Combining Logistic Regression and Markov Chain Monte-Carlo Describe the Relationship between Exposure to a Given Dose of Radiation and its Effect on Clostridium tyrobutyricum Strains

Using the Markov Chain Monte-Carlo method to estimate the parameters in the Logistic regression model, we constructed a non-periodic irreducible Markov Chain with the posterior distribution of the parameters as stationary distribution, and then used the sample points extracted from the stationary distribution to calculate the Monte-Carlo integral. The above theoretical method can solve the difficult problem of classical logistic regression modeling because of the existence and limitation of the experimental sample data and the multicollinearity. In the classical regression setup with a continuous response, the predicted values can range over all real numbers. Therefore, a different modelling technique is needed. In this work, the results describe in detail a previously unknown lethality trend following ¹²C⁶⁺ heavy-ion irradiation of Clostridium tyrobutyricum. By Markov Chain Monte-Carlo can calculate the model fit for a randomly selected subset of the chain and calculate the predictive envelope of the model. The grey areas in the plot correspond to 50%, 90%, 95%, and 99% posterior regions. More importantly, although this study focused on the use of the method in heavy-ion irradiation of microbial, its results are broadly applicable.