This study develops a Bayesian decision-making model employing Markov chain Monte Carlo (MCMC) methods to enhance halal tourism governance in Pekalongan City, Indonesia. The model addresses the complexity of decision-making processes and supports data-driven policy formulation by local authorities.
This research uses both quantitative and qualitative data, including tourist preferences, economic conditions and regulatory frameworks. A Bayesian approach incorporates prior knowledge and stakeholder input, while MCMC computes posterior distributions of model parameters, ensuring a comprehensive analysis of governance challenges.
Combining Bayesian decision-making with MCMC improves halal tourism governance by providing insights into policy outcomes and risks, helping align strategies with religious and cultural needs, though satisfaction and cultural aspects need further study.
This study’s limitations include small sample size, focus on one region, and limited exploration of external factors, such as political influences, which may affect the generalizability of findings.
The developed model provides policymakers with practical tools to make informed decisions by considering uncertainties and stakeholder perspectives. It contributes to improving governance strategies in the halal tourism sector, ensuring alignment with religious and cultural expectations.
This study contributes to the social sustainability of halal tourism by promoting inclusive and culturally sensitive governance frameworks that cater to diverse Muslim travelers. By integrating Bayesian decision-making, policymakers can design adaptive tourism policies that balance economic growth, environmental responsibility and cultural preservation, ensuring that local communities benefit from sustainable tourism practices. Additionally, improving halal certification standardization and enhancing infrastructure for Muslim-friendly tourism fosters greater social acceptance and integration between local and international visitors, strengthening cross-cultural interactions and economic opportunities for local businesses.
This research is one of the first to apply Bayesian decision-making and MCMC methods in halal tourism governance, offering a novel, adaptive framework for local governments and stakeholders to optimize policy decisions.
1. Introduction
Halal tourism has become an increasingly significant sector within the global tourism industry, driven by the rising demand from Muslim travelers seeking destinations that align with their religious beliefs and lifestyle preferences. With the global Muslim population expected to exceed 2 billion by 2050, halal tourism represents a rapidly growing market that is reshaping the tourism sector (Azam and Abdullah, 2021). This trend has led destinations worldwide to develop halal-friendly services, including halal-certified accommodations, food, and culturally inclusive experiences (Akhsanty et al., 2023). However, despite its potential, the governance of halal tourism remains complex, particularly in cities like Pekalongan, where economic, cultural, and religious factors must be carefully balanced.
Pekalongan, renowned for its batik heritage, is developing itself as a halal tourism destination. However, it faces serious environmental and economic challenges. The batik industry, while culturally and economically important, contributes to water pollution from dye waste (Firmansyah et al., 2020; Mukadar et al., 2021; Pramesti, 2022). The city also struggles with coastal erosion, land subsidence, poor waste management, and tidal flooding, threatening tourism sustainability (Ayasy et al., 2023; Bantacut and Zulaikha, 2019; Fattah et al., 2023; Pratama, 2019; Wahyuddin et al., 2023). These issues conflict with the core values of halal tourism: cleanliness, sustainability, and environmental care (Abdullah et al., 2020). Policymakers must balance economic gains from batik with halal tourism compliance and environmental responsibility.
Existing studies on halal tourism governance have examined economic impact, tourist satisfaction (Adinugraha et al., 2020; Battour et al., 2022), and culture integration with regulatory frameworks (Sholehuddin et al., 2021). In Pekalongan, a key challenge is balancing cultural heritage, especially batik, with environmental and religious demands of halal tourism. Though studies link environmental sustainability with cultural integration (Baloch et al., 2023), in Pekalongan, economic and regulatory factors may be more dominant. Traditional governance often uses static assumptions, making it hard to respond to changing tourist preferences and environmental shifts (Thouki, 2019). Therefore, a flexible, data-driven model is needed—one that accounts for uncertainty and supports more effective and adaptive policy-making in halal tourism.
Despite the growing interest in halal tourism governance, there is a notable gap in the literature regarding probabilistic decision-making models that integrate economic, environmental, and regulatory complexities. Existing models often fail to incorporate both quantitative and qualitative data to predict how governance strategies impact tourist satisfaction, economic performance, and environmental sustainability. Furthermore, while tourism governance research has explored various analytical approaches, no studies have specifically applied Bayesian decision-making combined with Markov Chain Monte Carlo (MCMC) simulations to address the governance challenges of halal tourism in Pekalongan. This gap underscores the necessity for an advanced, adaptive model capable of handling the inherent uncertainties in halal tourism policy decisions.
This study aims to develop a Bayesian decision-making framework integrated with MCMC methods to address the complexities and uncertainties of halal tourism governance in Pekalongan City. By leveraging probabilistic modeling, this research provides a robust tool for policymakers to dynamically refine governance strategies based on evolving data and stakeholder preferences. The objective is to ensure that governance approaches align with the religious and cultural expectations of Muslim tourists while simultaneously promoting environmental sustainability and supporting economic growth in the batik industry.
