Overview

• Computational statistics is statistics that uses computation, often a lot of computation,
• While statistical computing is computational mathematics.
• Both fields are hybrids, but it seems that
  • in computational statistics the emphasis is on the statistics
  • in statistical computation the emphasis is on the tools.
• Statistics means numerical descriptions to most people.
• Statistics does not just mean numerical fact, collection or summarization of the data.
• It also means that the whole body of systematic methods for collecting, summarizing, analyzing and interpreting data, and to make decisions.

• In recent decades, the statistical methods have been successfully used in
  • Manufacturing,
  • Development of food products,
  • Computer software,
  • Pharmaceuticals,
  • Many other areas,
• Examples: Japanese industrial miracle; High-quality products. Improvement of quality in American industry
• The use of statistical methods involves the gathering of information of scientific data.
• Statistical methods are designed to make scientific judgements in the face of uncertainty and variation.
• Two types of statistics:
  1. Inferential statistics
  2. Descriptive statistics

• Inferential statistics are the mathematical procedures hereby we convert information about the sample into intelligent guesses about the population.
• Population. A collection of all elements whose characteristics are being study. By countability, it can be either finite or infinite.
• Sample. A properly selected subset of the population, which is used to gain insight about the population.
  • (Simple) Random Sample: A sample drawn in such a way that each element of the population has an equal chance of being selected.
• Parameter. The characteristic(s) or attribute(s) of the population, which is generally unknown. e.g. $\mu$ (population mean).
• Statistic. The characteristic of the sample, which is a function of the data. It is usually numerical facts. e.g. $\bar{x}$ (sample mean).
• Example: a manufacturer of computer boards wish to eliminate defects
  • 50 computer boards are sampled from the process to collect information.
  • Here, the population is all computer boards manufactured over a specific period of time.
• It utilizes sample data to make estimates, decisions, predictions, or other generalizations about larger set of data.
• This is also called inductive reasoning or inductive statistics.
  • Deduction - From the general facts to particular cases: Mathematics.
  • Induction - From a particular case to a general one: Statistics.

• Descriptive statistics consists of methods for organizing, displaying, and describing data (to convey information) by using tables, graphs, and summary measures.
  • Descriptive statistics are just descriptive. They do not involve generalizing beyond the data at hand.
  • It utilizes graphical and numerical methods to look for patterns, to summarize, and to present the information in a set of data.
  • Descriptive statistics are central to the professional sports and other areas.
• With descriptive statistics, we are simply describing what the data shows.
• With inferential statistics, we are trying to make inferences from our data to more general conditions.