Question

In: Math

Question: Discuss the reasons for using Bayesian analysis when faced with uncertainty in making decisions. Discussion...

Question:

Discuss the reasons for using Bayesian analysis when faced with uncertainty in

making decisions.

Discussion Requirements:

How would you describe Bayesian Theorem?

Describe the assumptions of Bayesian analysis.

Provide the example of problem where one can use Bayesian analysis in Big Data Analytics.

Describe the the problems with Bayesian analysis.

Solutions

Expert Solution

Bayes theorem describes the probability of an event based on other information that might be relevant. Essentially, you are estimating a probability, but then updating that estimate based on other things that you know. This is something that you already do every day in real life. For instance, if your friend is supposed to pick you up to go out to dinner, you might have a mental estimate of if she will be on time, be 15 minutes late, or be a half hour late. That would be your starting probability. If you then look outside and see that there are 8 inches of new snow on the ground, you would update your probabilities to account for the new data. Bayes theorem is a formal way of doing that.

Example of Bayesian analyis in Big Data Analytics

In any application area where you have lots of heterogeneous or noisy data or anywhere you need a clear understanding of your uncertainty are areas that you can use Bayesian Statistics. From discussions with experts some of the areas that have seen early adoption have been e-commerce, insurance, finance and healthcare.

example, A represents the proposition that it rained today, and B represents the evidence that the sidewalk outside is wet:

p(rain | wet) asks, "What is the probability that it rained given that it is wet outside?" To evaluate this question, let's walk through the right side of the equation. Before looking at the ground, what is the probability that it rained, p(rain)? Think of this as the plausibility of an assumption about the world. We then ask how likely the observation that it is wet outside is under that assumption, p(wet | rain)? This procedure effectively updates our initial beliefs about a proposition with some observation, yielding a final measure of the plausibility of rain, given the evidence.

This procedure is the basis for Bayesian inference, where our initial beliefs are represented by the prior distribution p(rain), and our final beliefs are represented by the posterior distribution p(rain | wet). The denominator simply asks, "What is the total plausibility of the evidence?", whereby we have to consider all assumptions to ensure that the posterior is a proper probability distribution.

Bayesians are uncertain about what is true (the value of a KPI, a regression coefficient, etc.), and use data as evidence that certain facts are more likely than others. Prior distributions reflect our beliefs before seeing any data, and posterior distributions reflect our beliefs after we have considered all the evidence.

problems with Bayesian analysis

  1. hoice of prior. This is the usual carping for a reason, though in my case it's not the usual "priors are subjective!" but that coming up with a prior that's well reasoned and actually represents your best attempt at summarizing a prior is a great deal of work in many cases. An entire aim of my dissertation, for example, can be summed up as "estimate priors".
  2. It's computationally intensive. Especially for models involving many variables. For a large dataset with many variables being estimated, it may very well be prohibitively computationally intensive, especially in certain circumstances where the data cannot readily be thrown onto a cluster or the like. Some of the ways to resolve this, like augmented data rather than MCMC, are somewhat theoretically challenging, at least to me.
  3. Posterior distributions are somewhat more difficult to incorporate into a meta-analysis, unless a frequentist, parametric description of the distribution has been provided.
  4. Depending on what journal the analysis is intended for, either the use of Bayes generally, or your choice of priors, gives your paper slightly more points where a reviewer can dig into it. Some of these are reasonable reviewer objections, but some just stem from the nature of Bayes and how familiar people in some fields are with it.

Related Solutions

*What is the difference between risk and uncertainty? *Different techniques of making decisions under risk, uncertainty,...
*What is the difference between risk and uncertainty? *Different techniques of making decisions under risk, uncertainty, no risk or uncertainty, under risk and uncertainty. *Why do we need to consider economic equivalence to evaluate alternatives (single and multiple)? *What are the different economic equivalences that may be considered?
Discuss both the quantitative and qualitative factors that managers should consider when making decisions using differential...
Discuss both the quantitative and qualitative factors that managers should consider when making decisions using differential analysis. Apply these factors to a specific example of a decision under consideration.   
Discuss decision making under conditions of uncertainty, specifically using expected monetary value.
Discuss decision making under conditions of uncertainty, specifically using expected monetary value.
Discuss the differences among decision-making under certainty, decision-making under risk, and decision-making under uncertainty. Using the...
Discuss the differences among decision-making under certainty, decision-making under risk, and decision-making under uncertainty. Using the EMV criterion with a decision tree, describe how you would determine the best decision. Briefly discuss how a utility function can be assessed. What is a standard gamble, and how is it used in determining utility values?
What reasons are not suitable for using Cost Benefit Analysis as a decision making tool for...
What reasons are not suitable for using Cost Benefit Analysis as a decision making tool for public sector infrastructure projects(High speed rail) in Hong Kong?
1. Discuss the various implications for managers when making capital structure decisions.
1. Discuss the various implications for managers when making capital structure decisions.
Discuss uncertainty variability and how it relates to making or buying:
Discuss uncertainty variability and how it relates to making or buying:
write a discussion on -Economics is a science of making decisions in the presence of scarce...
write a discussion on -Economics is a science of making decisions in the presence of scarce resources.” With examples from personal experience, briefly explain how you apply economics in your daily life or would expect to apply economics in your life. Or. “No man can be a good citizen unless he has a wage more than sufficient to cover the bare cost of living” (Teddy Roosevelt, August 31, 1910). Recently both the Federal Government and the States are pushing hard...
Discuss some of the important considerations when making decisions around dropping products or departments that are...
Discuss some of the important considerations when making decisions around dropping products or departments that are less profitable than desired.
Provide an argument against using cost-benefit analysis as the only way of making social decisions Environmental...
Provide an argument against using cost-benefit analysis as the only way of making social decisions Environmental and natural resource economics
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT