We are going to try to keep this as light as possible, but you will to think outside of your traditional training. For most of you, you'll likely see this as a new way of thinking and may even appear to be counterintuitive - however you may find this idea of iterative refining of one's beliefs is a fundamental principle of being human
If you are interested in learning more about the statistics, here is an absolutely biased selection of texts you may want to look at. While both employ R, the one on the right uses it significantly less than the text sitting on the left.
We are going to try to keep this as light as possible, but you will to think outside of your traditional training. For most of you, you'll likely see this as a new way of thinking and may even appear to be counterintuitive - however you may find this idea of iterative refining of one's beliefs is a fundamental principle of being human
If you are interested in learning more about the statistics, here is an absolutely biased selection of texts you may want to look at. While both employ R, the one on the right uses it significantly less than the text sitting on the left.
We are going to try to keep this as light as possible, but you will to think outside of your traditional training. For most of you, you'll likely see this as a new way of thinking and may even appear to be counterintuitive - however you may find this idea of iterative refining of one's beliefs is a fundamental principle of being human
If you are interested in learning more about the statistics, here is an absolutely biased selection of texts you may want to look at. While both employ R, the one on the right uses it significantly less than the text sitting on the left.
Begin with
a hypothesis
a degree of belief (in the hypothesis)
So based on domain expertise or prior knowledge, we assign a non-zero probability to that hypothesis
Then
gather data
Collection is probability based and done without a purpose
Finally
update our initial beliefs (if needed)
If the data supports the hypothesis then the probability goes up, and if not then it goes down. Then recursively begin the cycle again with the updated probabilities
Begin with
a hypothesis
a degree of belief (in the hypothesis)
So based on domain expertise or prior knowledge, we assign a non-zero probability to that hypothesis
Then
gather data
Collection is probability based and done without a purpose
Finally
update our initial beliefs (if needed)
If the data supports the hypothesis then the probability goes up, and if not then it goes down. Then recursively begin the cycle again with the updated probabilities
Is your understanding of conditional probability a bit fuzzy or possibly even non existent? That is understandable - you probably took statistics from a frequentist, that's ok! Take a look at the two videos from the wonderful series Crash Course Statistics. I'm 95% sure you won't regret it!
P(AandB)
P(AandB)=P(B|A)⋅P(A)
P(B)
P(B)=P(AandB)+P(B|¬A)⋅(1−P(A))
1 ¬A is one of many ways to write shorthand for the statement NOT A. In an absolutely non confusing way, you may also see variants like ∼A, ˜A, or ¯A just to name a few that all denote the same
thing
Still a bit or all the way confused? Then try going through through this incredible video by Josh Starmer. Now I'm 98% sure you won't regret it!
Let's say the chance of a test for infection coming back positive given a person was bitten by a zombie is P(+|zombie bite)=0.90
And the chance of a test for infection coming back negative
given a person was NOT bitten by a zombie is
P(−|NO zombie bite)=0.95
Let's say the chance of a test for infection coming back positive given a person was bitten by a zombie is P(+|zombie bite)=0.90
And the chance of a test for infection coming back negative
given a person was NOT bitten by a zombie is
P(−|NO zombie bite)=0.95
P(+|NO zombie bite)=1−P(−|NO zombie bite)=1−0.95=0.05
Let's say the chance of a test for infection coming back positive given a person was bitten by a zombie is P(+|zombie bite)=0.90
And the chance of a test for infection coming back negative
given a person was NOT bitten by a zombie is
P(−|NO zombie bite)=0.95
P(+|NO zombie bite)=1−P(−|NO zombie bite)=1−0.95=0.05
Remember that all test, especially medical tests have some error
Given a person was bitten by a zombie, what is
the probability that their test is positive?
Given that their test is positive, what is
the probability that person was bitten by a zombie?