2. Literature review
2.1 Bayesian decision making with MCMC
Bayesian Decision Theory is a probabilistic approach to decision-making that allows for continuous updating of beliefs as new information becomes available (Assaf et al., 2021; van de Schoot et al., 2021). This approach leverages Bayes’ theorem, which mathematically expresses how prior knowledge P(θ) is updated with new evidence to obtain a posterior distribution
where is the posterior probability of parameter given data D, is the likelihood function, is the prior distribution, and P(D) is the marginal likelihood ensuring normalization. This approach is particularly advantageous in scenarios characterized by uncertainty and incomplete information, as it provides a systematic framework for updating beliefs in light of new data. Recent studies highlight the benefits of Bayesian inference in addressing complex decision-making challenges that require adaptability and real-time learning (Philip and AlJassmi, 2024). For example, Bayesian methods have been successfully applied in healthcare, environmental management, and tourism, where data-driven decision-making is crucial (Karagöz and Ergün, 2020; Plummer, 2024; Taka et al., 2020; Yuan et al., 2023).
However, in many real-world applications, computing the posterior distribution analytically is challenging due to the high-dimensional nature of the parameter space. To address this issue, Markov Chain Monte Carlo (MCMC) methods are employed to approximate the posterior distribution through a sampling-based approach. MCMC algorithms, such as Metropolis-Hastings and Gibbs Sampling, iteratively generate samples from the posterior distribution, allowing for more accurate probability estimation in complex models. The Metropolis-Hastings algorithm generates a sequence of parameter values by proposing a new candidate value and accepting or rejecting it based on an acceptance probability:
where represents the proposal distribution, which determines how candidate values are sampled. Alternatively, Gibbs Sampling simplifies the process by sequentially updating each parameter while keeping all other parameters fixed, using the conditional distribution:
This method is particularly efficient when conditional distributions are available in closed form, allowing for faster convergence than Metropolis-Hastings. MCMC is particularly useful for analyzing complex datasets, such as those related to dynamic tourism trends, where high-dimensional interactions exist between tourist behaviors, economic fluctuations, and regulatory frameworks. Studies have demonstrated that MCMC-based Bayesian decision-making enhances the ability to model uncertainties in tourism and environmental governance, providing policymakers with robust probabilistic estimates of future outcomes (Morato et al., 2021; Wu et al., 2020).
In the context of tourism governance, Bayesian Decision Making with MCMC is particularly valuable due to the inherent uncertainties within the sector. Tourist preferences often fluctuate, influenced by various factors such as economic shifts and geopolitical stability, making it challenging for policymakers to anticipate changes in demand. Additionally, seasonal variations play a crucial role in determining travel patterns, as fluctuations in weather and holiday periods significantly impact both tourism demand and revenue generation. Furthermore, macroeconomic conditions, including exchange rate fluctuations and inflation, affect tourists’ purchasing power and spending behavior, adding another layer of complexity to tourism management. By leveraging Bayesian inference and MCMC simulations, decision-makers can develop more adaptive and data-driven policies that respond effectively to these dynamic and interconnected factors.
The ability to continuously update governance models based on new data ensures that policies remain relevant and adaptive. Studies like Thipsingh et al. (2022) demonstrate how Bayesian MCMC models can be applied to forecast tourism trends, evaluate policy impacts in real-time, and support risk management strategies. This adaptability makes Bayesian MCMC an ideal tool for managing complex tourism sectors, such as halal tourism, which must integrate economic, cultural, and religious considerations alongside sustainability initiatives.
2.2 Halal tourism
Halal tourism, as a subset of the broader tourism industry, is specifically designed to cater to Muslim travelers by offering services aligned with Islamic principles, including halal food, prayer facilities, and gender-segregated amenities. This segment has experienced substantial growth due to the increasing global Muslim population and rising disposable income. In addition to its economic significance, halal tourism contributes to the broader “halal lifestyle” industry, which encompasses sectors such as Islamic finance, halal food production, and modest fashion (Abror et al., 2019; Zulvianti et al., 2022). However, governance challenges persist, particularly due to the lack of standardized halal certification systems across different regions, leading to inconsistencies in service quality (Azam and Abdullah, 2021). Addressing these issues requires enhanced collaboration among industry stakeholders, religious authorities, and policymakers to improve trust and service quality.
A key challenge in halal tourism governance is integrating sustainability, especially where tourism grows alongside industrial sectors. In Pekalongan, where halal tourism coexists with batik production, environmental sustainability is critical. Water pollution from dye waste, poor waste management, and coastal degradation threatens long-term tourism viability (Ayasy et al., 2023; Fattah et al., 2023). Bayesian Decision Making with Markov Chain Monte Carlo (MCMC) offers a probabilistic framework to assess environmental policies and optimize sustainability strategies. By using real-time data, policymakers can predict the long-term impacts of waste management policies on tourism sustainability. This approach ensures that governance remains adaptive and evidence-based, reducing environmental risks while preserving economic benefits.
