For pharmacometricians, probability theory is the very first obstacle towards the statistics since it is solely founded on mathematics. The purpose of this tutorial is to provide a simple version of introduction to a univariate random variable, its mean, variance, and the correlation coefficient of two random variables using as simple mathematics as possible. The definitions and theorems in this tutorial appear in most of the statistics books in common. Most examples are small and free of subjects like coins, dice, and binary signals so that the readers can intuitively understand them.
Mathematics ; Numismatics ; Probability Theory

BACKGROUND: Maintenance operations on-board ships are highly demanding. Maintenance operations are intensive activities requiring high manemachine interactions in challenging and evolving conditions. The evolving conditions are weather conditions, workplace temperature, ship motion, noise and vibration, and workload and stress. For example, extreme weather condition affects seafarers' performance, increasing the chances of error, and, consequently, can cause injuries or fatalities to personnel. An effective human error probability model is required to better manage maintenance on-board ships. The developed model would assist in developing and maintaining effective risk management protocols. Thus, the objective of this study is to develop a human error probability model considering various internal and external factors affecting seafarers' performance. METHODS: The human error probability model is developed using probability theory applied to Bayesian network. The model is tested using the data received through the developed questionnaire survey of >200 experienced seafarers with >5 years of experience. The model developed in this study is used to find out the reliability of human performance on particular maintenance activities. RESULTS: The developed methodology is tested on the maintenance of marine engine's cooling water pump for engine department and anchor windlass for deck department. In the considered case studies, human error probabilities are estimated in various scenarios and the results are compared between the scenarios and the different seafarer categories. The results of the case studies for both departments are also compared. CONCLUSION: The developed model is effective in assessing human error probabilities. These probabilities would get dynamically updated as and when newinformation is available on changes in either internal (i.e., training, experience, and fatigue) or external (i.e., environmental and operational conditions such asweather conditions, workplace temperature, ship motion, noise and vibration, and workload and stress) factors.
Humans* ; Noise ; Probability Theory ; Risk Management ; Ships ; Vibration ; Water ; Weather

Randomized controlled trial is widely accepted as the best design for evaluating the efficacy of a new treatment because of the advantages of randomization (random allocation). Randomization eliminates accidental bias, including selection bias, and provides a base for allowing the use of probability theory. Despite its importance, randomization has not been properly understood. This article introduces the different randomization methods with examples: simple randomization; block randomization; adaptive randomization, including minimization; and response-adaptive randomization. Ethics related to randomization are also discussed. The study is helpful in understanding the basic concepts of randomization and how to use R software.
Bias (Epidemiology) ; Ethics ; Probability Theory ; Random Allocation ; Selection Bias

Over the half of last century, epidemiology has witnessed that tobacco causes lung cancer. Therefore, lung cancer lawsuits against tobacco companies have been raised in many countries. However, a discrepancy between epidemiology dealing with population-based causal association and lawsuit dealing with individual-based evidence has happened. This article discusses application of epidemiology to the tobacco lawsuit cases in Korea. Epidemiological studies such as double blind randomized controlled clinical trials and cohort studies give clinicians important information on decision-making for the treatment of an individual patient and predicting prognosis. Epidemiological data have also been applied to the diagnosis of a worker's claim on occupational disease or work-related disorder. Illegality is generally recognized in the court when direct causal relationship between offending action(s) and damage(s) is proved and the damaged must prove illegality of the offender(s). The probability theory was emerged to reduce the responsibility especially when a plaintiff has a difficulty in proving causal relationship and illegality due to long-term duration or complexity or poor condition of the plaintiff such as environmental lawsuit cases. In relation to the probability theory, a theory was raised that a causal relationship is proved legally if an epidemiological causal relationship between offending action(s) and damage(s) is proved. Based on these evidences and theories, we show our opinion that epidemiological data are applicable to the individuals such as tobacco lawsuit cases in Korea.
Cohort Studies ; Diagnosis ; Epidemiologic Studies ; Epidemiology* ; Humans ; Korea* ; Lung Neoplasms ; Occupational Diseases ; Probability Theory ; Prognosis ; Tobacco*

Profile hidden Markov models (HMMs) based on classical HMMs have been widely applied for protein sequence identification. The formulation of the forward and backward variables in profile HMMs is made under statistical independence assumption of the probability theory. We propose a fuzzy profile HMM to overcome the limitations of that assumption and to achieve an improved alignment for protein sequences belonging to a given family. The proposed model fuzzifies the forward and backward variables by incorporating Sugeno fuzzy measures and Choquet integrals, thus further extends the generalized HMM. Based on the fuzzified forward and backward variables, we propose a fuzzy Baum-Welch parameter estimation algorithm for profiles. The strong correlations and the sequence preference involved in the protein structures make this fuzzy architecture based model as a suitable candidate for building profiles of a given family, since the fuzzy set can handle uncertainties better than classical methods.
Algorithms ; Animals ; Computational Biology ; Databases, Protein ; Fuzzy Logic ; Globins ; chemistry ; genetics ; Humans ; Markov Chains ; Models, Statistical ; Probability Theory ; Protein Kinases ; chemistry ; genetics ; Sequence Alignment ; statistics & numerical data ; Sequence Analysis, Protein ; statistics & numerical data