Unit I - Statistical parameter estimation.pptx

Computer aided drug development
M. Pharm Sem II

1. PES MODERN COLLEGE OF PHARMACY (Ladies) MOSHI, PUNE Savitribai Phule Pune University M .PHARM Semester- II By Mrs. Sneha Patil Assistant Professor Dept. of Pharmaceutics Statistical parameter estimation A lecture on CADD

2. Content Introduction Types Point estimation Interval estimation Reference

3. 1. Introduction Once the model functional form has been decided upon and the experimental data have been collected , a value for the model parameters (point estimation) and a confidence region for this value (interval estimation) must be estimated from the available data One of the main tasks of statistical interference is the estimation of population parameters from the available sample statistics which are also called estimator From the sample data we can estimate the population data like population mean

4. 2. Types of statistical parameter estimation

5. 3. Point estimation Point estimation requires the use of sample data to measure a single value that acts as an unknown population parameter's 'best estimate‘ Generally , data from a sample is used to calculate the population data in the inferential statistics Sample mean is the unbiased estimate of the population mean ( u) Maximum-likelihood estimation (MLE) uses the mean and variance as parameters and seeks parametric values that make the observed outcomes the most likely MLE is a method of estimating parameters of a statistical model It provides estimates of a parameter when applied to a data set and with a given statistical model In general, the maximum likelihood approach selects the set of values of the model parameters for a fixed data set and the underlying statistical model that maximizes the probability function MLE provides a unified estimation method, which is well defined in the case of normal distribution and several other problems MLE are not suitable for certain complex problems

6. Point estimation continue.… Linear least square method is another popular estimation approach Linear least squares is a method that suits a mathematical model with data where the desired value is expressed linearly for any data point in terms of the unknown model parameters To summarize the data, understand the mechanism of the system and to estimate unobserved values, the resulting fitted model can be used Mathematically , the problem of approximately solving an over-determined set of linear equations is linear least squares, where the best approximation is defined as minimizing the number of square differences between the values of the data and their corresponding modelled values The assumed function is linear to the parameters to be estimated, the approach is called linear least squares

7. 4 . Interval estimation This is the estimation of a population parameter specified by two values (lower and upper) This is better than the point estimation because this indicates range or precision of an estimate Upper confidence limit (UL) and Lower confidence limit (LL) are present in the confidence interval of the interval estimation A probability is assigned that this interval contains true population. We can't get the exact population parameter if we report or have a point estimate Population and sample size influence the width of confidence interval It is suggested to have a certain range of confidence in our estimate and the statistic should lie within the confidence range

8. Interval estimation continue.… The most prevalent forms of interval estimation are Confidence intervals (frequentist method) and Credible intervals(Bayesian Method) A probability is assigned to the hypothesis in a Bayesian method In contrary to the Bayesian method, in a Frequentist method a hypothesis is tested without assigning a probability to the hypothesis

9. 4 . Reference Karri V V S Narayana Reddy, K Gowthamarajan , Arun Radhakrishnan , Arun Radhakrishnan . A Textbook of Computer aided drug development. S. vikas and company, PV Publication; 2021 edition; Pg. no. 270, 271

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