Another major governance issue is the harmonization of halal certification standards across different countries and regions. The absence of a unified global standard has led to inconsistencies in halal service quality, affecting Muslim travelers’ trust in different destinations (Azam and Abdullah, 2021). Bayesian inference can be used to model the likelihood of tourist preferences for various certification schemes and assess the effectiveness of different standardization policies. By analyzing prior data on tourist behavior, a Bayesian approach can help predict how variations in certification influence destination choices, thereby supporting policymakers in designing harmonization frameworks that align with global Muslim travelers’ expectations.
Cultural integration is a key aspect of halal tourism governance, especially in destinations where Muslim and non-Muslim travelers coexist. Countries like Malaysia, Indonesia, and the UAE have positioned themselves as leaders in halal tourism while remaining inclusive to non-Muslim visitors. Push-Pull Theory explains that internal motivations (e.g. religious obligations) interact with external attractions (e.g. cultural offerings and infrastructure) to shape tourist behavior (Pahlufi and Paturusi, 2021). In mixed-religion settings, Bayesian models offer insights into how cultural factors influence satisfaction and predict the effects of policy changes on visitor experiences. For instance, such models can estimate how halal-certified hotel availability impacts the likelihood of attracting both Muslim and non-Muslim tourists, helping policymakers design balanced tourism strategies.
As halal tourism continues to grow, there is also an increasing emphasis on technological advancements to enhance the travel experience. Mobile applications for halal service navigation, AI-driven tourism management systems, and real-time data analytics are being integrated to improve service quality (Battour et al., 2022; Jaelani et al., 2021). These innovations align with Bayesian methodologies, as predictive analytics based on Bayesian models can optimize travel recommendations by continuously updating information on tourist preferences, destination ratings, and service availability. By integrating Bayesian Decision Making and MCMC, halal tourism governance can be more adaptive and evidence-based, addressing key challenges related to environmental sustainability, certification harmonization, and cultural integration. This probabilistic approach ensures that policy adjustments remain responsive to evolving market trends while maintaining alignment with Islamic principles and sustainability goals.
2.3 Sustainable development
Sustainable development in tourism governance requires balancing economic growth, environmental conservation, and cultural preservation. Recent studies emphasize that responsible tourism practices, including community engagement and environmental conservation, are essential for ensuring long-term sustainability (Raveendran, 2024). In halal tourism, sustainability aligns with Islamic ethical principles, particularly in maintaining cleanliness, fairness, and responsible resource management, which can be integrated into broader sustainable tourism governance frameworks (Verances et al., 2024).
Sustainable tourism practices, such as eco-friendly accommodations, waste management, and green certifications, enhance both tourist satisfaction and local cultural integration (Daneshwar and Revaty, 2024). However, in Pekalongan, where the batik industry coexists with halal tourism, environmental concerns like water pollution and inadequate waste management pose challenges, requiring stronger sustainability efforts (Chandran and Bhattacharya, 2022). Comparatively, Bali emphasizes community-driven sustainability, while Dubai integrates technological solutions to enhance green tourism practices (Kaithlin, 2024). These models offer valuable insights into balancing economic priorities with environmental responsibility.
Environmental challenges in halal tourism require adaptive decision-making frameworks. Bayesian Decision Making with Markov Chain Monte Carlo (MCMC) provides a probabilistic approach for evaluating sustainability policies. Given observed environmental data (D), Bayesian inference updates the probability of policy success (S):
where prior knowledge P(S) and observed outcomes refine governance decisions. MCMC simulations allow policymakers to estimate the long-term effectiveness of policies on pollution control, resource management, and community engagement.
Sustainability influences the economic-tourist satisfaction relationship, where destinations with strong sustainability measures experience greater economic gains (Zainudin, 2023). This relationship can be modeled as:
where sustainability (S) interacts with economic conditions (E) to shape tourist satisfaction (Y). Applying this model in Pekalongan, Bali, and Dubai helps quantify how eco-friendly policies enhance visitor experiences and industry competitiveness (Nguyen et al., 2023). By integrating Bayesian Decision Making and MCMC, policymakers can continuously update sustainability strategies based on real-time environmental and economic data, ensuring that halal tourism governance remains evidence-based, adaptable, and aligned with sustainability goals (Dibiku, 2023).
2.4 Theoretical framework and hypothesis development
Tourist preferences have been widely recognized as a pivotal determinant of satisfaction and behavioral outcomes, particularly within the domain of halal tourism, where alignment between personal expectations and religious values is paramount. Jalil and Akbar (2024) emphasize that Muslim tourist satisfaction is significantly shaped by the compatibility of destination features with religious norms. Similarly, Putra et al. (2024) argue that perceived behavioral control and subjective norms play a substantial role in influencing destination loyalty and satisfaction in Muslim-friendly contexts. These findings collectively suggest that tourist preferences constitute a critical variable in evaluating the effectiveness of halal tourism governance.
