Simplified Bayes’s Theorem

Bayes’s theorem is the fundamental concept behind Bayesian statistics and there are several machine learning and deep learning algorithm depends upon Bayes’s theorem like Naive Bayes, Gaussian Naive Bayes, Bayesian Network etc click here for more categorizations of algorithm So in this tutorial we will learn about basic concept of probability, conditional probability and Bayes’s theorem.

Probability:

A probability is number between 0 and 1 (including both) that represents a degree of belief in a fact or prediction. The value 1 represent certainly that the fact is true or that prediction will come true. The value 0 represent certainly that the fact is false ie  1==>True   and 0==>False.

Intermediate value represent degree of certainty like the value 0.5 represent 50% means the predicted value is likely to happen or not. For example tossing a coin will land head is 1/2 or 0.5  or 50% .

Conditional Probability:

Conditional probability is the probability which is depends on some background information. For example i want to know the probability of  a particular person will have a heart attack in the next year and i found some data that the rate of heart attack on particular state is 0.4%  but we know that there are some factors exists by which person can decrease the probability of heart attack and for that particular person the heart attack rate is 0.2% which is lower than the state average. This is conditional probability because it based on number of factor that depends upon number of factors that make person’s condition.

The usual notations of conditional probability is p(A|B) which is probability of a given that B is true. A represents the prediction that particular person will have heart attack next year and B is set of conditions by which he reduced his chance.

Conjoint Probability:

Conjoint probability is the fancy way to say the probability the two things are true. If i write the p(A and B) means that the probability of A and B are both  true.

For example if  i toss coins and A means the first coin lands Head and B means the second coin lands Head also the p(A)=p(B)=0.5 and sure enough                             P(A and B)=P(A)p(B)=0.25 but this formula only works because in this case A and B are independent, that is knowing of outcomes of first event does not  change  the probability of second or p(B|A)=p(B).

Here is different example where the event are not independent. Suppose that A means that it rains today and B means that is rains tomorrow. If i know that it rained today, it is more likely that it will rain tomorrow so p(B|A)>p(B)

probability of conjunction is: p(A and B) =p(A)p(B|A)—————-(1)

if we interchange them

probability of conjunction is: p(B and A) =p(B)p(A|B)——————(2)

Conjunction is commutative ie, p(A and B) = p(B and A) for any event A and B.

Bayes’s Theorem:

combine both equations (1) and (2)=> p(B)p(A|B)=p(A)p(B|A)—————(3)

From equation (3) it means that when there are two ways to compute the conjunctions if you have p(A) you multiply by the conditional probability p(B|A) and if you have p(B) you have to multiply by p(A|B).

On dividing p(B) of equation(1) we get,

This is called Bayes’s Theorem. It tells that how often A happens given that B happens written p(A|B), when we know how often B happens given that A happens written p(B|A) and how likely A and B are their own way.

  •  p(A|B) is “probability of A given B”
  • P(A) is “probability of A”
  • p(B|A) is “probability of B given A”
  • p(B) is “probability of B” 

 

About Mitra N Mishra 35 Articles
Mitra N Mishra is working as a full-stack data scientist.

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  143. Nice post. I learn something new and challenging on blogs I stumbleupon on a daily basis. It will always be helpful to read through articles from other authors and practice a little something from their sites.

  144. Can I simply say what a comfort to discover somebody who actually knows what they are talking about on the web. You definitely realize how to bring a problem to light and make it important. More people ought to read this and understand this side of the story. I can’t believe you aren’t more popular because you certainly possess the gift.

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  146. Having read this I thought it was extremely informative. I appreciate you spending some time and effort to put this informative article together. I once again find myself personally spending a significant amount of time both reading and commenting. But so what, it was still worthwhile!

  147. I really love your site.. Very nice colors & theme. Did you create this amazing site yourself? Please reply back as I’m trying to create my own website and would love to find out where you got this from or exactly what the theme is called. Appreciate it!

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  156. This is the right site for anybody who really wants to understand this topic. You realize so much its almost hard to argue with you (not that I personally will need to…HaHa). You certainly put a brand new spin on a subject which has been written about for years. Excellent stuff, just wonderful!

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  167. Can I simply say what a relief to find someone that genuinely understands what they’re discussing on the net. You certainly understand how to bring an issue to light and make it important. More and more people need to read this and understand this side of your story. It’s surprising you are not more popular since you most certainly have the gift.

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  171. Having read this I believed it was really informative. I appreciate you spending some time and effort to put this informative article together. I once again find myself personally spending a lot of time both reading and posting comments. But so what, it was still worthwhile!

  172. After I originally commented I seem to have clicked on the -Notify me when new comments are added- checkbox and now each time a comment is added I receive 4 emails with the same comment. There has to be a way you can remove me from that service? Thank you!

