In this article, I will provide a basic introduction to Bayesian learning and explore topics such as frequentist statistics, the drawbacks of the frequentist method, Bayes's theorem (introduced with an example), and the differences between the frequentist and Bayesian methods using the coin flip experiment as the example. To begin, let's try to answer this question: what is the frequentist method? When we flip a coin, there are two possible outcomes -- heads or tails. Of course, there is a third rare possibility where the coin balances on its edge without falling onto either side, which we assume is not a possible outcome of the coin flip for our discussion. We conduct a series of coin flips and record our observations i.e. the number of the heads (or tails) observed for a certain number of coin flips. In this experiment, we are trying to determine the fairness of the coin, using the number of heads (or tails) that we observe.
The use of formal statistical methods to analyse quantitative data in data science has increased considerably over the last few years. One such approach, Bayesian Decision Theory (BDT), also known as Bayesian Hypothesis Testing and Bayesian inference, is a fundamental statistical approach that quantifies the tradeoffs between various decisions using distributions and costs that accompany such decisions. In pattern recognition it is used for designing classifiers making the assumption that the problem is posed in probabilistic terms, and that all of the relevant probability values are known. Generally, we don't have such perfect information but it is a good place to start when studying machine learning, statistical inference, and detection theory in signal processing. BDT also has many applications in science, engineering, and medicine.
Uncertainty involves making decisions with incomplete information, and this is the way we generally operate in the world. Handling uncertainty is typically described using everyday words like chance, luck, and risk. Probability is a field of mathematics that gives us the language and tools to quantify the uncertainty of events and reason in a principled manner. In this post, you will discover a gentle introduction to probability. Photo by Emma Jane Hogbin Westby, some rights reserved.
We propose a new Bayesian method for spatial cluster detection, the "Bayesian spatial scan statistic," and compare this method to the standard (frequentist) scan statistic approach. We demonstrate that the Bayesian statistic has several advantages over the frequentist approach, including increased power to detect clusters and (since randomization testing is unnecessary) much faster runtime. We evaluate the Bayesian and frequentist methodson the task of prospective disease surveillance: detecting spatial clusters of disease cases resulting from emerging disease outbreaks. Wedemonstrate that our Bayesian methods are successful in rapidly detecting outbreaks while keeping number of false positives low.
Bayesian Statistics continues to remain incomprehensible in the ignited minds of many analysts. Being amazed by the incredible power of machine learning, a lot of us have become unfaithful to statistics. Our focus has narrowed down to exploring machine learning. We fail to understand that machine learning is only one way to solve real world problems. In several situations, it does not help us solve business problems, even though there is data involved in these problems. To say the least, knowledge of statistics will allow you to work on complex analytical problems, irrespective of the size of data. In 1770s, Thomas Bayes introduced'Bayes Theorem'.