You are definitely not alone, but this silly example is indicative a pretty important result because it parallels the nature of many realistic testing contexts such as HIV and DNA testing, criminal profiling, and even your standard run of the mill statistical significance testing
You are definitely not alone, but this silly example is indicative a pretty important result because it parallels the nature of many realistic testing contexts such as HIV and DNA testing, criminal profiling, and even your standard run of the mill statistical significance testing
Now for the time being, forget about the result that you may be dismissing as garbage and try to make sense think about why the probability was so low. After you come to conclusion or get stuck, move on
Whenever the condition of interest is very rare, having a test that finds all the true cases is still no guarantee that a positive result carries much information at all
Remember that zombies are pretty rare, only making up 0.1% of the population. As of this writing, there are about 7.93 billion people in the world. While 8 million zombies appears to be a lot, consider that in this scenario they would be spread out over the globe. Even if you restrict that number to the United States, the country alone has a population of about 333 million people making zombies about 2.4% of the total count of "people". or to put it another way, as of 2021 the number of zombies could almost equal the state population of Virginia
Whenever the condition of interest is very rare, having a test that finds all the true cases is still no guarantee that a positive result carries much information at all
Remember that zombies are pretty rare, only making up 0.1% of the population. As of this writing, there are about 7.93 billion people in the world. While 8 million zombies appears to be a lot, consider that in this scenario they would be spread out over the globe. Even if you restrict that number to the United States, the country alone has a population of about 333 million people making zombies about 2.4% of the total count of "people". or to put it another way, as of 2021 the number of zombies could almost equal the state population of Virginia
Whenever the condition of interest is very rare, having a test that finds all the true cases is still no guarantee that a positive result carries much information at all
Remember that zombies are pretty rare, only making up 0.1% of the population. As of this writing, there are about 7.93 billion people in the world. While 8 million zombies appears to be a lot, consider that in this scenario they would be spread out over the globe. Even if you restrict that number to the United States, the country alone has a population of about 333 million people making zombies about 2.4% of the total count of "people". or to put it another way, as of 2021 the number of zombies could almost equal the state population of Virginia
Whenever the condition of interest is very rare, having a test that finds all the true cases is still no guarantee that a positive result carries much information at all
Remember that zombies are pretty rare, only making up 0.1% of the population. As of this writing, there are about 7.93 billion people in the world. While 8 million zombies appears to be a lot, consider that in this scenario they would be spread out over the globe. Even if you restrict that number to the United States, the country alone has a population of about 333 million people making zombies about 2.4% of the total count of "people". or to put it another way, as of 2021 the number of zombies could almost equal the state population of Virginia
Now through testing and larger samples, if the prior probability changes then there is a good chance that the narrative above also changes with it
In 2005 John Ioannidis, a professor at the Stanford School of Medicine, published a very famous and highly controversial paper named Why Most Published Research Findings Are False. He used Bayes' Theorem to establish a weak basis, though one did not exist prior to his publication. His calculation led to a broader argument and warnings that have been for the most part accepted by the broader research community
We barely scratched the surface of Bayesian thinking. Unfortunately it is underutilized in the social sciences and education and that will become an issue as areas such as machine learning and the data sciences in general become prevalent. If you find this area interesting, I am happy to point you to resources that may be useful. In the meantime, you may wish to take a look at the papers below by hovering over the pills
If you have any questions, please reach out
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We are going to try to keep this as light as possible, but you will to think outside of your traditional training. For most of you, you'll likely see this as a new way of thinking and may even appear to be counterintuitive - however you may find this idea of iterative refining of one's beliefs is a fundamental principle of being human
If you are interested in learning more about the statistics, here is an absolutely biased selection of texts you may want to look at. While both employ R, the one on the right uses it significantly less than the text sitting on the left.
We are going to try to keep this as light as possible, but you will to think outside of your traditional training. For most of you, you'll likely see this as a new way of thinking and may even appear to be counterintuitive - however you may find this idea of iterative refining of one's beliefs is a fundamental principle of being human
If you are interested in learning more about the statistics, here is an absolutely biased selection of texts you may want to look at. While both employ R, the one on the right uses it significantly less than the text sitting on the left.
We are going to try to keep this as light as possible, but you will to think outside of your traditional training. For most of you, you'll likely see this as a new way of thinking and may even appear to be counterintuitive - however you may find this idea of iterative refining of one's beliefs is a fundamental principle of being human
If you are interested in learning more about the statistics, here is an absolutely biased selection of texts you may want to look at. While both employ R, the one on the right uses it significantly less than the text sitting on the left.
Begin with
a hypothesis
a degree of belief (in the hypothesis)
So based on domain expertise or prior knowledge, we assign a non-zero probability to that hypothesis
Then
gather data
Collection is probability based and done without a purpose
Finally
update our initial beliefs (if needed)
If the data supports the hypothesis then the probability goes up, and if not then it goes down. Then recursively begin the cycle again with the updated probabilities
Begin with
a hypothesis
a degree of belief (in the hypothesis)
So based on domain expertise or prior knowledge, we assign a non-zero probability to that hypothesis
Then
gather data
Collection is probability based and done without a purpose
Finally
update our initial beliefs (if needed)
If the data supports the hypothesis then the probability goes up, and if not then it goes down. Then recursively begin the cycle again with the updated probabilities
Is your understanding of conditional probability a bit fuzzy or possibly even non existent? That is understandable - you probably took statistics from a frequentist, that's ok! Take a look at the two videos from the wonderful series Crash Course Statistics. I'm 95% sure you won't regret it!
