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Joint modeling of different data sources in decision-making processes is crucial for understanding decision dynamics in consumer behavior models. Sequential Sampling Models (SSMs), grounded in neuro-cognitive principles, provide a systematic approach to combining information from multi-source data, such as those based on response times and choice outcomes. However, parameter estimation of SSMs is challenging due to the complexity of joint likelihood functions. Likelihood-Free inference (LFI) approaches enable Bayesian inference in complex models with intractable likelihoods, like SSMs, and only require the ability to simulate synthetic data from the model. Extending a popular approach to simulation efficient LFI for single-source data, we propose Multi-objective Bayesian Optimization for Likelihood-Free Inference (MOBOLFI) to estimate the parameters of SSMs calibrated using multi-source data. MOBOLFI models a multi-dimensional discrepancy between observed and simulated data, using a discrepancy for each data source. Multi-objective Bayesian Optimization is then used to ensure simulation efficient approximation of the SSM likelihood. The use of a multivariate discrepancy allows for approximations to individual data source likelihoods in addition to the joint likelihood, enabling both the detection of conflicting information and a deeper understanding of the importance of different data sources in estimating individual SSM parameters. We illustrate the advantages of our approach in comparison with the use of a single discrepancy in a simple synthetic data example and an SSM example with real-world data assessing preferences of ride-hailing drivers in Singapore to rent electric vehicles. Although we focus on applications to SSMs, our approach applies to the Likelihood-Free calibration of other models using multi-source data., Comment: 42 pages, 17 figures

Urban metro systems can provide highly efficient and effective movements of vast passenger volumes in cities, but they are often affected by disruptions, causing delays, crowding, and ultimately a decline in passenger satisfaction and patronage. To manage and mitigate such adverse consequences, metro operators could benefit greatly from a quantitative understanding of the causal impact of disruptions. Such information would allow them to predict future delays, prepare effective recovery plans, and develop real-time information systems for passengers on trip re-routing options. In this paper, we develop a performance evaluation tool for metro operators that can quantify the causal effects of service disruptions on passenger flows, journey times, travel speeds and crowding densities. Our modelling framework is simple to implement, robust to statistical sources of bias, and can be used with high-frequency large-scale smart card data (over 4.85 million daily trips in our case) and train movement data. We recover disruption effects at the points of disruption (e.g. at disrupted stations) as well as spillover effects that propagate throughout the metro network. This allows us to deliver novel insights on the spatio-temporal propagation of delays in densely used urban public transport networks. We find robust empirical evidence that the causal impacts of disruptions adversely affect service quality throughout the network, in ways that would be hard to predict absent a causal model.

We propose a group-level agent-based mixed (GLAM) logit model that is estimated using market-level choice share data. The model non-parametrically represents taste heterogeneity through market-specific parameters by solving a multiagent inverse utility maximization problem, addressing the limitations of existing market-level choice models with parametric taste heterogeneity. A case study of mode choice in New York State is conducted using synthetic population data of 53.55 million trips made by 19.53 million residents in 2019. These trips are aggregated based on population segments and census block group-level origin-destination (OD) pairs, resulting in 120,740 markets/agents. We benchmark in-sample and out-of-sample predictive performance of the GLAM logit model against multinomial logit, nested logit, inverse product differentiation logit, and random coefficient logit (RCL) models. The results show that GLAM logit outperforms benchmark models, improving the overall in-sample predictive accuracy from 78.7% to 96.71% and out-of-sample accuracy from 65.30% to 81.78%. The price elasticities and diversion ratios retrieved from GLAM logit and benchmark models exhibit similar substitution patterns among the six travel modes. GLAM logit is scalable and computationally efficient, taking less than one-tenth of the time taken to estimate the RCL model. The agent-specific parameters in GLAM logit provide additional insights such as value-of-time (VOT) across segments and regions, which has been further utilized to demonstrate its application in analyzing NYS travelers' mode choice response to the congestion pricing. The agent-specific parameters in GLAM logit facilitate their seamless integration into supply-side optimization models for revenue management and system design.

