide inefficient estimates of the ARs if the data contain ARCH and asymmetric effects. To minimise this problem of estimation efficiency we re-estimated the ARs using GJR-GARCH estimation method. We find that there is variation in the results both as regards the choice models and estimation methods. Besides these variations in the estimated models and the choice of estimation methods, we also tested whether the ARs are affected by the degree of liquidity of the stocks and the size of the firm. We document significant positive post-announcement cumulative ARs (CARs) for target firm shareholders under both the OLS and GJR-GARCH methods across all three methodologies. However, post-event CARs for acquiring firm shareholders were insignificant for both sets of estimation methods under the three methodologies. The GJR-GARCH method seems to generate larger CARs than those of the OLS method. Using both market capitalization and trading volume as a measure of liquidity and the size of the firm, we observed strong return continuations in the medium firms relative to small and large firms for target shareholders. We consistently observed market efficiency in small and large firm. This implies that target firms for small and large firms overreact to new information resulting in a more efficient market. For acquirer firms, our measure of liquidity captures strong return continuations for small firms under the OLS estimates for both CAPM and Fama-French three-factor models, whilst under the GJR-GARCH estimates only for Carhart model. Post-announcement bootstrapping simulated CARs confirmed our earlier results.

Optimal choice of electoral preference data

Electoral researchers are so much accustomed to analyzing the choice of the single most preferred party as the left-hand side variable of their models of electoral behavior that they often ignore revealed preference data. Drawing on random utility theory, their models predict electoral behavior at the extensive margin of choice. Since the seminal work of Luce and others on individual choice behavior, however, many social science disciplines (consumer research, labor market research, travel demand, etc.) have extended their inventory of observed preference data with, for instance, multiple paired comparisons, complete or incomplete rankings, and multiple ratings. Eliciting (voter) preferences using these procedures and applying appropriate choice models is known to considerably increase the efficiency of estimates of causal factors in models of (electoral) behavior. In this paper, we demonstrate the efficiency gain when adding additional preference information to first preferences, up to full ranking data. We do so for multi-party systems of different sizes. We use simulation studies as well as empirical data from the 1972 German election study. Comparing the practical considerations for using ranking and single preference data results in suggestions for choice of measurement instruments in different multi-candidate and multi-party settings.

Probability and Common-Sense: Tandem Towards Robust Robotic Object Recognition in Ambient Assisted Living

The suitable operation of mobile robots when providing Ambient Assisted Living (AAL) services calls for robust object recognition capabilities. Probabilistic Graphical Models (PGMs) have become the de-facto choice in recognition systems aiming to e ciently exploit contextual relations among objects, also dealing with the uncertainty inherent to the robot workspace. However, these models can perform in an inco herent way when operating in a long-term fashion out of the laboratory, e.g. while recognizing objects in peculiar con gurations or belonging to new types. In this work we propose a recognition system that resorts to PGMs and common-sense knowledge, represented in the form of an ontology, to detect those inconsistencies and learn from them. The utilization of the ontology carries additional advantages, e.g. the possibility to verbalize the robot's knowledge. A primary demonstration of the system capabilities has been carried out with very promising results.

Reliability driven reconfiguration of rural power distribution systems

This paper presents a reliability-based reconfiguration methodology for power distribution systems. Probabilistic reliability models of the system components are considered and Monte Carlo method is used while evaluating the reliability of the distribution system. The reconfiguration is aimed at maximizing the reliability of the power supplied to the customers. A binary particle swarm optimization (BPSO) algorithm is used as a tool to determine the optimal configuration of the sectionalizing and tie switches in the system. The proposed methodology is applied on a modified IEEE 13-bus distribution system.