Tourist preferences positively influence halal tourism governance effectiveness.
In parallel, the quality of governance remains a crucial determinant of tourist experience. Poor infrastructure, ineffective regulations, and environmental degradation are widely reported as sources of dissatisfaction, particularly in developing tourism markets. Seow et al. (2024) demonstrate that effective governance enhances visitor satisfaction by providing stable institutional and regulatory support. In the case of Pekalongan, chronic issues such as industrial waste pollution and tidal flooding (Ayasy et al., 2023; Fattah et al., 2023) pose serious threats to tourism viability. Furthermore, Baloch et al. (2023) affirm that environmental sustainability and regulatory clarity are essential components of positive tourist perception.
Governance challenges negatively impact tourist satisfaction
Given the inherent complexity of halal tourism governance—which demands sensitivity to religious, cultural, and environmental dimensions—decision-making frameworks must accommodate uncertainty and change. Bayesian decision theory offers a flexible, data-driven alternative to static models, allowing continuous updates based on new evidence. Philip and AlJassmi (2024) Bayesian decision support systems in infrastructure planning, while (Thipsingh et al., 2022) employ MCMC techniques to enhance predictive accuracy in tourism policy design. Such models are particularly suited to volatile, data-sparse environments like those encountered in emerging halal tourism regions.
Bayesian decision-making enhances governance adaptability by reducing uncertainty
3. Methodology
This study adopts a sequential mixed-methods approach to examine the implementation of Bayesian decision-making with Markov Chain Monte Carlo (Wu et al., 2020). Conducted in Pekalongan City from January to March 2024, the research addresses governance challenges in developing halal tourism alongside environmental and regulatory constraints.
A stratified random sampling method was used to select 589 respondents, including tourism staff, religious leaders, community leaders, hotel managers, food vendors, hotel visitors, and local community members (Table 1). This ensures a balanced representation of key stakeholders.
3.1 Data collection and analysis
This study employs a sequential explanatory design, where quantitative analysis informs qualitative interpretation (Haryanto et al., 2024). Data were collected through multiple methods to ensure a comprehensive understanding of halal tourism governance. First, surveys were conducted to gather quantitative data on tourist preferences, expectations, and satisfaction levels. These surveys provided measurable insights into the factors influencing decision-making in halal tourism (Bahrudin, 2022). Second, semi-structured interviews were carried out with policymakers and business owners, offering qualitative perspectives on governance challenges and policy implementation. These interviews allowed for a deeper exploration of the complexities surrounding halal tourism development and its regulatory framework.
To further validate the findings, Focus Group Discussions (FGDs) were conducted, enabling cross-verification of themes emerging from the qualitative data. This approach ensured that diverse stakeholder viewpoints were incorporated into the analysis. Additionally, document analysis was performed by reviewing local policies, halal tourism frameworks, and relevant regulations (Bahrudin, 2022). This helped contextualize the findings within existing governance structures and regulatory frameworks, ensuring that the analysis remained aligned with contemporary halal tourism policies (Pulungan and Indra, 2024).
The data analysis process involved three key stages. First, descriptive statistics were applied to summarize survey responses, identifying trends in tourist behavior and stakeholder expectations. Second, thematic analysis was used to interpret qualitative data, allowing for the identification of major governance challenges and policy recommendations (Xiao, 2024). Third, Bayesian decision-making models were developed using R statistical software, with MCMC simulations executed through the “rjags” package to optimize policy strategies and improve predictive accuracy (Alsing et al., 2023).
To ensure the reliability of the Bayesian model, Gelman-Rubin diagnostics and autocorrelation checks were conducted, confirming the convergence of MCMC chains (Duttweiler et al., 2024). Additionally, sensitivity analysis was performed to test different prior distributions, ensuring the robustness and stability of the model under varying assumptions (Nguyen et al., 2024). By integrating these methods, the study provides a data-driven framework for evaluating halal tourism governance, ensuring that policy recommendations are supported by both empirical data and probabilistic modeling (Darges et al., 2023).
3.2 Bayesian decision-making and MCMC simulations
Bayesian inference updates the probability of policy effectiveness given observed data:
where represents the posterior probability of a policy being effective, and P(θ) incorporate empirical data and expert knowledge. MCMC simulations generate posterior distributions, providing probabilistic estimates of governance outcomes (Sun and Kowal, 2023). This framework enables policymakers to dynamically adjust tourism strategies based on real-time environmental and economic factors, ensuring sustainable and adaptive halal tourism governance (Thach, 2023).