Ride-sourcing services offered by companies like Uber and Didi have grown rapidly in the last decade. Understanding the demand for these services is essential for planning and managing modern transportation systems. Existing studies develop statistical models for ride-sourcing demand estimation at an aggregate level due to limited data availability. These models lack foundations in microeconomic theory, ignore competition of ride-sourcing with other travel modes, and cannot be seamlessly integrated into existing individual-level (disaggregate) activity-based models to evaluate system-level impacts of ride-sourcing services. In this paper, we present and apply an approach for estimating ride-sourcing demand at a disaggregate level using discrete choice models and multiple data sources. We first construct a sample of trip-based mode choices in Chicago, USA by enriching household travel survey with publicly available ride-sourcing and taxi trip records. We then formulate a multivariate extreme value-based discrete choice with sampling and endogeneity corrections to account for the construction of the estimation sample from multiple data sources and endogeneity biases arising from supply-side constraints and surge pricing mechanisms in ride-sourcing systems. Our analysis of the constructed dataset reveals insights into the influence of various socio-economic, land use and built environment features on ride-sourcing demand. We also derive elasticities of ride-sourcing demand relative to travel cost and time. Finally, we illustrate how the developed model can be employed to quantify the welfare implications of ride-sourcing policies and regulations such as terminating certain types of services and introducing ride-sourcing taxes.

An ideal synthetic population, a key input to activity-based models, mimics the distribution of the individual- and household-level attributes in the actual population. Since the entire population's attributes are generally unavailable, household travel survey (HTS) samples are used for population synthesis. Synthesizing population by directly sampling from HTS ignores the attribute combinations that are unobserved in the HTS samples but exist in the population, called 'sampling zeros'. A deep generative model (DGM) can potentially synthesize the sampling zeros but at the expense of generating 'structural zeros' (i.e., the infeasible attribute combinations that do not exist in the population). This study proposes a novel method to minimize structural zeros while preserving sampling zeros. Two regularizations are devised to customize the training of the DGM and applied to a generative adversarial network (GAN) and a variational autoencoder (VAE). The adopted metrics for feasibility and diversity of the synthetic population indicate the capability of generating sampling and structural zeros -- lower structural zeros and lower sampling zeros indicate the higher feasibility and the lower diversity, respectively. Results show that the proposed regularizations achieve considerable performance improvement in feasibility and diversity of the synthesized population over traditional models. The proposed VAE additionally generated 23.5% of the population ignored by the sample with 79.2% precision (i.e., 20.8% structural zeros rates), while the proposed GAN generated 18.3% of the ignored population with 89.0% precision. The proposed improvement in DGM generates a more feasible and diverse synthetic population, which is critical for the accuracy of an activity-based model.

Despite astonishing progress, generating realistic images of complex scenes remains a challenging problem. Recently, layout-to-image synthesis approaches have attracted much interest by conditioning the generator on a list of bounding boxes and corresponding class labels. However, previous approaches are very restrictive because the set of labels is fixed a priori. Meanwhile, text-to-image synthesis methods have substantially improved and provide a flexible way for conditional image generation. In this work, we introduce dense text-to-image (DT2I) synthesis as a new task to pave the way toward more intuitive image generation. Furthermore, we propose DTC-GAN, a novel method to generate images from semantically rich region descriptions, and a multi-modal region feature matching loss to encourage semantic image-text matching. Our results demonstrate the capability of our approach to generate plausible images of complex scenes using region captions.

China and India, the world's two most populous developing economies, are also among the world's largest automotive markets and carbon emitters. To reduce carbon emissions from the passenger car sector, both countries have considered various policy levers affecting fuel prices, car prices and fuel economy. This study estimates the responsiveness of new car buyers in China and India to such policy levers and drivers including income. Furthermore, we estimate the potential for rebound effect and the effectiveness of a feebate policy. To accomplish this, we developed a joint discrete-continuous model of car choice and usage based on revealed preference survey data from approximately 8000 new car buyers from India and China who purchased cars in 2016-17. Conditional on buying a new car, the fuel consumption in both markets is found to be relatively unresponsive to fuel price and income, with magnitudes of elasticity estimates ranging from 0.12 to 0.15. For both markets, the mean segment-level direct elasticities of fuel consumption relative to car price and fuel economy range from 0.57 to 0.65. The rebound effect on fuel savings due to cost-free fuel economy improvement is found to be 17.1% for India and 18.8% for China. A revenue-neutral feebate policy, with average rebates and fees of up to around 15% of the retail price, resulted in fuel savings of around 0.7% for both markets. While the feebate policy's rebound effect is low - 7.3% for India and 1.6% for China - it does not appear to be an effective fuel conservation policy.

