Category Archives: Probability theory

Bayesian Skepticism: Why skepticism is not denialism.

Note: All credit goes to Kristoffer Rypdal as this post borrows heavily from his paper Testing hypotheses about climate change: the Bayesian approach which is available at click here. I am merely an information summarizer and disseminator, nothing fancy about me 

Also Im not an expert on climate science this post is just about a scientific way of thinking, the example is merely illustrative.

Have you realized that people believe things which are supported by no evidence and choose to disregard theories supported by mountains of evidence with the pitiful excuse, “Its only a theory, your evidence doesn’t prove anything”. I am a skeptic, but that doesn’t make me a denialist. I do not reject theories which are solidly grounded in evidence. So today I present a post on why skepticism and denialism are actually the opposites of each other and an approach on how to look at and understand evidence. This approach was first gifted to mankind by Thomas Bayes and has been usually transferred onto students as a formula in a textbook that everyone by hearts to pass the class. I really hope I will be able to say something here about why Bayes’ theorem is more than a formula to plug in values and get an answer. Why it is a new approach to think about how we think or should be thinking.

As a skeptic and a lover of statistics, I must admit, the first time I realized the true beauty of Bayes’ theorem I was blown over by it. The formula at its simplest is frankly, very simple and derives very quickly from well-known laws of conditional probability. I will not talk about its derivation because

1)      It’s fairly simple, you probably already know it.

2)      It’ll make my post too long

3)      If you really like my post you will go Google it anyway.

That is the formula, where A and B are two events. P(A) and P(B) are the probabilities of occurrence of events A and B respectively. P(A|B) is the probability that event A occurred knowing that you already know B has occurred and vice versa.

So why is this theorem so important to skeptics? To interpret this, let us think of somebody making a claim you are skeptical of I am borrowing heavily from Rypdal’s paper here and talking about climate change.

Fine you are skeptical about global climate change, well you should be, I always say Question Everything! But how long should you be skeptical? Only until the evidence doesn’t convince you, If you continue being skeptical despite insurmountable evidence, you are well, going wrong.

Taking climate change as the hypothesis and the above formula, let A be the event that climate change occurs. You are a skeptic, so you are allowed to assign the event a 50-50 prior probability before you have an evidence (lesser if you want to). So P(A) = 0.5.

Now you need evidence to back up the claim or disprove it, of course, in most non purely mathematical situations evidence only backs up the theory and it doesn’t prove or disprove it a hundred percent. So how do you analyze the evidence?

In the case of climate change, hurricanes are an important source of evidence. We know that if climate change is true, we would have more catastrophic hurricanes; however that does not imply that a hurricane is a proof for climate change. A certain number of hurricanes occur naturally.

Scientists can however build their toy models and look at historical data to arrive at the probability of occurrence of frequent hurricanes in the presence and absence of climate change.

Let B be the event that there occurs a large hurricane more than once per century.

Now I’ll go ahead and make a little change to the Bayes formula above, it derives in a simple manner from the one above, but I don’t want to go into the details.

So what does this equation tell us,

Well the first equation tells us a few things, the term P(A) is the probability of climate change being true, which is assigned a value of 0.5 prior to experimentation as we are agnostic. We call this the prior probability of A.

The term P(A|B) tells us how we should revise our probability of A being true after observing event B. (frequent hurricanes)

The ratio  P(B|A)/P(B) tells us how the evidence should change our mind about the prior probability of A.  If the probability of frequent hurricanes given climate change is true, is greater than the absolute probability of frequent hurricanes, the ratio is greater than one and it increases our prior probability. Therefore if this is the case we cannot be agnostic anymore.

The second equation is just a better way of looking at the denominator P(B). Here we are accounting for the fact that frequent hurricanes can occur even in the absence of climate change.

P(B|~A) tells us the probability that frequent hurricanes occur though climate change is not true. Note here that a high value for this probability is detrimental to the updation of our prior probability for climate change being true to a higher value. This term captures the honesty of science, we account for all possibilities.

Now assume that scientific theories, models and data tell us that P(B|A) that is frequent hurricanes given global climate change is 0.5

And P(B|~A) that is the probability that frequent hurricanes occur despite climate change being not true be 0.1

Now, plugging in values, our posterior probability P(A|B) that is the new probability of climate change being true In the light of this evidence is 0.83. We are not totally agnostic anymore.

This is how science and evidence based reasoning convinces us of theories. This is why skepticism is not denialism and they are the opposites of each other. Skepticism is a position of giving unlikely events low prior probabilities not shutting our eyes to the posterior probabilities.

I hope I have made some sense here .

Picture Courtesy: free digital photos


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