  173. Having read this I believed it was very enlightening. I appreciate you spending some time and energy to put this short article together. I once again find myself personally spending a lot of time both reading and leaving comments. But so what, it was still worth it!

  174. Hello there! This article couldn’t be written much better! Going through this post reminds me of my previous roommate! He constantly kept talking about this. I’ll send this article to him. Pretty sure he’s going to have a great read. Many thanks for sharing!

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  176. Hello there, I do believe your website might be having web browser compatibility problems. Whenever I look at your site in Safari, it looks fine however when opening in Internet Explorer, it’s got some overlapping issues. I simply wanted to provide you with a quick heads up! Besides that, excellent website!

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  179. When I initially commented I seem to have clicked on the -Notify me when new comments are added- checkbox and now every time a comment is added I receive 4 emails with the same comment. Is there a way you are able to remove me from that service? Thanks!

  180. I would like to thank you for the efforts you have put in writing this site. I really hope to see the same high-grade blog posts from you later on as well. In truth, your creative writing abilities has encouraged me to get my own website now 😉

  181. May I simply just say what a relief to find somebody that really understands what they’re talking about on the web. You actually know how to bring an issue to light and make it important. A lot more people have to look at this and understand this side of your story. I was surprised that you aren’t more popular given that you most certainly possess the gift.

  182. A motivating discussion is worth comment. I do think that you need to publish more about this subject, it might not be a taboo matter but usually people do not speak about such topics. To the next! Best wishes!!

  183. I seriously love your website.. Great colors & theme. Did you create this amazing site yourself? Please reply back as I’m attempting to create my own personal website and would like to learn where you got this from or exactly what the theme is called. Kudos!

  184. Howdy! This article could not be written much better! Going through this article reminds me of my previous roommate! He continually kept talking about this. I’ll forward this information to him. Fairly certain he’s going to have a very good read. Thank you for sharing!

  185. I have to thank you for the efforts you have put in writing this blog. I am hoping to view the same high-grade content by you in the future as well. In truth, your creative writing abilities has encouraged me to get my own, personal site now 😉

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  189. Hi there! This post could not be written any better! Going through this article reminds me of my previous roommate! He constantly kept talking about this. I most certainly will send this information to him. Pretty sure he will have a very good read. I appreciate you for sharing!

  190. I need to to thank you for this wonderful read!! I definitely loved every little bit of it. I have you bookmarked to check out new things you post…

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  192. I absolutely love your website.. Very nice colors & theme. Did you make this web site yourself? Please reply back as I’m wanting to create my own site and would love to know where you got this from or just what the theme is named. Thank you!

  193. Hello there! I just would like to give you a huge thumbs up for your excellent information you’ve got here on this post. I will be coming back to your site for more soon.

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  200. Aw, this was an extremely good post. Taking a few minutes and actual effort to produce a good article… but what can I say… I procrastinate a lot and never seem to get anything done.

  201. When I originally left a comment I appear to have clicked the -Notify me when new comments are added- checkbox and now every time a comment is added I receive 4 emails with the same comment. There has to be an easy method you are able to remove me from that service? Kudos!

  202. Oh my goodness! Amazing article dude! Many thanks, However I am experiencing issues with your RSS. I don’t understand the reason why I am unable to join it. Is there anyone else getting the same RSS problems? Anybody who knows the answer will you kindly respond? Thanx!!

  203. Hi there! I could have sworn I’ve visited your blog before but after going through many of the articles I realized it’s new to me. Anyhow, I’m certainly pleased I discovered it and I’ll be bookmarking it and checking back frequently!

  204. Hello there, I think your website could possibly be having web browser compatibility issues. Whenever I look at your website in Safari, it looks fine however, if opening in I.E., it’s got some overlapping issues. I merely wanted to give you a quick heads up! Other than that, excellent blog!

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  211. An impressive share! I’ve just forwarded this onto a co-worker who has been conducting a little research on this. And he actually ordered me breakfast simply because I discovered it for him… lol. So allow me to reword this…. Thanks for the meal!! But yeah, thanks for spending time to talk about this matter here on your web page.

  212. Aw, this was an incredibly good post. Taking the time and actual effort to produce a superb article… but what can I say… I put things off a lot and never seem to get anything done.

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  218. Hi there! This blog post couldn’t be written any better! Reading through this post reminds me of my previous roommate! He continually kept talking about this. I’ll forward this article to him. Fairly certain he’s going to have a very good read. Thank you for sharing!

  219. Your style is really unique in comparison to other people I have read stuff from. Thank you for posting when you’ve got the opportunity, Guess I will just book mark this page.

  220. Having read this I believed it was very enlightening. I appreciate you taking the time and effort to put this content together. I once again find myself personally spending a significant amount of time both reading and leaving comments. But so what, it was still worthwhile!