Due to the unavailability of prototypes, the early adopters of novel products actively seek information from multiple sources (e.g., media and social networks) to minimize the potential risk. The existing behavior models not only fail to capture the information propagation within the individual's social network, but also they do not incorporate the impact of such word-of-mouth (WOM) dissemination on the consumer's risk preferences. Moreover, even cutting-edge forecasting models rely on crude/synthetic consumer behavior models. We propose a general framework to forecast the adoption of novel products by developing a new consumer behavior model and integrating it into a population-level agent-based model. Specifically, we extend the hybrid choice model to estimate consumer behavior, which incorporates social network effects and interplay between WOM and risk aversion. The calibrated consumer behavior model and synthetic population are passed through the agent-based model for forecasting the product market share. We apply the proposed framework to forecast the adoption of autonomous vehicles (AVs) in Nashville, USA. The consumer behavior model is calibrated with a stated preference survey data of 1,495 Nashville residents. The output of the agent-based model provides the effect of the purchase price, post-purchase satisfaction, and safety measures/regulations on the forecasted AV market share. With an annual AV price reduction of 5% at the initial purchase price of $40,000 and 90% of satisfied adopters, AVs are forecasted to attain around 85% market share in thirty years. These findings are crucial for policymakers to develop infrastructure plans and manufacturers to conduct an after-sales cost-benefit analysis.

India's mass vaccination efforts have been slow due to high levels of vaccine hesitancy. This study uses data from an online discrete choice experiment with 1371 respondents to rigorously examine the factors shaping vaccine preference in the country. We find that vaccine efficacy, presence of side effects, protection duration, distance to vaccination centre and vaccination rates within social networks play a critical role in determining vaccine demand. We apply a non-parametric model to uncover the heterogeneity in the effects of these factors. We derive two novel insights from this analysis. First, even though, on average, domestically developed vaccines are preferred, around 30 percent of the sample favours foreign-developed vaccines. Second, the vaccine preference of around 15 percent of the sample is highly sensitive to the presence of side effects and vaccination uptake among their peer group. These results provide insights into the ongoing policy debate around vaccine adoption in India.

The COVID-19 pandemic has drastically impacted people's travel behaviour and out-of-home activity participation. While countermeasures are being eased with increasing vaccination rates, the demand for public transport remains uncertain. To investigate user preferences to travel by London Underground during the pandemic, we conducted a stated choice experiment among its pre-pandemic users (N=961). We analysed the collected data using multinomial and mixed logit models. Our analysis provides insights into the sensitivity of the demand for the London Underground with respect to travel attributes (crowding density and travel time), the epidemic situation (confirmed new COVID-19 cases), and interventions (vaccination rates and mandatory face masks). Mandatory face masks and higher vaccination rates are the top two drivers of travel demand for the London Underground during COVID-19. The positive impact of vaccination rates on the Underground demand increases with crowding density, and the positive effect of mandatory face masks decreases with travel time. Mixed logit reveals substantial preference heterogeneity. For instance, while the average effect of mandatory face masks is positive, preferences of around 20% of the pre-pandemic users to travel by the Underground are negatively affected. The estimated demand sensitivities are relevant for supply-demand management in transit systems and the calibration of advanced epidemiological models.

