1. Probability and Random Variables
- Concept: Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true. A random variable is a variable whose possible values are numerical outcomes of a random phenomenon.
- General Application: In many fields including computer science, statistics, finance, and engineering, probability and random variables are used to model uncertainty and to make predictions about future events.
- Drug Discovery Application:
- Assessing the likelihood of a drug-target interaction based on physicochemical properties of the drug and the target.
- Predicting potential side effects of a drug by modeling the interaction between the drug and various biological systems as random variables.
- Analyzing genetic variations (SNPs) and their correlation with drug efficacy and adverse drug reactions.
2. pmf (probability mass function), pdf (probability density function), cdf (cumulative distribution function)
- Concept: A pmf is a function that gives the probability that a discrete random variable is equal to some value. A pdf is a function whose value at any given sample in the sample space can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample. A cdf is a function used to specify the probability of a random variable falling within a range of values.
- General Application: They are used in statistics and probability theory to describe and analyze random variables and their distributions.
- Drug Discovery Application:
- PMF can be used to calculate the probability of a specific genetic mutation in a population, which may influence the effectiveness of a drug.
- PDF can be used to model the distribution of different dosage levels of a drug in a patient population.
- CDF can be used to quantify the cumulative probability of a drug achieving a certain level of effectiveness.
3. Mean and Variance
- Concept: The mean is the average of a set of numbers, while the variance measures how spread out the numbers are from the mean.
- General Application: They are used in statistics and probability theory to summarize data and to measure the dispersion of data.
- Drug Discovery Application:
- The mean and variance can be used to measure the average effectiveness of a drug and the variability in effectiveness among patients.
- These metrics can also be used in the analysis of 'omic' data (genomic, proteomic, metabolomic), helping to identify potential drug targets.
4. Markov and Chebyshev inequalities, Chernoff bounds
- Concept: These are mathematical inequalities that provide bounds on the tail probabilities of random variables.
- General Application: They are used in probability theory and statistics to make estimations and predictions about random variables.
- Drug Discovery Application:
- These inequalities and bounds can be used to estimate the probability of rare adverse drug reactions.
- They can also be used to estimate the range within which the majority of responses to a drug will fall in a population.
5. Estimation (LMSE - Least Mean Square Error, MMSE - Minimum Mean Square Error, MLE - Maximum Likelihood Estimation)
- Concept: These are methods for estimating the parameters of a statistical model. LMSE and MMSE are methods used to estimate a signal in the presence of noise, whereas MLE is a method for estimating the parameters of a statistical model, given observations.
- General Application: They are used in statistics and machine learning for parameter estimation and prediction.
- Drug Discovery Application:
- These estimation methods can be used in bioinformatics to predict the structure of proteins or the interaction between proteins and potential drugs.
- They can also be used in pharmacokinetic and pharmacodynamic modeling to predict the absorption, distribution, metabolism, and excretion of drugs in the body.