# Computational and Mathematical Methods for Neuroscience
## 2 Fields of Neuroscience
### Theoretical Neuroscience
Statistical neuroscience applies advanced statistical techniques to analyze and interpret the complex data generated by neuroscience experiments, addressing challenges such as high dimensionality, noise, and the temporal structure of neural activity. By providing robust tools for managing the variability inherent in neural data, statistical neuroscience helps researchers identify patterns, relationships, and statistical dependencies, which are essential for testing hypotheses and making inferences about neural function. Key methods in statistical neuroscience include Spike Train Analysis (STA), Dimensionality Reduction (DR), Bayesian inference, and information theory. STA encompasses statistical techniques for analyzing the timing and patterns of neuronal spikes, which carry critical information about neural signaling. DR techniques, such as Principal Component Analysis (PCA) and t-distributed Stochastic Neighbor Embedding (t-SNE), simplify high-dimensional neural data, making them more accessible for interpretation. Bayesian inference introduces a probabilistic approach to understanding neural data, commonly applied to decode sensory information and predict neural responses. Information theory, meanwhile, quantifies the amount of information transmitted within neural circuits, providing insights into the efficiency and mechanisms of neural coding. These statistical approaches are essential for analyzing data from electrophysiological recordings, neuroimaging, and behavioral experiments. They allow researchers to draw reliable conclusions about brain activity, predict behaviors, and even forecast events like epileptic seizures [10]. Through statistical neuroscience, scientists gain critical insights into the principles of neural organization and function, advancing our understanding of brain dynamics. Neuroinformatics plays a crucial role in neuroscience by developing algorithms, data management tools, and computational techniques to organize, integrate, and share large datasets, thereby facilitating discovery and enhancing collaboration across studies. This field focuses on establishing standardized formats and databases that enable diverse types of neuroscience data to be combined, compared, and interpreted across studies and institutions. By streamlining the organization and accessibility of complex datasets, neuroinformatics supports efficient data sharing, reproducibility, and broader analyses. Popular neuroinformatics tools include Brainstorm, Brainsuite, Statistical Parametric Mapping (SPM), and FMRIB Software Library (FSL), containing image analysis and statistical tools for functional, structural, and diffusion MRI. Additionally, platforms such as Neuron and Brain Imaging Data Structure (BIDS) provide standardized data formatting and processing pipelines that enhance consistency in data analysis. Neuroinformatics also involves creating computational models that simulate brain processes, providing valuable insights into brain dynamics, neural circuits, and cognitive functions. A key goal of neuroinformatics is to promote open science by facilitating data sharing across labs, institutions, and even international boundaries, accelerating discovery, enhancing reproducibility, and allowing for larger-scale and more diverse analyses. Platforms like the NeuroInformatics Framework (NIF) exemplify this approach, providing standardized access to a wide range of neuroscience datasets and tools. One of the primary applications of neuroinformatics is brain mapping, which involves creating detailed maps of the brain's structural and functional connectivity to better understand regional interactions. By comparing large datasets from both healthy and diseased brains, neuroinformatics enables the identification of biomarkers and genetic markers associated with neurological and psychiatric disorders. Moreover, neuroinformatics contributes to the development of algorithms for processing data from Brain-Computer Interfaces (BCIs), facilitating direct communication between the brain and external devices [11; 12].