4. Results and discussion
The data analysis follows three main stages. First, descriptive statistics summarize survey data, offering insights into respondent demographics, preferences, and behaviors forming a baseline for the Bayesian decision-making model. Next, the Bayesian model is built using R software, with MCMC (Markov Chain Monte Carlo) simulations run via the “rjags” package. These simulations generate posterior distributions, enabling probabilistic estimates of governance outcomes under various policy scenarios. This approach addresses uncertainty and complexity, keeping governance adaptive and data-driven. Table 2 presents summary statistics for estimated parameters, including economic conditions, tourist preferences, cultural influences, and satisfaction. These variables were chosen based on their theoretical importance in halal tourism governance, aligning with earlier studies applying Bayesian frameworks in tourism-related decision-making.
Summary statistics for model parameters
| Parameter | Mean | SD | Naive SE | Time-series SE |
|---|---|---|---|---|
| beta_c | 0.0056 | 0.0400 | 0.0003 | 0.0034 |
| beta_e | 0.1157 | 0.0450 | 0.0004 | 0.0040 |
| beta_p | 0.1792 | 0.0549 | 0.0004 | 0.0060 |
| beta_s | −0.0595 | 0.0482 | 0.0004 | 0.0046 |
| mu | 59.4160 | 3.5650 | 0.0291 | 0.3973 |
| sigma | 8.9574 | 0.2628 | 0.0021 | 0.0029 |
The selection of these parameters is justified by their role in influencing governance strategies in halal tourism, where economic factors (beta_e) and tourist preferences (beta_p) are expected to be the most significant drivers of decision-making. Satisfaction (beta_s) and cultural influences (beta_c) were included to assess their secondary impact, which aligns with previous findings on tourist behavior in Muslim-friendly destinations.
To improve clarity in the statistical reporting, the distinction between Naive Standard Error (Naive SE) and Time-series Standard Error (Time-series SE) is explicitly addressed. The Naive SE represents the standard error of the parameter estimates based on independent sampling assumptions, whereas the Time-series SE accounts for the autocorrelation within MCMC chains, ensuring a more accurate measure of uncertainty in Bayesian inference. The use of Time-series SE is particularly important in assessing the reliability of posterior estimates, as it provides a more conservative estimate of variability compared to Naive SE.
By incorporating these refinements, the study ensures that the statistical reporting is transparent, theoretically grounded, and methodologically robust, reinforcing the validity of the Bayesian decision-making framework in halal tourism governance.
The density plot (Figure 1) provides a visual representation of the posterior distributions of key governance parameters, including Preferences, Satisfaction, Economy, Culture, and Regulatory Policies. Higher density regions indicate a greater probability of parameter values occurring within specific ranges, helping to assess their relative influence on governance outcomes. The Economy variable (blue) peaks around the 60–70 range, reinforcing the significant impact of economic factors on decision-making (beta_e = 0.1157). Meanwhile, Regulatory Policies (green) display a broader density distribution, suggesting that respondents have varied perceptions regarding the effectiveness of governance regulations.
The horizontal axis, labeled “Values,” ranges from 40 to 100 in increments of 20 units. The vertical axis, labeled “Density,” ranges from 0.00 to 0.04 in increments of 0.01 units. A legend at the top right shows the different variables represented by different colors: Preferences is shown in light blue, Satisfaction is in orange, Economy is in light blue, Culture is in pink, and Regulatory Policies is shown in green. The curve for Regulatory Policies starts at (40, 0.00), moves horizontally to (53, 0.00), rises concave down to a peak at (67, 0.031), falls slightly to a point at (71, 0.029), rises again to another peak at (81, 0.036), and finally drops concave down to end at (97, 0.00). The curve for Economy starts at (40, 0.00), rises linearly to a peak at (60, 0.038), falls slightly to a point at (63, 0.037), rises again to another peak at (67, 0.038), and finally drops concave up to end at (90, 0.00). The other curves resemble a bell shape, starting at (40, 0.00) and ending at (97, 0.00). The curve for Culture shows the highest peak around 0.044, and the lowest peak for Satisfaction is around 0.035. Note: All numerical data values are approximated.Density plot for all variables. Source(s): The authors
The horizontal axis, labeled “Values,” ranges from 40 to 100 in increments of 20 units. The vertical axis, labeled “Density,” ranges from 0.00 to 0.04 in increments of 0.01 units. A legend at the top right shows the different variables represented by different colors: Preferences is shown in light blue, Satisfaction is in orange, Economy is in light blue, Culture is in pink, and Regulatory Policies is shown in green. The curve for Regulatory Policies starts at (40, 0.00), moves horizontally to (53, 0.00), rises concave down to a peak at (67, 0.031), falls slightly to a point at (71, 0.029), rises again to another peak at (81, 0.036), and finally drops concave down to end at (97, 0.00). The curve for Economy starts at (40, 0.00), rises linearly to a peak at (60, 0.038), falls slightly to a point at (63, 0.037), rises again to another peak at (67, 0.038), and finally drops concave up to end at (90, 0.00). The other curves resemble a bell shape, starting at (40, 0.00) and ending at (97, 0.00). The curve for Culture shows the highest peak around 0.044, and the lowest peak for Satisfaction is around 0.035. Note: All numerical data values are approximated.Density plot for all variables. Source(s): The authors
These density distributions directly support the study’s hypotheses, particularly the assertion that economic factors (H1) and tourist preferences (H2) have the strongest impact on governance outcomes. Conversely, the lower and more dispersed density of Satisfaction (beta_s = −0.0595) confirms its weaker and inconsistent influence on decision-making, aligning with the hypothesis that satisfaction alone does not always translate to better governance strategies. The overlapping density distributions between economic conditions and tourist preferences also indicate a potential interaction effect, where economic stability may reinforce preference-driven governance decisions.