P(AandB)
P(AandB)=P(B|A)⋅P(A)
P(B)
P(B)=P(AandB)+P(B|¬A)⋅(1−P(A))
1 ¬A is one of many ways to write shorthand for the statement NOT A. In an absolutely non confusing way, you may also see variants like ∼A, ˜A, or ¯A just to name a few that all denote the same
thing
Still a bit or all the way confused? Then try going through through this incredible video by Josh Starmer. Now I'm 98% sure you won't regret it!
Let's say the chance of a test for infection coming back positive given a person was bitten by a zombie is P(+|zombie bite)=0.90
And the chance of a test for infection coming back negative
given a person was NOT bitten by a zombie is
P(−|NO zombie bite)=0.95
Let's say the chance of a test for infection coming back positive given a person was bitten by a zombie is P(+|zombie bite)=0.90
And the chance of a test for infection coming back negative
given a person was NOT bitten by a zombie is
P(−|NO zombie bite)=0.95
P(+|NO zombie bite)=1−P(−|NO zombie bite)=1−0.95=0.05
Let's say the chance of a test for infection coming back positive given a person was bitten by a zombie is P(+|zombie bite)=0.90
And the chance of a test for infection coming back negative
given a person was NOT bitten by a zombie is
P(−|NO zombie bite)=0.95
P(+|NO zombie bite)=1−P(−|NO zombie bite)=1−0.95=0.05
Remember that all test, especially medical tests have some error
Given a person was bitten by a zombie, what is
the probability that their test is positive?
Given that their test is positive, what is
the probability that person was bitten by a zombie?
You are definitely not alone, but this silly example is indicative a pretty important result because it parallels the nature of many realistic testing contexts such as HIV and DNA testing, criminal profiling, and even your standard run of the mill statistical significance testing
You are definitely not alone, but this silly example is indicative a pretty important result because it parallels the nature of many realistic testing contexts such as HIV and DNA testing, criminal profiling, and even your standard run of the mill statistical significance testing
Now for the time being, forget about the result that you may be dismissing as garbage and try to make sense think about why the probability was so low. After you come to conclusion or get stuck, move on
Whenever the condition of interest is very rare, having a test that finds all the true cases is still no guarantee that a positive result carries much information at all
Remember that zombies are pretty rare, only making up 0.1% of the population. As of this writing, there are about 7.93 billion people in the world. While 8 million zombies appears to be a lot, consider that in this scenario they would be spread out over the globe. Even if you restrict that number to the United States, the country alone has a population of about 333 million people making zombies about 2.4% of the total count of "people". or to put it another way, as of 2021 the number of zombies could almost equal the state population of Virginia
Whenever the condition of interest is very rare, having a test that finds all the true cases is still no guarantee that a positive result carries much information at all
Remember that zombies are pretty rare, only making up 0.1% of the population. As of this writing, there are about 7.93 billion people in the world. While 8 million zombies appears to be a lot, consider that in this scenario they would be spread out over the globe. Even if you restrict that number to the United States, the country alone has a population of about 333 million people making zombies about 2.4% of the total count of "people". or to put it another way, as of 2021 the number of zombies could almost equal the state population of Virginia
Whenever the condition of interest is very rare, having a test that finds all the true cases is still no guarantee that a positive result carries much information at all
Remember that zombies are pretty rare, only making up 0.1% of the population. As of this writing, there are about 7.93 billion people in the world. While 8 million zombies appears to be a lot, consider that in this scenario they would be spread out over the globe. Even if you restrict that number to the United States, the country alone has a population of about 333 million people making zombies about 2.4% of the total count of "people". or to put it another way, as of 2021 the number of zombies could almost equal the state population of Virginia
Whenever the condition of interest is very rare, having a test that finds all the true cases is still no guarantee that a positive result carries much information at all
Remember that zombies are pretty rare, only making up 0.1% of the population. As of this writing, there are about 7.93 billion people in the world. While 8 million zombies appears to be a lot, consider that in this scenario they would be spread out over the globe. Even if you restrict that number to the United States, the country alone has a population of about 333 million people making zombies about 2.4% of the total count of "people". or to put it another way, as of 2021 the number of zombies could almost equal the state population of Virginia
Now through testing and larger samples, if the prior probability changes then there is a good chance that the narrative above also changes with it
In 2005 John Ioannidis, a professor at the Stanford School of Medicine, published a very famous and highly controversial paper named Why Most Published Research Findings Are False. He used Bayes' Theorem to establish a weak basis, though one did not exist prior to his publication. His calculation led to a broader argument and warnings that have been for the most part accepted by the broader research community
We barely scratched the surface of Bayesian thinking. Unfortunately it is underutilized in the social sciences and education and that will become an issue as areas such as machine learning and the data sciences in general become prevalent. If you find this area interesting, I am happy to point you to resources that may be useful. In the meantime, you may wish to take a look at the papers below by hovering over the pills
If you have any questions, please reach out