Monte Carlo Models, Chains and Monte Carlo Simulation

By pjain      Published March 30, 2020, 2:30 a.m. in blog AI-Analytics-Data   

Part of series - AI, Data Science, Analytics, Visualization Series Guide - Series

Markov Models and Monte Carlo - Business Review

Overview

What

Applications of Markov models

  • Peoples actions based on weather - eg if average ice creams per customer can be 1,2,3 it can relate to temperature.
  • The stock market - based on sentiment, related news, other countries' stock futures, etc.
  • Tweet generators! Chatbot suggestions for replies.
  • You could use a corpus to create and generate new content based on a Markov Model.

Markov Models and Monte Carlo - Technical Review

Random variables, processes, states and probabilities

  • Consider rolling a dice, or customers selecting an item from a menu. This is an example of a random process with associated probability.

Domain - possible states of outcome - eg for dice domain(O) = {1,2,3,3,5,6}

Probability Distribution - in case of dice should be an uniform distribution P(o) - 1/6 ∀ ∈ domain(O)

  • Domain Random Distributions
  • discrete random variables - in dice and menus cases since domain of variables are fixed choices
  • continous random variables - in some cases eg analog height of children it could range say 1'-7'.

  • Random processes

  • Sets of random variables that represent random variables over a period of time are also known as random processes. For example a stock price over a day can range over a series of values.
  • Random processes are often time-based but can depend on some other event.

  • Deterministic processes - if we have a definite output value eg position of a dropped ball given initial height and gravitational constant, then we know y(t) by that. So even though range can be continuous i.e. this is a random deterministic process.

  • Stochastic random processes - however, most vary due to many factors so are NOT determined eg stock price can fluctuate and not explained very easily - but depend on overall market, news of related stocks, or earnings release or news or product announcements or just sentiment.

Inference on random processes is more interesting if we can infer from that. For example candlestick charting reduces the entire days to a pattern eg hammer, red-down-day, green-up-day, etc. One might be able to state, that a breakout above say a 50-day moving average is a high probability that next day will also be an up day.

Markov Models and processes

In probability theory, a Markov model is a stochastic model used to model randomly changing systems where it is assumed that future states depend only on the current state not on the events that occurred before it. This assumption is called the Markov property. Generally, this assumption enables reasoning and computation with the model that would otherwise be intractable.

Markov model - Transition Probabilities diagrams, Histograms

  • For every key token -> value or set of possible depending on domain you have
    • Probabilities of state Transitions
    • Histogram of tokens either overall for corpus or

Markov model Order

Increasing the size of the window is known as bringing the Markov Model to a “higher order”. The current examples we have worked with have been first order markov models. If we use a second order Markov Model our window size would be two! Similarly, for a third order → window size of three.

ORDERs and Randomness. Lower order Markov models help you generate more random outputs. But, if you have 2 or 3 order markov models then you need a HUGE corpus of 100k+ tokens or even 1m+. Otherwise just given a couple of tokens third is likely to be highly limited.

Markov chains or discrete-time Markov processes

Continuous-time Markov chains

Markov Chains and Markov chain model

You need to learn some of the ways to represent a Markov chain like a state diagram and transition matrix.

Once you have an analysis of the probabilities of state transitions, you can construct a Markov chain model ie. which can generate predictive models.

Hidden Markov Models HMM

Monte Carlo Simulation

Resources

Business, Applications, Understanding Impact

Intermediate Books

  • Handbook of Markov Chain Monte Carlo by Steve Brooks, Andrew Gelman, Galin L. Jones, Xiao-Li Meng

Monte Carlo Simulation

Intermediate Simulation

  • Markov Chain Monte Carlo Stochastic Simulation for Bayesian Inference by Dani Gamerman, Hedibert Freitas Lopes

Advanced Markov Methods

  • Advanced Markov Chain Monte Carlo Methods_ Learning from Past Samples - hv

27 comments

Comment 1 by kobe basketball shoes Oct. 23, 2020, 3:27 a.m.

I want to show some thanks to this writer for rescuing me from this particular situation. Just after looking throughout the world-wide-web and obtaining techniques that were not beneficial, I thought my entire life was gone. Being alive minus the solutions to the difficulties you have resolved through the site is a crucial case, and the kind which may have negatively damaged my career if I had not come across your blog. That mastery and kindness in controlling all the pieces was precious. I don't know what I would've done if I hadn't come across such a point like this. I'm able to now look forward to my future. Thanks very much for your high quality and effective guide. I will not hesitate to recommend the blog to any person who wants and needs recommendations on this topic.
[url=http://www.kobebasketballshoes.net]kobe basketball shoes[/url]

Comment 2 by stone island Oct. 26, 2020, 7:22 a.m.