Several non-linear functions and machine learning methods have been developed for flexible specification of the systematic utility in discrete choice models. However, they lack interpretability, do not ensure monotonicity conditions, and restrict substitution patterns. We address the first two challenges by modelling the systematic utility using the Choquet Integral (CI) function and the last one by embedding CI into the multinomial probit (MNP) choice probability kernel. We also extend the MNP-CI model to account for attribute cut-offs that enable a modeller to approximately mimic the semi-compensatory behaviour using the traditional choice experiment data. The MNP-CI model is estimated using a constrained maximum likelihood approach, and its statistical properties are validated through a comprehensive Monte Carlo study. The CI-based choice model is empirically advantageous as it captures interaction effects while maintaining monotonicity. It also provides information on the complementarity between pairs of attributes coupled with their importance ranking as a by-product of the estimation. These insights could potentially assist policymakers in making policies to improve the preference level for an alternative. These advantages of the MNP-CI model with attribute cut-offs are illustrated in an empirical application to understand New Yorkers' preferences towards mobility-on-demand services.

The fundamental relationship of traffic flow is empirically estimated by fitting a regression curve to a cloud of observations of traffic variables. Such estimates, however, may suffer from the confounding/endogeneity bias due to omitted variables such as driving behaviour and weather. To this end, this paper adopts a causal approach to obtain an unbiased estimate of the fundamental flow-density relationship using traffic detector data. In particular, we apply a Bayesian non-parametric spline-based regression approach with instrumental variables to adjust for the aforementioned confounding bias. The proposed approach is benchmarked against standard curve-fitting methods in estimating the flow-density relationship for three highway bottlenecks in the United States. Our empirical results suggest that the saturated (or hypercongested) regime of the estimated flow-density relationship using correlational curve fitting methods may be severely biased, which in turn leads to biased estimates of important traffic control inputs such as capacity and capacity-drop. We emphasise that our causal approach is based on the physical laws of vehicle movement in a traffic stream as opposed to a demand-supply framework adopted in the economics literature. By doing so, we also aim to conciliate the engineering and economics approaches to this empirical problem. Our results, thus, have important implications both for traffic engineers and transport economists.

Animal-vehicle collisions (AVCs) are common around the world and result in considerable loss of animal and human life, as well as significant property damage and regular insurance claims. Understanding their occurrence in relation to various contributing factors and being able to identify locations of high risk are valuable to AVC prevention, yielding economic, social and environmental cost savings. However, many challenges exist in the study of AVC datasets. These include seasonality of animal activity, unknown exposure (i.e., the number of animal crossings), very low AVC counts across most sections of extensive roadway networks, and computational burdens that come with discrete response analysis using large datasets. To overcome these challenges, a Bayesian hierarchical model is proposed where the exposure is modeled with nonparametric Dirichlet process, and the number of segment-level AVCs is assumed to follow a Binomial distribution. A P\'olya-Gamma augmented Gibbs sampler is derived to estimate the proposed model. By using the AVC data of multiple years across about 100,000 segments of state-controlled highways in Texas, U.S., it is demonstrated that the model is scalable to large datasets, with a preponderance of zeros and clear monthly seasonality in counts, while identifying high-risk locations (for application of design treatments, like separated animal crossings with fencing) and key explanatory factors based on segment-specific factors (such as changes in speed limit) can be done within the modelling framework, which provide useful information for policy-making purposes.

Consumer preference elicitation is critical to devise effective policies for the diffusion of electric vehicles (EVs) in India. This study contributes to the EV demand literature in the Indian context by (a) analysing the EV attributes and attitudinal factors of Indian car buyers that determine consumers' preferences for EVs, (b) estimating Indian consumers' willingness to pay (WTP) to buy EVs with improved attributes, and c) quantifying how the reference dependence affects the WTP estimates. We adopt a hybrid choice modelling approach for the above analysis. The results indicate that accounting for reference dependence provides more realistic WTP estimates than the standard utility estimation approach. Our results suggest that Indian consumers are willing to pay an additional USD 10-34 in the purchase price to reduce the fast charging time by 1 minute, USD 7-40 to add a kilometre to the driving range of EVs at 200 kilometres, and USD 104-692 to save USD 1 per 100 kilometres in operating cost. These estimates and the effect of attitudes on the likelihood to adopt EVs provide insights about EV design, marketing strategies, and pro-EV policies (e.g., specialised lanes and reserved parking for EVs) to expedite the adoption of EVs in India.

