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### If someone has been diagnosed with a disease does he actually have the disease? [duplicate]

Say in a certain population one person is infected with a contagious virus. To prevent the virus from spreading the government tests the entire population whether one individual has this disease or ...
11k views

### Combining probabilities/information from different sources

Lets say I have three independent sources and each of them make predictions for the weather tomorrow. The first one says that the probability of rain tomorrow is 0, then the second one says that the ...
2k views

### Is everyday probability just a way of dealing with the unknown (not talking quantum physics here)?

It seems like in everyday probability (not quantum physics), probabilities are really just a substitute for an unknown. Take a coin flip for example. We say it's "random," a 50% change of head and a ...
1k views

### Conditional probabilities - are they unique to Bayesianism?

I wonder whether conditional probabilities are unique to Bayesianism, or whether they are more of a general concept that is shared among several schools of thought among statistcs/probability people. ...
1k views

### Is sensitivity or specificity a function of prevalence?

Standard teaching says that sensitivity and specificity are properties of the test and are independent of prevalence. But isn't this just an assumption? Harrison's principles of internal medicine ...
2k views

### What's the difference between prior and marginal probabilities?

Let's say I have a distribution for a random variable S: s | P(S=s) --+------- 0 | .28 1 | .72 That's a prior, right? It ...
2k views

### Posterior vs conditional probability

When talking about events, there is the following formula called Bayes' rule, where $A$ and $B$ are random events: $$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$$ Now let's say that for now only $A$ happened. I ...
1k views

### How to do Bayesian updating for a simple practical problem?

All the previous questions are more sophisticated than I can understand and also slightly different to my puzzle. Say you observe a crime and you have one possible suspect, so I have a belief about ...
379 views

### Bayesian exercise

I struggle to understand the following example... A new breast cancer screening method is tested to see if it performs better than existing methods in detecting breast cancer. To measure the ...
119 views

### What's the difference between estimating on a dataset $P(X|Y)$ and $P(Y)$ vs $P(Y|X)$? [closed]

In chapter 3 of his excellent book ("Generative and discriminative classifiers: Naive Bayes and logistic regression") , Tom Mitchell says that, when learning classifiers based on Bayes rule, one can ...
97 views

### Bayes theorem in a clinical setting

Say I have a test with the following characteristics: $P(B|A)$ = positive test in disease population = 0.8 $P(A)$ = incidence of disease = $\frac{1}{5,000}$ $P(B)$ = positive test in general ...
64 views

### In courts, should we assume that $\Pr(Y=y)$ is constant, for all $y \in \mathcal{Y}$?

In the case of supervised classification, we wish to predict the label of unseen observation $x\in\mathcal{X}$ by assigning it to some label $y \in \mathcal{Y}$. Specifically, we want to find label \$y^...