To ensure the reliability of the Bayesian decision-making model, we evaluated MCMC convergence using the Gelman-Rubin diagnostic, also known as the Potential Scale Reduction Factor (PSRF). The results indicate that the multivariate PSRF is 1.00, which suggests excellent convergence, as values close to 1.00 indicate that the MCMC chains have mixed well. Recent studies reinforce the effectiveness of PSRF in assessing convergence across various Bayesian models, particularly when applied alongside other diagnostics like Geweke’s test. The individual PSRF values for key parameters are presented in Table 3, with beta_c, beta_e, beta_p, beta_s, and σ all at 1.00, while μ has a slightly higher value of 1.01, still within the acceptable range. The upper confidence interval (Upper C.I.) remains below 1.02, further confirming that the number of iterations is sufficient to achieve convergence.
Gelman-Rubin diagnostic results
| Parameter | Point estimate | Upper C.I. |
|---|---|---|
| beta_c | 1.00 | 1.01 |
| beta_e | 1.00 | 1.00 |
| beta_p | 1.00 | 1.00 |
| beta_s | 1.00 | 1.00 |
| mu | 1.01 | 1.02 |
| sigma | 1.00 | 1.00 |
These findings validate the robustness of the Bayesian model applied in this study, ensuring that inference is drawn from well-mixed MCMC chains that accurately represent the posterior distribution.
The trace plot of the sigma parameter in the MCMC analysis (Figure 2) demonstrates that the chain has reached a stationary state and reflects a stable posterior distribution. The random fluctuations over the iteration range of 150,000 to 200,000, without any clear upward or downward trend, indicate that the samples have been drawn from a well-mixed distribution. Additionally, the range of sigma values, fluctuating between approximately 8.0 and 10.0, suggests no significant drift or long-term dependence, further confirming that the sampling process has been conducted effectively.
The horizontal axis, labeled “Iterations,” ranges from 150000 to 200000 in increments of 10000 units. The vertical axis, labeled “Sigma,” ranges from 8.0 to 10.0 in increments of 0.5 units. The graph displays multiple trace lines, each representing a different series: The green shaded region highlights the range between 8.4 and 10.0 on the vertical axis across all iterations. Black, red, and green dashed lines represent different trace series for sigma, showing their variation over the iterations. The traces fluctuate around the central value, with some spikes above and below the green shaded region, indicating the variability of sigma during the iterations.Trace plot of sigma parameter in MCMC analysis. Source(s): The authors
The horizontal axis, labeled “Iterations,” ranges from 150000 to 200000 in increments of 10000 units. The vertical axis, labeled “Sigma,” ranges from 8.0 to 10.0 in increments of 0.5 units. The graph displays multiple trace lines, each representing a different series: The green shaded region highlights the range between 8.4 and 10.0 on the vertical axis across all iterations. Black, red, and green dashed lines represent different trace series for sigma, showing their variation over the iterations. The traces fluctuate around the central value, with some spikes above and below the green shaded region, indicating the variability of sigma during the iterations.Trace plot of sigma parameter in MCMC analysis. Source(s): The authors
These findings align with the convergence assessment using the Gelman-Rubin diagnostic, which reports a Potential Scale Reduction Factor (PSRF) ≈ 1.00 for all parameters, including sigma. This value confirms that the between-chain variance has merged with the within-chain variance, ensuring the reliability of the posterior estimates. In other words, the trace plot not only indicates that the chains have mixed well but also reinforces the conclusion that the number of iterations used is sufficient to achieve convergence.
While the convergence diagnostics confirm the stability of the MCMC chains, it is essential to further validate the robustness of the Bayesian model through sensitivity analysis. This involves testing the impact of different prior distributions on parameter estimation, ensuring that the findings are not unduly influenced by prior assumptions. The results of this sensitivity analysis are presented in Table 4 and further discussed below.