In this paper, we revisit McFadden (1978)'s correction factor for sampling of alternatives in multinomial logit (MNL) and mixed multinomial logit (MMNL) models. McFadden (1978) proved that consistent parameter estimates are obtained when estimating MNL models using a sampled subset of alternatives, including the chosen alternative, in combination with a correction factor. We decompose this correction factor into i) a correction for overestimating the MNL choice probability due to using a smaller subset of alternatives, and ii) a correction for which a subset of alternatives is contrasted through utility differences and thereby the extent to which we learn about the parameters of interest in MNL. Keane and Wasi (2016) proved that the overall expected positive information divergence - comprising the above two elements - is minimised between the true and sampled likelihood when applying a sampling protocol satisfying uniform conditioning. We generalise their result to the case of positive conditioning and show that whilst McFadden (1978)'s correction factor may not minimise the overall expected information divergence, it does minimise the expected information loss with respect to the parameters of interest. We apply this result in the context of Bayesian analysis and show that McFadden (1978)'s correction factor minimises the expected information loss regarding the parameters of interest across the entire posterior density irrespective of sample size. In other words, McFadden (1978)'s correction factor has desirable small and large sample properties. We also show that our results for Bayesian MNL models transfer to MMNL and that only McFadden (1978) correction factor is sufficient to minimise the expected information loss in the parameters of interest. Monte Carlo simulations illustrate the successful application of sampling of alternatives in Bayesian MMNL models.

Congestion; operational delays due to a vicious circle of passenger-congestion and train-queuing; is an escalating problem for metro systems because it has negative consequences from passenger discomfort to eventual mode-shifts. Congestion arises due to large volumes of passenger boardings and alightings at bottleneck stations, which may lead to increased stopping times at stations and consequent queuing of trains upstream, further reducing line throughput and implying an even greater accumulation of passengers at stations. Alleviating congestion requires control strategies such as regulating the inflow of passengers entering bottleneck stations. The availability of large-scale smartcard and train movement data from day-to-day operations facilitates the development of models that can inform such strategies in a data-driven way. In this paper, we propose to model station-level passenger-congestion via empirical passenger boarding-alightings and train flow relationships, henceforth, fundamental diagrams (FDs). We emphasise that estimating FDs using station-level data is empirically challenging due to confounding biases arising from the interdependence of operations at different stations, which obscures the true sources of congestion in the network. We thus adopt a causal statistical modelling approach to produce FDs that are robust to confounding and as such suitable to properly inform control strategies. The closest antecedent to the proposed model is the FD for road traffic networks, which informs traffic management strategies, for instance, via locating the optimum operation point. Our analysis of data from the Mass Transit Railway, Hong Kong indicates the existence of concave FDs at identified bottleneck stations, and an associated critical level of boarding-alightings above which congestion sets-in unless there is an intervention.

Outliers in discrete choice response data may result from misclassification and misreporting of the response variable and from choice behaviour that is inconsistent with modelling assumptions (e.g. random utility maximisation). In the presence of outliers, standard discrete choice models produce biased estimates and suffer from compromised predictive accuracy. Robust statistical models are less sensitive to outliers than standard non-robust models. This paper analyses two robust alternatives to the multinomial probit (MNP) model. The two models are robit models whose kernel error distributions are heavy-tailed t-distributions to moderate the influence of outliers. The first model is the multinomial robit (MNR) model, in which a generic degrees of freedom parameter controls the heavy-tailedness of the kernel error distribution. The second model, the generalised multinomial robit (Gen-MNR) model, is more flexible than MNR, as it allows for distinct heavy-tailedness in each dimension of the kernel error distribution. For both models, we derive Gibbs samplers for posterior inference. In a simulation study, we illustrate the excellent finite sample properties of the proposed Bayes estimators and show that MNR and Gen-MNR produce more accurate estimates if the choice data contain outliers through the lens of the non-robust MNP model. In a case study on transport mode choice behaviour, MNR and Gen-MNR outperform MNP by substantial margins in terms of in-sample fit and out-of-sample predictive accuracy. The case study also highlights differences in elasticity estimates across models.