I needed to compose you that bit of word to say thank you once again for those striking techniques you've featured on this site. It has been certainly shockingly open-handed with people like you to provide publicly what exactly a few individuals would have sold as an e book to end up making some cash for themselves, principally since you might have tried it if you desired. The techniques likewise acted as the good way to fully grasp most people have the same zeal really like mine to grasp somewhat more in respect of this condition. I know there are many more pleasurable moments ahead for individuals who discover your blog.
stone island

Comment 3 by longchamp outlet Oct. 27, 2020, 9:49 p.m.

I wanted to draft you one little bit of note to thank you very much again over the wonderful tips you've contributed at this time. It was quite wonderfully generous of people like you to give freely what exactly some people would have made available for an e-book in order to make some money for their own end, certainly considering that you might have done it if you considered necessary. These good tips also served to become a good way to be certain that most people have a similar dreams much like my own to understand a lot more with reference to this condition. I am certain there are thousands of more pleasant occasions ahead for those who take a look at your site.
longchamp outlet

Comment 4 by calvin klein outlet Oct. 29, 2020, 11:52 a.m.

I precisely needed to thank you so much once more. I am not sure the things I might have tried in the absence of those techniques discussed by you on such area of interest. Certainly was a very frustrating issue in my opinion, however , taking note of a new professional mode you processed it made me to weep over gladness. I will be happy for this support as well as have high hopes you are aware of a powerful job you were carrying out educating some other people through a site. I know that you've never got to know all of us.
calvin klein outlet

Comment 5 by jordan shoes Oct. 31, 2020, 2:35 a.m.

I am just writing to let you be aware of what a amazing encounter my friend's daughter went through browsing your web site. She picked up many things, most notably how it is like to possess a marvelous coaching spirit to let other people without hassle understand selected tortuous topics. You undoubtedly did more than people's expected results. Thank you for delivering such useful, healthy, informative not to mention fun thoughts on the topic to Lizeth.
jordan shoes

Comment 6 by off white nike Oct. 31, 2020, 2:35 a.m.

My wife and i got now satisfied that Raymond managed to finish up his web research by way of the ideas he got using your web page. It's not at all simplistic to simply happen to be releasing information some other people have been trying to sell. We really take into account we've got you to thank for this. Those illustrations you made, the straightforward site navigation, the friendships you assist to foster - it is many great, and it is helping our son and the family feel that the concept is entertaining, which is highly indispensable. Thanks for all!
off white nike

Comment 7 by moncler Oct. 31, 2020, 2:40 a.m.

My wife and i got absolutely lucky that Edward could finish up his web research using the precious recommendations he gained out of your blog. It's not at all simplistic to just be giving freely procedures a number of people have been selling. Therefore we do understand we have got the website owner to thank for this. The type of explanations you've made, the straightforward website navigation, the relationships your site make it easier to engender - it's got everything awesome, and it's really assisting our son in addition to our family believe that that article is amusing, which is certainly extremely serious. Many thanks for all!
moncler

Comment 8 by bape clothing Oct. 31, 2020, 2:40 a.m.

I simply needed to say thanks yet again. I am not sure the things that I would've tried without those points provided by you concerning this problem. This has been a real fearsome concern in my opinion, nevertheless coming across this skilled style you solved the issue took me to jump over happiness. I am just happier for this work as well as wish you really know what a great job that you're undertaking instructing men and women by way of a site. I know that you have never got to know any of us.
bape clothing

Comment 9 by golden goose Nov. 4, 2020, 8:44 p.m.

My husband and i have been very delighted when Peter managed to conclude his homework with the precious recommendations he was given from your own site. It is now and again perplexing just to always be giving away helpful hints which often the others might have been trying to sell. We realize we have the website owner to appreciate because of that. Those illustrations you have made, the simple website navigation, the relationships you assist to engender - it is all fantastic, and it's really helping our son and the family reason why this issue is interesting, and that is incredibly fundamental. Thank you for everything!
golden goose

Comment 10 by adidas yeezy Nov. 6, 2020, 8:25 a.m.