Sensitivity analysis: Comparison of default and alternative prior models
| Param | Mean_Default mean | Mean_Alternative | Mean_Alternative | SD_Alternative |
|---|---|---|---|---|
| beta_c | 0.00004 | 0.00025 | 0.05001 | 0.10017 |
| beta_e | 0.09985 | 0.10005 | 0.05000 | 0.10027 |
| beta_p | 0.20003 | 0.20070 | 0.06003 | 0.11970 |
| beta_s | −0.04988 | −0.04994 | 0.05002 | 0.09998 |
| mu | 59.99410 | 59.97412 | 4.98928 | 10.00372 |
| sigma | 8.74710 | 9.98741 | 0.72080 | 2.88023 |
Based on Table 4, the mean estimates for the key parameters remain relatively stable between the default prior and alternative prior settings. For example, the economic factor (beta_e) shows a slight shift from 0.09985 under the default prior to 0.10005 under the alternative prior, indicating minimal sensitivity to prior specification. Similarly, other parameters such as beta_p and beta_s exhibit only minor changes in their mean values, demonstrating the robustness of the model in terms of central tendency. However, the standard deviations of the parameters increase under the alternative prior, particularly for sigma, which rises from 0.7208 to 2.8802. This suggests that while the mean estimates are stable, the model’s uncertainty grows when alternative priors are introduced.
In this context, although the trace plot confirms good mixing and adequate iterations for convergence, it does not completely eliminate the impact of prior selection on result robustness. The wider posterior distributions observed under the alternative prior highlight the role of prior assumptions in influencing parameter uncertainty. To enhance model robustness, selecting more informative priors or further exploring various prior distributions that better fit empirical data could be effective strategies. This approach can help reduce estimation variability without compromising the flexibility of the Bayesian framework.
Nevertheless, when considering both key indicators—the stability of the trace plots and PSRF values close to 1.00, it is evident that the Bayesian inference conducted in this study remains highly reliable. While prior selection influences uncertainty to some extent, the overall convergence diagnostics confirm that the estimated parameters are unbiased and statistically valid. This ensures that the model provides credible and data-driven estimates, which can be effectively utilized for decision making in the context of halal tourism governance.
Beyond these findings, the study underscores the potential influence of macroeconomic factors, including exchange rate fluctuations and global economic conditions, on halal tourism governance. This is supported by research from Alrawadieh (2024), which found that exchange rate movements significantly affect tourism revenues in Organization of Islamic Cooperation (OIC) countries, particularly in terms of tourist arrivals and spending patterns. Additionally, Thanh et al. (2024) highlighted that exchange rate fluctuations impact international trade and investment, which in turn affect the economic stability of tourism-dependent regions.
Although this aspect was not the primary focus of the current model, the findings suggest that external economic conditions may shape decision-making processes in the sector. Therefore, future research should consider incorporating macroeconomic indicators and cross-regional comparisons to gain a more comprehensive understanding of their impact.
The Bayesian model indicates that tourist preferences (β_p) positively influence decision-making, with a mean of 0.1792, supporting H1. Prior studies also highlight that preferences shape tourist satisfaction, especially in halal tourism (Jalil and Akbar, 2024). Preferences are significantly influenced by perceived behavioral control and subjective norms, which affect satisfaction and loyalty (Putra et al., 2024). This is supported by interviews with community leaders in Pekalongan, who emphasized that halal tourism is not only about religious compliance but also about preserving cultural heritage, such as batik production. One leader stated, “Halal tourism in Pekalongan is about aligning Islamic values with local traditions to create a unique and meaningful experience for Muslim travelers.” However, challenges remain, as another leader highlighted, “Many small business owners lack awareness of the benefits of halal certification, which limits the sector’s growth potential.”
The results also strongly support H2, with economic conditions (beta_e) displaying a significant positive effect (mean = 0.1157) on decision-making. This aligns with conclusions from Seow et al. (2024), who found that improved infrastructure and stable economic environments contribute to better tourism performance, especially in emerging markets. Interviews with local tourism officers reinforced this, as one official noted, “Pekalongan has strong potential as a halal tourism hub, but we need to address infrastructure gaps and environmental concerns.” Similarly, interviews with syariah hotel managers revealed that while adherence to halal standards enhances marketability, poor environmental conditions, such as pollution from batik waste, negatively impact guest satisfaction and deter repeat visits.
Contrary to expectations, environmentally sustainable practices (beta_c) demonstrated a minimal direct impact on cultural integration (mean = 0.0056), indicating a weaker link between environmental sustainability and cultural alignment than anticipated. This finding contrasts with Baloch et al. (2023), who reported a significant association between sustainability initiatives and cultural preservation. However, interviews with religious leaders suggested that economic and religious factors play a more dominant role than environmental sustainability in cultural integration. One leader explained, “Islamic principles and economic incentives drive the halal tourism industry more than environmental considerations alone.” Nevertheless, syariah hotel managers and restaurant owners noted that improper waste disposal and pollution negatively affect the overall tourist experience, highlighting the need for improved waste management strategies.
A comparative analysis between Bali and Pekalongan further contextualizes these findings. Bali, as Indonesia’s primary tourist destination, benefits from well-developed infrastructure supported by foreign investment and government policies tailored to international travelers (Jama et al., 2024). In contrast, Pekalongan’s tourism industry relies on local economic drivers, particularly batik production and community-based tourism initiatives (Syakira, 2024). Interviews with local business owners revealed that economic challenges, such as fluctuating demand and the impact of tidal flooding (rob), pose significant barriers to tourism growth. One café owner stated, “The smell from the polluted river affects the dining experience, making it hard to retain customers despite offering quality halal food.” These insights suggest that economic and environmental factors must be considered together in designing governance models for sustainable tourism development.
