Linked Questions

-1
votes
1answer
37 views

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 ...
26
votes
7answers
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 ...
20
votes
4answers
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 ...
9
votes
5answers
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. ...
10
votes
7answers
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 ...
3
votes
2answers
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 ...
3
votes
1answer
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 ...
0
votes
1answer
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 ...
2
votes
2answers
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 ...
0
votes
3answers
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 ...
0
votes
1answer
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 ...
3
votes
1answer
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^...
3
votes
1answer
64 views

In real clinical diagnostic data set how can we know the “true label” of a patient?

When we were taught about Bayesian probability, we often saw the following example: in a population, there are 5% of people who has disease X, and among the people who have disease X, the current ...
1
vote
0answers
48 views

Bayes' theorem in a medical context

Imagine an essentially random, very large population of people (say 50 million individuals). A given subset of them have a disease 'D'. By inspecting this subset, we observe that 40% of the people ...