I in addition to my guys came analyzing the excellent thoughts on your web site while unexpectedly I got an awful suspicion I had not expressed respect to the site owner for those secrets. Most of the boys are already as a consequence joyful to learn all of them and have in effect actually been taking advantage of those things. Thanks for truly being so thoughtful and then for deciding on this form of great themes millions of individuals are really eager to discover. My very own sincere regret for not saying thanks to you earlier.
adidas yeezy

Comment 11 by curry 6 Nov. 9, 2020, 4:53 p.m.

Thank you for your entire work on this website. Gloria loves working on internet research and it's really simple to grasp why. Most of us hear all about the dynamic means you provide insightful solutions on this web blog and in addition improve participation from the others about this point plus our own daughter is studying a great deal. Take advantage of the remaining portion of the new year. You're the one performing a wonderful job.
curry 6

Comment 12 by longchamp bags Nov. 11, 2020, 1:32 a.m.

Thank you for all your valuable work on this blog. My mom takes pleasure in going through research and it is easy to see why. Most of us know all about the powerful way you give important thoughts through the web site and as well as encourage contribution from website visitors on this area plus my girl is undoubtedly understanding a whole lot. Take advantage of the remaining portion of the new year. Your doing a first class job.
longchamp bags

Comment 13 by air jordan shoes Nov. 12, 2020, 5:17 p.m.

I must express some appreciation to the writer just for rescuing me from such a problem. Right after scouting throughout the internet and getting basics that were not productive, I thought my life was over. Existing devoid of the approaches to the issues you've resolved by means of the review is a serious case, and ones that could have negatively affected my career if I had not come across your blog post. Your good knowledge and kindness in playing with all things was valuable. I am not sure what I would've done if I hadn't discovered such a solution like this. I'm able to at this point relish my future. Thanks a lot very much for this reliable and effective help. I won't hesitate to recommend the sites to anybody who should receive guidance on this subject.
air jordan shoes

Comment 14 by moncler jackets Nov. 14, 2020, 6:23 a.m.

I intended to create you that tiny note just to thank you so much yet again regarding the wonderful tips you have featured on this site. It has been so seriously open-handed with people like you in giving without restraint exactly what most people would've advertised as an e book to make some dough for their own end, and in particular now that you could have done it in the event you considered necessary. The smart ideas likewise acted to be a fantastic way to fully grasp other individuals have the identical desire just like mine to see whole lot more on the topic of this condition. I am sure there are lots of more pleasant opportunities in the future for those who scan your website.
moncler jackets

Comment 15 by kyrie 3 Nov. 15, 2020, 10:10 p.m.

I have to show my respect for your kind-heartedness supporting people that must have help on that field. Your real dedication to getting the solution all-around had become really important and have continuously allowed people just like me to realize their dreams. Your own invaluable hints and tips means much to me and especially to my office workers. Many thanks; from all of us.
kyrie 3

Comment 16 by supreme clothing Nov. 17, 2020, 8 a.m.

I needed to draft you a bit of observation in order to thank you so much again relating to the gorgeous ideas you've contributed on this website. It's so pretty open-handed of you to allow extensively precisely what many people could possibly have offered for sale as an e book to help make some profit on their own, mostly given that you might have tried it in the event you considered necessary. The creative ideas also worked to provide a great way to know that some people have the identical zeal really like my very own to know the truth a little more in regard to this issue. Certainly there are a lot more fun sessions ahead for many who go through your blog post.
supreme clothing

Comment 17 by supreme clothing Nov. 18, 2020, 8:53 p.m.

Thanks so much for providing individuals with such a remarkable opportunity to read from this web site. It is always very superb and as well , full of a great time for me personally and my office mates to search your web site at the least three times every week to learn the new items you have got. Of course, I'm just at all times amazed with all the perfect ideas you give. Selected 4 areas on this page are in reality the finest we have all had.
supreme clothing

Comment 18 by kd 13 Nov. 18, 2020, 8:53 p.m.

Needed to put you a very small observation so as to thank you as before with the stunning pointers you have shared on this site. This is shockingly generous of you to provide without restraint exactly what some people might have marketed as an ebook to make some cash for themselves, primarily now that you might have done it in case you considered necessary. These creative ideas also worked to become a easy way to be aware that other people have a similar zeal just as my very own to know a little more in terms of this problem. Certainly there are some more pleasurable times up front for people who discover your site.
kd 13

Comment 19 by yeezy shoes Nov. 18, 2020, 8:53 p.m.

