Statistical Inference in Biological and Diagnostic Systems
Biological systems are exceptionally good at sensing their environment with extraordinary precision. Certain single cellular organisms are even capable of detecting chemicals of the order of a single molecule. To achieve this, these systems need to robustly infer the required information from the data obtained from the noisy ligand-receptor interactions. One of the main goals of this thesis is to understand the inference strategies used in these cellular systems. From an application point of view, this analysis can also be extended to improve the performance of artificially engineered sensing systems such as diagnostic systems and chemotactic robots. Interestingly, unlike their biological counterparts, these artificial systems perform extremely poorly even in noise-free laboratory environments. One essential step towards improving the performance of these artificial sensors is to understand the fundamental difference in the inference mechanisms between these systems and the biological sensing systems. In general, analyzing the working mechanisms of biological systems using mechanistic physical models is extremely challenging due to the sheer complexity of these systems. In most cases, even the number and identity of the parameters and their relations, leading to the observed phenomenon is not known precisely. Therefore, to study the behavior of these complex systems, one needs to use a data-driven approach where specific information about the system needs to be inferred from the available experimental data. Whether it is the system (living/artificial) that wants to learn about its environment or a physicist who wants to learn about the system, the problem is common: i.e., given a dataset, how does one infer the information of interest? The field of statistics that deals with this particular problem is called statistical inference. Typically, statistical inference concepts are used in the numerical analysis where the experimental data is available. In this work, I have taken a different approach where I have implemented the statistical inference framework to theoretically model systems. To this end, I have considered independent problems from biological and diagnostic systems and analytically derived fundamental properties of these systems using statistical inference concepts.