Name: Markov chains application (weather forecasting )
Uploaded: 2022-01-09
Duration: 6 min 43 s
Description: Markov chains application (weather forecasting ).

Markov chains application (weather forecasting ). 

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Markov chains application (weather forecasting )

ID Name 18011165 عمر  مفتاح عبدالسلام عطايا  19015660 رشاد السيد ابراهيم احمد شحاته 19017182 كريم محمود عبدالسلام غنيم  19016343 محمد حمدى عبدالعزير خليفة 19016377 محمد سامى محمد  عبدالعزيز عشرة  19016685 مصطفى محمد محمد الحسينى  محمد

Introduction Markov Chains Application “ Weather Forecasting”. 

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Introduction  Markov Chains   Application    “ Weather Forecasting”

محمد حمدي عبد العزيز خليفة

Markov chains are an important mathematical tool in stochastic processes. They are used widely in many different disciplines. A Markov chain is a stochastic process that satisfies the Markov property , which means that the past and future are independent when the present is known . This means that if one knows the current state of the process , then no additional information of its past states is required to make the best possible prediction of its future. This simplicity allows for great reduction of the number of parameters when studying such a process.. 

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Markov chains are an important mathematical tool in stochastic processes.  They  are used widely in  many different  disciplines.  A  Markov chain is a stochastic process that satisfies the  Markov property , which means that the past and future are independent when the present is known . This  means that if one knows the current state of  the process , then no additional  information of  its past states is required to make the best possible prediction of its future.  This simplicity allows  for great reduction of the number of parameters when studying such a  process.

Markov Chains State Space The state space is considered a group of all possible states that a random system can be in . It is called S. There are many examples of S such as taking some numbers like , , or etc . Transition Probabilities The transition probabilities are defined as a table of probabilities and considered The second component. . Each entry in the table informs us about the probability of an object transitioning from states “entries” , there will be a probability associated with all of the states which need to be equal or greater than 0. Plus, the sum of probability values needs to be 1.. 

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Markov Chains  State  Space The state space is  considered a group  of all possible states that a random system can be in . It is called S. There are many examples of S such as taking some numbers like , , or etc . Transition Probabilities The transition probabilities are defined as  a table of probabilities and considered The second component. . Each entry in the table informs us about the probability of an object transitioning from states “entries” , there will be a probability associated with all of the states which need to be equal or greater than 0. Plus, the sum of probability values needs to be 1.

محمد سامي محمدعبد العزيز عشرة

State Space. محمد سامي محمدعبد العزيز عشرة. 

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Transition probability table Where :. Transition Probabilities. 

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Applications Markov chain is defined as a useful tool for prediction it is possible to predict future trends by analyzing the object’s previous behaviors , so there are a variety of applications of it in the area of natural sciences and population , weather predictions ”forecasting” , economics and finances etc .. 

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Applications Markov chain is  defined as a  useful tool  for   prediction  it is possible to predict future trends by analyzing the object’s previous  behaviors    , so there  are a variety of  applications   of it in  the area  of natural  sciences and  population  ,  weather  predictions ”forecasting” ,  economics and  finances  etc .

مصطفي محمد محمد الحسيني

Weather Forecasting . In our simplified universe weather can be in of 3 states as following : Sunny Cloudy Rainy The probability of how it being tomorrow, depends on its state today whether its sunny, cloudy or rainy.. 

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Weather Forecasting   . In our simplified universe weather can be  in of 3 states as following :  Sunny Cloudy Rainy The  probability of how it being tomorrow, depends on its state today whether its sunny, cloudy or rainy.

If we assumed that the weather of tomorrow depends only on today’s weather, that can be called Markov chain first order . For Example : - if today is sunny, what is the probability that the coming days are sunny, rainy, cloudy, cloudy, sunny so we go with the order (0.5)(0.4)(0.3)(0.5) (0.2) = 0.0054. 

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If we assumed that the weather of tomorrow depends only on today’s weather, that can be called Markov chain first order  . For Example : - if today is sunny, what is the probability that the coming days are sunny, rainy, cloudy, cloudy, sunny  so we go with the order (0.5)(0.4)(0.3)(0.5) (0.2) = 0.0054

كريم محمود عبد السلام غنيم

. كريم محمود عبد السلام غنيم. 

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. رشاد السيد ابراهيم أحمد. 

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رشاد السيد ابراهيم أحمد

Markov chains are an important concept in stochastic processes. They can be used to greatly simplify processes that satisfy the Markov property, namely that the future state of a stochastic variable is only dependent on its present state. Mathematically , Markov chains consist of a state space, which is a vector whose elements are all the possible states of a stochastic variable, the present state of the variable, and the transition matrix. The transition matrix contains all the probabilities that the variable will transition from one state to another or remain the same. To calculate the probabilities of a variable ending up in certain states after n discrete partitions of time, one simply multiplies the present state vector with the transition matrix raised to the power of n . There are different types of concepts regarding Markov chains depending on the nature of the parameters and application areas. They can be computed over discrete or continuous time . The state space can vary to be finite or countably infinite and depending on which, behave in different ways .. 

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Markov chains are an important concept in stochastic processes.  They  can be used to  greatly   simplify  processes that satisfy the Markov property, namely that the future state of  a   stochastic  variable is only dependent on its present state.  Mathematically , Markov chains consist of a state space, which is a vector whose elements  are   all  the possible states of a stochastic variable, the present state of the variable, and the transition matrix.  The  transition matrix contains all the probabilities that the variable will transition from one state to another or remain the same.  To  calculate the probabilities of  a variable  ending up in certain states after n discrete partitions of time, one simply  multiplies the  present state vector with the transition matrix raised to the power of n . There  are different types of concepts regarding Markov chains depending on the nature of  the parameters  and application areas.  They  can be computed over discrete or continuous time . The  state space can vary to be finite or  countably   infinite and depending on which, behave  in   different  ways .

عمر مفتاح عبدالسلام عطايا