Bayesian Inference: Prob of Dry Pavement Outside House

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So, to answer the OP's question, the probability of the pavement being dry is 1 - P(W), which is 0.48 or 48%. In summary, the probability of the pavement being dry is 48%. This is calculated by taking the complement of the probability of the pavement being wet, which is 52%. The probability of the pavement being wet is calculated by considering the chances of rain and no rain, and the sprinkler being on or off. With these probabilities, the maximum value of P(W) is 0.52 and the minimum value is 0.48, which is based on certain assumptions and the use of Bayes' Theorem.
  • #1
zli034
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(Moderator's note: thread moved from "Set Theory, Logic, Probability, Statistics")

Hi guys,

Say outside of my house, there are 20% chance of rain, and 40% chance the sprinker is on.

When it is rain the pavement outside of house must be wet. And if the sprinkler is on, it also wet my pavement. If there is no rain and the sprinkler is off, my pavement is just dry.

How do I calculate the probability of my pavement is dry?

And I got the answer 52% from Netica. I think you all know netica is for bayesian network.
 
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  • #2
Let's consider the chance of rain and no rain:

--- 20% chance of rain ---
20% chance of pavement wet (it doesn't matter if the sprinkler is on or off)

--- 80% chance of no rain ---
80% * 40% chance of pavement wet due the sprinkler
80% * 60% chance of pavement dry (cause there is no rain, and the sprinkler is off)

So, the chance of pavement wet is
20% + 80% * 40% = 52%
 
  • #3
Kittel Knight said:
Let's consider the chance of rain and no rain:

--- 20% chance of rain ---
20% chance of pavement wet (it doesn't matter if the sprinkler is on or off)

--- 80% chance of no rain ---
80% * 40% chance of pavement wet due the sprinkler
80% * 60% chance of pavement dry (cause there is no rain, and the sprinkler is off)

So, the chance of pavement wet is
20% + 80% * 40% = 52%

The answer is correct, but it's a straight (frequentist) probability calculation if the probabilities of rain (R) and sprinkler use (S) are independent. If so, then the probability the pavement is wet (W) is: P(R)+P(S)-P(R)P(S)= P(W)=0.2+0.4-(0.2)(0.4)= 0.52.

Realistically P(R) and P(S) should not be independent and you would need some additional information on this such as P(R|S) or P(S|R).
 
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  • #4
Thanks guys. I should worked it out. I was just spent whole afternoon working til brain damaged. :p
 
  • #5
zli034 said:
Thanks guys. I should worked it out. I was just spent whole afternoon working til brain damaged. :p

I hope your brain has recovered by now. Since your question was entitled "Bayesian Inference", I 'm wondering if you understand why it is Bayesian. The result P(W)=0.52 is just one of an infinite number of results under a continuum of prior assumptions with fixed P(S) and P(R).

What is the maximum value that P(W) can have? Set P(S|R)= 0 and use Bayes' Theorem to calculate the max P(W).

What is the minimum value that P(W) can have? Set P(S|R) = 1 and repeat the calculation for min P(W).

Hint: Note the role of the "interaction" term P(S)P(R) in the original calculation under the assumption of independence.
 
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  • #6
zli034 said:
(Moderator's note: thread moved from "Set Theory, Logic, Probability, Statistics")

Hi guys,

Say outside of my house, there are 20% chance of rain, and 40% chance the sprinker is on.

When it is rain the pavement outside of house must be wet. And if the sprinkler is on, it also wet my pavement. If there is no rain and the sprinkler is off, my pavement is just dry.

How do I calculate the probability of my pavement is dry?

And I got the answer 52% from Netica. I think you all know netica is for bayesian network.

While I agree the probability of the pavement being wet is 52%, the question as asked (see above) was for the probability of the pavement being dry. I hope the OP doesn't go away thinking 52% is the right answer.
 
  • #7
skeptic2 said:
While I agree the probability of the pavement being wet is 52%, the question as asked (see above) was for the probability of the pavement being dry. I hope the OP doesn't go away thinking 52% is the right answer.

You're right. I responded to Kittel Knight's somewhat round-about approach and simply assumed P(W) was the OP's question. I think I made clear that P(W) was the object of my calculation.
 

1. What is Bayesian inference?

Bayesian inference is a method used to update beliefs or hypotheses about a particular event or phenomenon based on new evidence or data. It involves using prior knowledge or assumptions, along with new observations, to calculate the probability of a hypothesis being true.

2. How does Bayesian inference apply to the probability of dry pavement outside a house?

In this scenario, Bayesian inference would involve using prior knowledge or assumptions about the weather, along with new observations or data (such as the current weather conditions), to calculate the probability of the pavement outside a house being dry. This probability would be continuously updated as new evidence is gathered.

3. What factors influence the probability of dry pavement outside a house?

The probability of dry pavement outside a house can be influenced by a variety of factors, such as the current weather conditions (e.g. precipitation, temperature, wind), the type of pavement (e.g. concrete, asphalt), the amount of time since the last rainfall, and the location of the house (e.g. in a dry or wet climate).

4. How accurate is Bayesian inference in predicting the probability of dry pavement?

The accuracy of Bayesian inference in predicting the probability of dry pavement depends on the quality and relevance of the prior knowledge or assumptions used, as well as the reliability and relevance of the new evidence or data. With a strong foundation of prior knowledge and high-quality data, Bayesian inference can be a very accurate method for predicting probabilities.

5. Can Bayesian inference be used for other types of predictions?

Yes, Bayesian inference can be used for a variety of predictions in fields such as statistics, machine learning, and artificial intelligence. It is a versatile and powerful tool for updating beliefs and making predictions based on new evidence or data.

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