Recent crash frequency studies incorporate spatiotemporal correlations, but these studies have two key limitations: i) none of these studies accounts for temporal variation in model parameters; and ii) Gibbs sampler suffers from convergence issues due to non-conjugacy. To address the first limitation, we propose a new count data model that identifies the underlying temporal patterns of the regression parameters while simultaneously allowing for time-varying spatial correlation. The model is also extended to incorporate heterogeneity in non-temporal parameters across spatial units. We tackle the second shortcoming by deriving a Gibbs sampler that ensures conditionally conjugate posterior updates for all model parameters. To this end, we take the advantages of P\'olya-Gamma data augmentation and forward filtering backward sampling (FFBS) algorithm. After validating the properties of the Gibbs sampler in a Monte Carlo study, the advantages of the proposed specification are demonstrated in an empirical application to uncover relationships between crash frequency spanning across nine years and pavement characteristics. Model parameters exhibit practically significant temporal patterns (i.e., temporal instability). For example, the safety benefits of better pavement ride quality are estimated to increase over time.

As travelers make their choices based on travel time, its prior information can be helpful for them in making more informed travel decisions. To achieve this goal, travel time prediction models have been proposed in literature, but identification of important predictors has not received much attention. Identification of important predictors reduces dimensions of input data, which not only lessens computational load, but also provides better understanding of underlying relationship between important predictors and travel time. Moreover, collection of only important predictors can lead to a significant equipment savings in data collection. Therefore, this study proposes a hybrid approach for feature selection (identifying important predictors) along with developing a robust freeway travel time prediction model. A framework integrating biogeography-based optimization (BBO) and support vector regression (SVR) has been developed. It was validated by predicting travel time at 36.1 km long segment of National Taiwan Freeway No. 1. The proposed hybrid approach is able to develop a prediction model with only six predictors, which is found to have accuracy equivalent to a stand-alone SVR prediction model developed with all forty three predictors.

VISSIM is a widely used microscopic traffic simulator, which not only provides a graphical user interface to simulate simple static controls (pre-timed or fixed-time) but also offers flexibility to dynamically control simulation through versatile programming languages (C++ and Java etc.). However, to implement various traffic control techniques, integration of computational tools may save lots of effort and time as compared to standard programming platforms. MATLAB falls in the category of a widely used computational tool and also fulfills the primary requirements to control VISSIM simulation dynamically. Therefore, this study proposes and develops a direct interface between MATLAB and VISSIM to extensively harness the computational power of MATLAB. The significance of developed interface is demonstrated on a practical scenario, by conducting an online optimization of green time splits on a study network.

Maximum simulated likelihood estimation of mixed multinomial logit (MMNL) or probit models requires evaluation of a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as shuffled and scrambled Halton sequences and modified Latin hypercube sampling (MLHS) are workhorse methods for integral approximation. A few earlier studies explored the potential of sparse grid quadrature (SGQ), but this approximation suffers from negative weights. As an alternative to QMC and SGQ, we looked into the recently developed designed quadrature (DQ) method. DQ requires fewer nodes to get the same level of accuracy as of QMC and SGQ, is as easy to implement, ensures positivity of weights, and can be created on any general polynomial spaces. We benchmarked DQ against QMC in a Monte Carlo study under different data generating processes with a varying number of random parameters (3, 5, and 10) and variance-covariance structures (diagonal and full). Whereas DQ significantly outperformed QMC in the diagonal variance-covariance scenario, it could also achieve a better model fit and recover true parameters with fewer nodes (i.e., relatively lower computation time) in the full variance-covariance scenario. Finally, we evaluated the performance of DQ in a case study to understand preferences for mobility-on-demand services in New York City. In estimating MMNL with five random parameters, DQ achieved better fit and statistical significance of parameters with just 200 nodes as compared to 1000 QMC draws, making DQ around five times faster than QMC methods.

Transit operators need vulnerability measures to understand the level of service degradation under disruptions. This paper contributes to the literature with a novel causal inference approach for estimating station-level vulnerability in metro systems. The empirical analysis is based on large-scale data on historical incidents and population-level passenger demand. This analysis thus obviates the need for assumptions made by previous studies on human behaviour and disruption scenarios. We develop four empirical vulnerability metrics based on the causal impact of disruptions on travel demand, average travel speed and passenger flow distribution. Specifically, the proposed metrics based on the irregularity in passenger flow distribution extends the scope of vulnerability measurement to the entire trip distribution, instead of just analysing the disruption impact on the entry or exit demand (that is, moments of the trip distribution). The unbiased estimates of disruption impact are obtained by adopting a propensity score matching method, which adjusts for the confounding biases caused by non-random occurrence of disruptions. An application of the proposed framework to the London Underground indicates that the vulnerability of a metro station depends on the location, topology, and other characteristics. We find that, in 2013, central London stations are more vulnerable in terms of travel demand loss. However, the loss of average travel speed and irregularity in relative passenger flows reveal that passengers from outer London stations suffer from longer individual delays due to lack of alternative routes.

Spatial count data models are used to explain and predict the frequency of phenomena such as traffic accidents in geographically distinct entities such as census tracts or road segments. These models are typically estimated using Bayesian Markov chain Monte Carlo (MCMC) simulation methods, which, however, are computationally expensive and do not scale well to large datasets. Variational Bayes (VB), a method from machine learning, addresses the shortcomings of MCMC by casting Bayesian estimation as an optimisation problem instead of a simulation problem. Considering all these advantages of VB, a VB method is derived for posterior inference in negative binomial models with unobserved parameter heterogeneity and spatial dependence. P\'olya-Gamma augmentation is used to deal with the non-conjugacy of the negative binomial likelihood and an integrated non-factorised specification of the variational distribution is adopted to capture posterior dependencies. The benefits of the proposed approach are demonstrated in a Monte Carlo study and an empirical application on estimating youth pedestrian injury counts in census tracts of New York City. The VB approach is around 45 to 50 times faster than MCMC on a regular eight-core processor in a simulation and an empirical study, while offering similar estimation and predictive accuracy. Conditional on the availability of computational resources, the embarrassingly parallel architecture of the proposed VB method can be exploited to further accelerate its estimation by up to 20 times.

Crowding valuation of subway riders is an important input to various supply-side decisions of transit operators. The crowding cost perceived by a transit rider is generally estimated by capturing the trade-off that the rider makes between crowding and travel time while choosing a route. However, existing studies rely on static compensatory choice models and fail to account for inertia and the learning behaviour of riders. To address these challenges, we propose a new dynamic latent class model (DLCM) which (i) assigns riders to latent compensatory and inertia/habit classes based on different decision rules, (ii) enables transitions between these classes over time, and (iii) adopts instance-based learning theory to account for the learning behaviour of riders. We use the expectation-maximisation algorithm to estimate DLCM, and the most probable sequence of latent classes for each rider is retrieved using the Viterbi algorithm. The proposed DLCM can be applied in any choice context to capture the dynamics of decision rules used by a decision-maker. We demonstrate its practical advantages in estimating the crowding valuation of an Asian metro's riders. To calibrate the model, we recover the daily route preferences and in-vehicle crowding experiences of regular metro riders using a two-month-long smart card and vehicle location data. The results indicate that the average rider follows the compensatory rule on only 25.5% of route choice occasions. DLCM estimates also show an increase of 47% in metro riders' valuation of travel time under extremely crowded conditions relative to that under uncrowded conditions.

The identification of accident hot spots is a central task of road safety management. Bayesian count data models have emerged as the workhorse method for producing probabilistic rankings of hazardous sites in road networks. Typically, these methods assume simple linear link function specifications, which, however, limit the predictive power of a model. Furthermore, extensive specification searches are precluded by complex model structures arising from the need to account for unobserved heterogeneity and spatial correlations. Modern machine learning (ML) methods offer ways to automate the specification of the link function. However, these methods do not capture estimation uncertainty, and it is also difficult to incorporate spatial correlations. In light of these gaps in the literature, this paper proposes a new spatial negative binomial model, which uses Bayesian additive regression trees to endogenously select the specification of the link function. Posterior inference in the proposed model is made feasible with the help of the Polya-Gamma data augmentation technique. We test the performance of this new model on a crash count data set from a metropolitan highway network. The empirical results show that the proposed model performs at least as well as a baseline spatial count data model with random parameters in terms of goodness of fit and site ranking ability.