Journal of Statistics and Mathematical Engineering

A Statistical and Probabilistic Method for Natural Language Processing (NLP)

Kirti Verma — 2025-10-14

Probabilistic and statistical approaches have become foundational to modern Natural Language Processing (NLP), enabling machines to process, understand, and generate human language with remarkable accuracy. These methods rely on the mathematical modeling of language phenomena using probability theory, statistics, and machine learning. Unlike rule-based systems, statistical NLP captures the inherent ambiguity and variability of human language by learning patterns from large corpora. Techniques such as n-gram models, Hidden Markov Models (HMM), Conditional Random Fields (CRF), and Probabilistic Context-Free Grammars (PCFG) are widely used for tasks like part-of-speech tagging, syntactic parsing, and named entity recognition. Additionally, Bayesian inference and maximum likelihood estimation help model linguistic uncertainty and optimize parameters in language models.

With the advent of big data and increased computational power, probabilistic models have evolved into more complex forms, such as topic models (e.g., Latent Dirichlet Allocation) and neural probabilistic language models, which serve as the basis for deep learning architectures like word embeddings and transformers. These models learn semantic and syntactic relationships from data without the need for explicit rules, significantly enhancing the performance of applications like machine translation, sentiment analysis, and question answering.

In essence, probabilistic and statistical methods provide a data-driven framework that is robust, scalable, and adaptable across languages and domains. They continue to play a crucial role in bridging the gap between human language and machine understanding, laying the groundwork for the development of more intelligent and context-aware NLP systems.

Multi-Criteria Decision-Making Framework to Identify Optimal Countries for Large-Scale Solar Farms

Tanvir Siraj — 2025-08-30

Global solar energy capacity is expanding rapidly, yet identifying the most suitable countries for large-scale solar farms remains a complex challenge due to varying geographical, meteorological, and technical factors. This study develops a Multi-Criteria Decision-Making (MCDM) framework to identify the most suitable countries for large-scale solar farms. Using data from the Global Solar Atlas, five key parameters, Global Horizontal Irradiance (GHI), Direct Normal Irradiance (DNI), Diffuse Horizontal Irradiance (DIF), Global Tilted Irradiance (GTI), and PV Output (PVOUT), were analyzed. Two MCDM techniques, Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Weighted Aggregated Sum Product Assessment (WASPAS), were applied to rank 186 countries based on solar energy potential. Spearman’s correlation coefficient was used to assess the consistency between the two ranking methods. Results indicate that African and Middle Eastern nations dominate the top ranks. Twelve countries ranked among the top positions in both ranking methods: Namibia, Egypt, Saudi Arabia, Algeria, Botswana, Chad, Jordan, Libya, Oman, Sudan, the United Arab Emirates, and Aruba. A strong correlation (0.9739) between the TOPSIS and WASPAS rankings confirms the reliability of the approach. These findings provide a data-driven basis for policymakers and investors to optimize solar energy deployment globally.

Comparison of Parametric and Nonparametric Methods in Real-World Data Analysis

Madhulika Shukla — 2025-10-13

Statistical analysis plays a critical role in interpreting real-world data, and the choice between parametric and nonparametric methods significantly influences the accuracy and reliability of results. Parametric methods rely on strong assumptions about the underlying data distribution, such as normality and homoscedasticity, offering high efficiency and interpretability when these assumptions are met. In contrast, nonparametric methods require minimal assumptions, making them ideal for skewed, ordinal, or heterogeneous data commonly found in real-world scenarios. This paper presents a comprehensive comparison of both approaches through theoretical discussion and practical application on diverse datasets, including income distribution, clinical trial data, and global temperature trends. The results highlight that parametric methods tend to perform well under controlled or ideal conditions, whereas nonparametric methods demonstrate greater robustness and flexibility, especially when data deviate from classical assumptions. By evaluating key statistical tasks such as estimation, hypothesis testing, and regression modeling—we show how each approach yields different insights depending on the data structure. The study emphasizes that no single method is universally superior; rather, effective analysis requires understanding the strengths, limitations, and appropriate contexts for each approach. This comparison provides practical guidance for researchers and analysts working with complex and imperfect real-world data.