  221. An outstanding share! I’ve just forwarded this onto a co-worker who was doing a little research on this. And he actually bought me breakfast because I found it for him… lol. So let me reword this…. Thanks for the meal!! But yeah, thanks for spending the time to talk about this matter here on your site.

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  223. An outstanding share! I have just forwarded this onto a co-worker who was doing a little homework on this. And he in fact ordered me dinner simply because I discovered it for him… lol. So allow me to reword this…. Thank YOU for the meal!! But yeah, thanks for spending time to talk about this issue here on your web site.

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  226. An outstanding share! I’ve just forwarded this onto a coworker who was doing a little research on this. And he actually bought me breakfast because I found it for him… lol. So allow me to reword this…. Thanks for the meal!! But yeah, thanks for spending some time to talk about this subject here on your blog.

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  230. I blog quite often and I really appreciate your information. This great article has really peaked my interest. I’m going to bookmark your site and keep checking for new information about once a week. I opted in for your RSS feed as well.

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  232. Good post. I learn something new and challenging on blogs I stumbleupon everyday. It will always be interesting to read through articles from other writers and practice a little something from other websites.

  233. When I initially left a comment I appear to have clicked on the -Notify me when new comments are added- checkbox and now each time a comment is added I recieve 4 emails with the same comment. Is there an easy method you are able to remove me from that service? Kudos!

  234. I absolutely love your website.. Pleasant colors & theme. Did you make this amazing site yourself? Please reply back as I’m hoping to create my own personal blog and would like to learn where you got this from or just what the theme is named. Thank you!

  235. You’re so awesome! I do not believe I’ve truly read anything like this before. So wonderful to find someone with genuine thoughts on this issue. Really.. thank you for starting this up. This web site is something that is needed on the web, someone with a little originality!

  236. When I initially left a comment I seem to have clicked the -Notify me when new comments are added- checkbox and now whenever a comment is added I get 4 emails with the same comment. Is there an easy method you are able to remove me from that service? Many thanks!

  237. I’m pretty pleased to find this website. I need to to thank you for ones time due to this wonderful read!! I definitely appreciated every little bit of it and I have you book-marked to check out new things in your web site.

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  244. Howdy! This post could not be written much better! Looking through this post reminds me of my previous roommate! He continually kept preaching about this. I will send this article to him. Fairly certain he’ll have a very good read. Thank you for sharing!

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  309. I truly love your blog.. Very nice colors & theme. Did you build this site yourself? Please reply back as I’m looking to create my own personal site and would love to know where you got this from or what the theme is named. Thank you!

  310. Aw, this was a very nice post. Finding the time and actual effort to produce a good article… but what can I say… I put things off a lot and never seem to get nearly anything done.

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  319. An outstanding share! I have just forwarded this onto a coworker who had been doing a little research on this. And he in fact ordered me breakfast simply because I stumbled upon it for him… lol. So allow me to reword this…. Thanks for the meal!! But yeah, thanx for spending time to talk about this issue here on your website.

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  332. An outstanding share! I have just forwarded this onto a coworker who has been doing a little research on this. And he actually bought me dinner due to the fact that I found it for him… lol. So let me reword this…. Thank YOU for the meal!! But yeah, thanks for spending the time to discuss this topic here on your website.

  333. An outstanding share! I’ve just forwarded this onto a friend who was doing a little research on this. And he in fact bought me breakfast simply because I discovered it for him… lol. So allow me to reword this…. Thanks for the meal!! But yeah, thanx for spending time to talk about this topic here on your web page.

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  347. May I simply just say what a relief to find somebody that really knows what they are talking about on the internet. You certainly know how to bring a problem to light and make it important. A lot more people have to read this and understand this side of your story. I was surprised you are not more popular since you certainly possess the gift.

  348. I have to thank you for the efforts you have put in writing this blog. I am hoping to see the same high-grade blog posts from you later on as well. In fact, your creative writing abilities has motivated me to get my own, personal website now 😉

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  357. Aw, this was a really nice post. Finding the time and actual effort to generate a superb article… but what can I say… I put things off a lot and don’t manage to get nearly anything done.

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  367. This is the right site for anybody who hopes to understand this topic. You understand a whole lot its almost tough to argue with you (not that I really would want to…HaHa). You certainly put a new spin on a subject that has been written about for decades. Great stuff, just excellent!

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  372. Aw, this was a really good post. Taking the time and actual effort to make a superb article… but what can I say… I hesitate a whole lot and never manage to get anything done.

  373. Hi there! This blog post could not be written much better! Reading through this article reminds me of my previous roommate! He constantly kept preaching about this. I am going to forward this information to him. Fairly certain he’s going to have a great read. Thanks for sharing!

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