Bayesian I-optimal designs for choice experiments with mixtures

Becerra, Mario; Goos, Peter

doi:10.1016/j.chemolab.2021.104395

Cited by 16 publications

(10 citation statements)

References 45 publications

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“…Contrary to thorough methods such as grid search or random search, which can lead to too much examination or use, Bayesian optimization chooses the next sampling locations based on the probability distribution that already exists. So, it enables a smart use of computational resources and makes it easier to get to ideal hyperparameters in an extremely effective manner. , …”

Section: Methodsmentioning

confidence: 99%

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Precise Prediction of Biochar Yield and Proximate Analysis by Modern Machine Learning and SHapley Additive exPlanations

Le,

Pandey,

Sirohi

et al. 2023

Energy Fuels

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Biochar is found to possess a large number of applications in energy and environmental areas. However, biochar could be produced from a variety of sources, showing that biochar yield and proximate analysis outcomes could change over a wide range. Thus, developing a high-accuracy machine learning-based tool is very necessary to predict biochar characteristics. In this study, a hybrid technique was developed by blending modern machine learning (ML) algorithms with cooperative game theory-based Shapley Additive exPlanations (SHAP). SHAP analysis was employed to help improve interpretability while offering insights into the decision-making process. In the ML models, linear regression was employed as the baseline regression method, and more advanced methodologies like AdaBoost and boosted regression tree (BRT) were employed. The developed prediction models were evaluated on a battery of statistical metrics, and all ML models were observed as robust enough. Among all three models, the BRT-based model delivered the best prediction performance with R 2 in the range of 0.982 to 0.999 during the model training phase and 0.968 to 0.988 during the model test. The value of the mean squared error was also quite low (0.89 to 9.168) for BRT-based models. SHAP analysis quantified the value of each input element to the expected results and provided a more in-depth understanding of the underlying dynamics. The SHAP analysis helped to reveal that temperature was the main factor affecting the response predictions. The hybrid technique proposed here provides substantial insights into the biochar manufacturing process, allowing for improved control of biochar properties and increasing the use of this sustainable and flexible material in numerous applications.

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Section: Methodsmentioning

confidence: 99%

“…So, it enables a smart use of computational resources and makes it easier to get to ideal hyperparameters in an extremely effective manner. 61,62 2.5. Model Evaluation.…”

Section: Bayesian Approach Formentioning

confidence: 99%

Precise Prediction of Biochar Yield and Proximate Analysis by Modern Machine Learning and SHapley Additive exPlanations

Le,

Pandey,

Sirohi

et al. 2023

Energy Fuels

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“…In the choice experiments literature, most of the Bayesian optimal designs define the Bayesian D-optimality criterion as an average of the D-optimality criterion over the prior distribution (Bliemer and Rose, 2011;Bliemer et al, 2009;Kessels et al, 2011b). Therefore, following Ruseckaite et al (2017) and Becerra and Goos (2021), we define the Bayesian D-optimality criterion for the multinomial logit model as…”

Section: Appendix 1 Optimal Design Of Experimentsmentioning

confidence: 99%

“…Therefore, following Ruseckaite et al . (2017) and Becerra and Goos (2021), we define the Bayesian D-optimality criterion for the multinomial logit model aswhere π ( β ) is the prior distribution of β . A design that minimizes the Bayesian D-optimality criterion is called a Bayesian D-optimal design.The assumptions for the prior parameter estimates in this work were that the ticket price would have a negative impact on the utility of the respondents, that an increasing strength of the opponent would lead to an increase in utility, that there was no difference in preference between the different days and times, that a side seat is more preferable to a goal and corner, that there is no difference between the latter and that Nations League and Qualifiers are equally preferable and more preferable than a friendly match.Using the previous assumptions, the prior values of the β parameter vector were set as follows β Corner = −0.25, β Goal = −0.25, β Side = 0.5, β Friendly = −0.5, β Qualification = 0.25, β NationsLeague = 0.25, β Weak = −0.5, β Medium = 0, β Strong = 0.5, β 75euros = −0.45, β 50euros = −0.15, β 25euros = 0.15, β 15euros = 0.45, β TimeAndDay1 = 0, β TimeAndDay2 = 0, β TimeAndDay3 = 0, β TimeAndDay4 = 0, β TimeAndDay5 = 0, and β TimeAndDay6 = 0.…”

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confidence: 99%

Why do fans go to football games? A discrete choice analysis of ticket buyers' preferences

Becerra,

Balliauw,

Goos

et al. 2023

IJSMS

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PurposeTicket sales are an essential source of income for football clubs and federations. Analyzing the determinants of fans' willingness-to-pay for tickets is therefore an important exercise. By knowing the match- and fan-related characteristics that influence how much a fan wants to pay for a ticket, as well as to what extent, football clubs and federations can modify their ticket offering and targeting in order to optimize this revenue stream.Design/methodology/approachUsing a detailed discrete choice experiment, based on McFadden's random utility theory, this paper formulates a Bayesian hierarchical multinomial logit model. Such models are very common in the discrete choice modeling literature. The analysis identifies to what extent match and personal attributes influence fans' willingness-to-pay for games of the Belgian men's and women's football national teams.FindingsThe results show that the strength of the opponent, the type of competition, the location of the seats in the stadium, the day and kick-off time of the match and the ticket price exert an influence on the choice of the respondent. Fans are attracted most by competitive games against strong opponents. They prefer to sit along the sideline, and they have clear preferences for specific kick-off days and times. The authors also find substantial variation between socio-demographic groups, defined in terms of factors such as age, gender and family composition.Practical implicationsThe authors use the results to estimate the willingness-to-pay for match tickets for different socio-demographic groups. Their findings are useful for football clubs and federations interested in optimizing the prices of their match tickets.Originality/valueTo the best of the authors' knowledge, no stated preference methods, such as discrete choice analysis, have been used to analyze the willingness-to-pay of sports fans. The advantage of discrete choice analysis is that options and variations in tickets that are not yet available in practice can be studied, allowing football organizations to increase revenues from new ticketing instruments.

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“…They have proven to be more informative for estimating the no-choice nested logit model than the traditional approach of adding a no-choice option to each choice set of a Bayesian D-optimal MNL design that is constructed ignoring the no-choice option. Also worthy of mentioning is the recent introduction of Bayesian D-and I-optimal mixture designs for DCEs, where food products are described as mixtures of ingredients (e.g., Ruseckaite et al, 2017;Goos & Hamidouche, 2019;Becerra & Goos, 2021). These designs are optimized for mixture-choice models where Scheffé mixture models (Scheffé, 1963) replace the systematic utilities of the choice models for these food products.…”

Section: Design Optionsmentioning

confidence: 99%