## 1 Introduction  
Abalone, a highly valued marine resource, holds significant economic importance, particularly in Korea, where its market value reached KRW 347.5 billion in 2016 (Korea National Statistical Office, 2018 [1]). This makes it the most valuable cultured shellfish in the country. However, abalone cultivation faces considerable challenges that threaten its sustainability and profitability. The species' inherently slow growth rate necessitates prolonged cultivation periods, leaving it vulnerable to environmental stresses. Thesechallenges are compounded by additional factors, including viral infections ([PERSON] et al., 2013 [2]) and the adverse effects of high-density farming practices ([PERSON] et al., 2013 [3]). Furthermore, fluctuations in water temperature present a critical concern, often resulting in mass mortality events. Such temperature shifts increase oxygen demand, leading to hypoxic conditions that severely stress the abalone ([PERSON] et al., 2013 [4]). The cultivation of abalone is not only vital for its economic contributions, but also for meeting the growing demand for high-value seafood products globally. Addressing the multifaceted challenges associated with its farming requires innovative strategies and tools. Specifically, there is an urgent need for advanced predictive models capable of accurately assessing the effects of environmental factors on abalone growth. By developing such models, we can mitigate risks, improve survival rates, and optimize growth conditions, contributing to more sustainable aquaculture practices. In this paper, we address these challenges by introducing a probabilistic machine learning-based approach using a Bayesian framework to assess the effects of key environmental factors, including water temperature, pH, salinity, nutrient supply, and dissolved oxygen levels. The proposed model is based on a Bayesian kernel machine regression model ([PERSON] et al., 2015 [5]; [PERSON] et al., 2018 [6]) with a Gaussian process prior ([PERSON], 2006 [7]). This model employs a spike-and-slab prior on the inverse of the length-scale parameters to determine the influence of growth-related factors. By leveraging Gaussian processes, the model captures complex, non-linear relationships among the factors. Furthermore, it addresses heteroscedasticity by modeling the error variance, allowing for varying levels of variance across observations. The spike-and-slab prior also enables automatic variable selection, identifying the key environmental factors with the most significant impact on growth. This approach provides not only accurate growth predictions, but also deeper insights into the relative importance of these factors, contributing to a better understanding of abalone growth dynamics. This paper makes the following key contributions:  
* We propose a novel weighted Bayesian kernel machine regression (WBKMR) model that integrates Gaussian processes with a spike-and-slab prior, enabling both accurate predictions and variable selection. * The model explicitly accounts for heteroscedasticity, allowing for varying levels of error variance across observations, which is critical for analyzing aquaculture data. * Using Posterior Inclusion Probability (PIP) analysis, the model identifies the most critical environmental factors, such as dissolved oxygen, nutrient supply, and salinity, and quantifies their relative influence on abalone growth. * Comparative experiments demonstrate that the proposed model achieves superior predictive accuracy compared to baseline methods. The remainder of this paper is organized as follows. Section 2 reviews the related work on abalone growth prediction and machine learning models. Section 3 introduces the definitions and properties of Gaussian processes and kernel machine regression, which are foundational to our proposed approach. Section 4 describes the growth data of northern and disk abalones, along with the Bayesian kernel machine regression model used for analysis.