Different types of modellings and the inference of model parameters for complex biological systems

---

Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, İstatistik Bölümü, Türkiye

Tezin Onay Tarihi: 2017

Öğrenci: MELİH AĞRAZ

Danışman: VİLDA PURUTÇUOĞLU GAZİ

Özet:

A reaction set that form a system can be modeled mathematically in different ways such as boolean, ordinary differential equations and stochastic modellings. Among them the random system is merely taken into account by the stochastic approach that is based on the known number of molecules in the reactions and if we consider the behaviour of the system under steady state condition, the modelling can be done via deterministic methods such as the ordinary differential equation. In this thesis, firstly, we aim to estimate the model parameters of a realistically complex biochemical system that is modelled to describe the steady state behaviour of the system. Among alternatives, we implement the Gaussian graphical models (GGM) which is one of the well known probabilistic model in this class. Here initially we develope an alternative approach of GGM in nonparametric distribution. For this purpose, we suggest LMARS (lasso-type multivariate adaptive regression spline) method. Then, we propose a normalization step called Bernstein polynomials for raw data to improve the performance of these models. Finally we suggest another alternative of GGM in parametric class and infer the model parameter via a novel estimation method, called the MMLE (modified maximum likelihood estimator). We evaluate all over findings with simulated and real data compute their accuracies as well as computational time behaviour of the system.