The dynamical systems are comprised of two components that change over time: the state space and the observation models. This study examines parameter inference in dynamical systems from the perspective of Bayesian inference. Inference on unknown parameters in nonlinear and non-Gaussian dynamical systems is challenging because the posterior densities corresponding to the unknown parameters do not have traceable formulations. Such a system is represented by the Ricker model, which is a traditional discrete population model in ecology and epidemiology that is used in many fields. This study, which deals with parameter inference, also known as parameter learning, is the central objective of this study. A sequential embedded estimation technique is proposed to estimate the posterior density and obtain parameter inference. The resulting algorithm is called the Augmented Sequential Markov Chain Monte Carlo (ASMCMC) procedure. Experiments are performed via simulation to illustrate the performance of the ASMCMC algorithm for observations from the Ricker dynamical system.

Optical bandpass filters, used to restrict certain wavelengths while allowing other wavelengths to pass, are a common element in many optical devices, such as spectroscopic sensors and hyperspectral imagers. Such filters can be implemented using interference filters, which operate on the principle of constructive and destructive interference. In this work, an interference bandpass filter with continuously varying thicknesses of the constituent films is designed and fabricated for the visible spectral range. Niobium pentoxide and silicon dioxide are used as the filter materials due to the high refractive index contrast between them, resulting in a smaller number of required material films. Ion beam sputter deposition is used as the deposition method due to its ability to produce accurate thickness high optical quality films. The fabricated filter has a transmission band of 130 nm, i.e., 470–600 nm, and can block wavelengths as low as 300 nm and as high as 1080 nm, which is sufficient for use with silicon-based detectors in the visible spectral range. The maximum and minimum transmission inside the transmission band is 96% and 71%, respectively, with an average transmission of 88%. The transmission outside the transmission band is less than 1.6%.

Human cognition is influenced by the way the nervous system processes information and is linked to this mechanical explanation of the human body’s cognitive function. Accuracy is the key emphasis in neuroscience which may be enhanced by utilising new hardware, mathematical, statistical, and computational methodologies. Feature extraction and feature selection also play a crucial function in gaining improved accuracy since the proper characteristics can identify brain states efficiently. However, both feature extraction and selection procedures are dependent on mathematical and statistical techniques which implies that mathematical and statistical techniques have a direct or indirect influence on prediction accuracy. The forthcoming challenges of the brain-computer interface necessitate a thorough critical understanding of the complicated structure and uncertain behavior of the brain. It is impossible to upgrade hardware periodically, and thus, an option is necessary to collect maximum information from the brain against varied actions. The mathematical and statistical combination could be the ideal answer for neuroscientists which can be utilised for feature extraction, feature selection, and classification. That is why in this research a statistical technique is offered together with specialised feature extraction and selection methods to increase the accuracy. A score fusion function is changed utilising an enhanced cumulants-driven likelihood ratio test employing multivariate pattern analysis. Functional MRI data were acquired from 12 patients versus a visual test that comprises of pictures from five distinct categories. After cleaning the data, feature extraction and selection were done using mathematical approaches, and lastly, the best match of the projected class was established using the likelihood ratio test. To validate the suggested approach, it is compared with the current methods reported in recent research.