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[[Bayesian statistics]] is a method of applying [[Bayes equation]] to data analysis. One of the biggest difference between Bayesian approaches and frequentist approaches is that Bayesians attempt to determine the probability that a given hypothesis is true given the data, while frequentist attempt to define the probability of getting the data given that a particular hypothesis is true.
[[Bayesian statistics]] is a method of applying [[Bayes equation]] to data analysis. One of the biggest difference between Bayesian approaches and frequentist approaches is that Bayesians attempt to determine the probability that a given hypothesis is true given the data, while frequentist attempt to define the probability of getting the data given that a particular hypothesis is true.
Bayesian approaches are becoming more and more popular in science because what most people are interested in is the probability of proposed hypothesis no the probability of the data. However, Bayesian methods have come under fire from many frequentist proponents. There is actually a very heated debate in statistical circles about the respective validity of both methods. The primary complaint leveled at Bayesian statistics is that it must use a [[prior probability]] of a hypothesis in its analysis. Often this prior is not known out right and assigned seemingly arbitrary values based on particular distributions such as the [[uniform distribution]] or [[beta distribution]].
Bayesian approaches are becoming more and more popular in science because what most people are interested in is the probability of proposed hypothesis no the probability of the data. It also does not need to make prior assumptions about the data such as [[Normal distribution | normality]] and [[homogeneity of variance]]. However, Bayesian methods have come under fire from many frequentist proponents. There is actually a very heated debate in statistical circles about the respective validity of both methods. The primary complaint leveled at Bayesian statistics is that it must use a [[prior probability]] of a hypothesis in its analysis. Often this prior is not known out right and assigned seemingly arbitrary values based on particular distributions such as the [[uniform distribution]] or [[beta distribution]].
===Descriptive statistics===
===Descriptive statistics===
==Non-parametric and Bootstrapping methods==
==Non-parametric and Bootstrapping methods==
One of the greatest problems in frequentist approaches to statistics is that it often relies on making prior assumptions about how the data looks and was collected. Most commonly the data must be a normal distribution and have homogeneity of variance. Different statistical methods are more or less robust to violations of these assumptions, and some techniques have attempted to avoid them all together. The end result though is usually a significant loss of power and increased likelihood of error.
[[Non-parametric statistics]] are any one of many methods that attempt to define descriptive characteristics or make inferential claims with out the need of tightly confined parameters. The main goals is to try and eliminate the need for assumptions without sacrificing power and accuracy.
[[Bootstrapping statistics]] is a particularly popular non-parametric approach. Bootstrapping is computationally costly and has only recently become feasible for most data sets. It involves [sampling with replacement]] from the given data set perhaps as many as 100,000 times in order to determine mean, error, best fits and comparisons of data sets.
[[Category:mathematics]]
[[Category:mathematics]]
[[category:Probability and Statistics]]
[[category:Probability and Statistics]]