I actually wanted to jot down a small remark so as to express gratitude to you for those superb tricks you are showing on this site. My particularly long internet investigation has at the end been rewarded with brilliant strategies to write about with my two friends. I would tell you that most of us readers are truly lucky to dwell in a really good place with so many perfect individuals with very beneficial tips. I feel very much fortunate to have seen the web pages and look forward to many more cool minutes reading here. Thank you once again for all the details.
yeezy shoes

Comment 20 by kd shoes Nov. 18, 2020, 8:53 p.m.

I happen to be commenting to make you be aware of of the useful experience my princess developed visiting the blog. She discovered a lot of details, including what it's like to possess an excellent giving mindset to make others without difficulty learn about various extremely tough issues. You really exceeded her desires. Many thanks for distributing those great, dependable, edifying not to mention cool tips about that topic to Kate.
kd shoes

Comment 21 by supreme hoodie Nov. 20, 2020, 6:12 a.m.

Thanks a lot for providing individuals with an exceptionally nice opportunity to discover important secrets from this site. It can be so kind and as well , jam-packed with a great time for me and my office colleagues to search your site really 3 times in one week to read the newest things you have. And of course, I am also actually fulfilled with all the mind-blowing tactics you give. Certain 1 tips in this article are essentially the finest I have ever had.
supreme hoodie

Comment 22 by balenciaga Nov. 21, 2020, 9:55 p.m.

I precisely desired to appreciate you yet again. I do not know the things I could possibly have worked on without the actual strategies discussed by you directly on this field. It was before the fearsome scenario in my position, but understanding a new expert style you managed that forced me to cry with contentment. Now i am happier for your advice and even have high hopes you are aware of an amazing job you have been carrying out educating most people via your blog post. Most probably you haven't come across all of us.
balenciaga

Comment 23 by retro jordans Nov. 21, 2020, 9:55 p.m.

I wish to point out my passion for your kindness giving support to folks who require guidance on this subject matter. Your personal commitment to getting the message throughout had become incredibly good and has continually helped people much like me to arrive at their aims. Your personal invaluable help and advice means a whole lot a person like me and additionally to my peers. Regards; from each one of us.
retro jordans

Comment 24 by off white Nov. 21, 2020, 9:55 p.m.

I just wanted to jot down a brief comment to be able to say thanks to you for all of the stunning suggestions you are placing here. My rather long internet search has at the end of the day been paid with awesome facts to write about with my companions. I 'd claim that many of us website visitors actually are undeniably endowed to live in a very good network with very many lovely individuals with useful principles. I feel very fortunate to have discovered your entire website page and look forward to so many more cool times reading here. Thanks once more for everything.
off white

Comment 25 by bape hoodie Nov. 21, 2020, 9:55 p.m.

My wife and i have been happy Ervin could finish off his preliminary research via the precious recommendations he grabbed in your blog. It's not at all simplistic to just find yourself freely giving key points which the others have been trying to sell. We recognize we've got you to appreciate for that. The main illustrations you made, the easy website menu, the relationships you will aid to engender - it's got everything astounding, and it's leading our son in addition to our family reason why the idea is brilliant, which is quite serious. Thanks for all!
bape hoodie

Comment 26 by lebron james shoes Nov. 24, 2020, 10:28 p.m.

Thank you a lot for giving everyone a very terrific chance to check tips from this web site. It's usually very amazing and also full of a great time for me personally and my office fellow workers to search your web site particularly thrice a week to learn the new issues you have got. And lastly, we are at all times satisfied considering the effective thoughts you serve. Some 3 tips in this posting are certainly the very best we have all had.
lebron james shoes

Comment 27 by jordan shoes Nov. 26, 2020, 10:22 a.m.

I and my pals have already been viewing the great procedures from your web site and so immediately got an awful feeling I never thanked the website owner for those techniques. The people ended up for that reason happy to learn them and have now certainly been enjoying these things. Appreciation for being very helpful and also for getting these kinds of exceptional guides most people are really desirous to know about. My personal sincere apologies for not saying thanks to you earlier.
jordan shoes

Add new comment

Similar posts

Markov Models Quickstart

Simulation

t SN Core DJ

SNs Series ST4US