Additionally, regulatory frameworks governing halal tourism differ between Bali and Pekalongan. Bali has successfully implemented Muslim-friendly tourism policies, such as halal food certification and prayer facilities, despite being a predominantly Hindu region. Pekalongan, on the other hand, has well-established halal regulations but lacks international standardization, limiting its appeal to global halal tourism markets. Interviews with tourism officers emphasized the need for globally recognized halal certification to enhance Pekalongan’s competitiveness. One officer remarked, “Standardizing halal certification to meet international standards will help us attract more Muslim travellers from abroad.”
To validate the robustness of the Bayesian model, we assessed MCMC convergence using the Gelman-Rubin diagnostic (Potential Scale Reduction Factor, PSRF). The multivariate PSRF value of 1.00 confirms excellent convergence, as values close to 1.00 indicate that the MCMC chains have mixed adequately. Recent research by Du et al. (2022) highlights the effectiveness of PSRF in assessing convergence, particularly in high-dimensional Bayesian models. Additionally, Duttweiler et al. (2024) demonstrate that combining PSRF with trace plots and alternative convergence diagnostics can enhance reliability in Bayesian inference.
5. Conclusion
This study has provided empirical insights into the governance of halal tourism in Indonesia by applying a Bayesian decision-making framework combined with Markov Chain Monte Carlo (MCMC) simulations. The findings confirm that tourist preferences and economic conditions are central determinants of policy outcomes, while environmental sustainability plays a more peripheral but contextually important role particularly in socio-economic settings where religious and financial considerations prevail. These results highlight the need for governance strategies that are both locally contextualized and empirically grounded, enabling the alignment of cultural identity, economic viability, and ecological responsibility.
Theoretically, this research contributes to the literature by advancing the application of Bayesian inference in tourism governance an area that has received limited attention despite its inherent complexity and uncertainty. By integrating probabilistic modeling with qualitative stakeholder insights, this study introduces a dynamic, adaptive approach that challenges the assumptions of traditional governance frameworks. Practically, the proposed model offers policymakers a robust analytical tool for decision-making under uncertainty. It facilitates real-time policy adjustment based on emerging data trends, enabling governance mechanisms that are both flexible and responsive to dynamic tourism environments.
While this study focuses on Pekalongan City, Indonesia, its methodological approach and findings offer transferable value to other regions facing comparable socio-environmental challenges. Nevertheless, several limitations must be acknowledged. First, the sample size was relatively limited, potentially constraining the generalizability of results. Second, the model does not explicitly account for external political or institutional factors that may influence tourism governance. Future research is encouraged to expand the empirical scope, incorporate comparative case studies across countries, and explore hybrid decision-making frameworks that integrate machine learning with Bayesian inference for even greater predictive utility.
6. Implications
These findings have broad implications for halal tourism governance. First, the results highlight the need for region-specific governance strategies that account for differences in economic structures, regulatory frameworks, and sustainability priorities. Pekalongan’s reliance on local industries necessitates policies that support sustainable economic growth, whereas Bali’s exposure to global economic fluctuations requires adaptive strategies that mitigate external risks. Second, while environmental sustainability is crucial, its role in cultural integration varies by context. In Pekalongan, integrating sustainability initiatives into traditional industries, such as batik production, may be more effective than standalone environmental policies. Future studies should explore how sustainability efforts can be better aligned with cultural preservation in halal tourism destinations.
Third, the study underscores the importance of internationally recognized halal certification for expanding tourism markets. Pekalongan could benefit from adopting global halal standards to attract international Muslim travelers, similar to Bali’s approach. Research on how regulatory flexibility impacts halal tourism growth in diverse contexts would provide valuable insights for policymakers. Finally, further research should explore the long-term effects of sustainability policies on cultural integration through longitudinal studies. Integrating macroeconomic indicators, such as exchange rates and foreign direct investment, into future Bayesian models could enhance the predictive accuracy of decision-making frameworks. By continuously refining probabilistic governance models, halal tourism policies can become more adaptive, evidence-based, and aligned with long-term sustainability goals.
Ethics Statement
This study was conducted in full compliance with ethical standards for research involving human participants. Informed consent was obtained from all participants prior to data collection, ensuring that they were aware of the study’s purpose, procedures, and their rights to withdraw at any time without penalty. The research was reviewed and approved by the relevant Institutional Review Board (IRB) or Ethics Committee at STAI Ki Ageng Pekalongan. All data collected was anonymized to protect the privacy and confidentiality of the participants. No vulnerable populations were involved, and the study adhered to the ethical guidelines outlined in the Declaration of Helsinki.
