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Bayesian model comparison with systematic error

I believe that your intuition is correct. From the problem description, I interpreted the systematic error $y_{sys}$ as being an unknown parameter that would be contributing additively to the ...
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When does a difference in means not capture the true treatment effects vs a regression with pre-treatment controls?

There is no confounding in your example because the treatment was generated completely independently of the predictor of the outcome. You basically implemented a randomized trial. In such a scenario, ...
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Can we calculate the MLE of $\mu$ and $\sigma^2$ of normally distributed data using the profile likelihood approach?

You don't need the profile likelihood approach for the normal case. Note that the restricted maximum likelihood estimator of $\mu$, given a value of the variance $\sigma^2$, $\hat{\mu}(\sigma^2) = \...
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1 vote

Correct Interpretation of Survival Curves

The type of inference you describe is one that would hinge on some implicit assumptions about the relationship between health risks and resources. Implicit in the suggestion to target funding to men/...
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4 votes

Correct Interpretation of Survival Curves

The answer is unfortunately no. These curves tell you about the survival profile of men and women under the standard of care. On the other hand, your question is asking about an alternative of care. ...
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1 vote

Chi square for three categorical variables

The short, not very useful answer, is YES. However, it's probably not going to work very well or provide any meaningful statistics. I presume when you say each variable has $k$ "dimensions,"...
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2 votes

Correct Interpretation of Survival Curves

I think that the answer is not easy and depends from a number of factors which cannot be captured only by the difference in survival curves. First: the situation depicted is uttermost theoretical and ...
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1 vote

Correct Interpretation of Survival Curves

A somewhat sobering answer is that I believe these types of issues can often be ignored. For example, during grad school I did an internship at a large Pharma company. At one point, one of the senior ...
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0 votes

How can I calculate Posterior Distribution, analytically with given information?

For $ x=1 $ $ \dfrac{p(\theta)p(x=1 | \theta)}{p(\theta_1)p(x=1 | \theta) + p(\theta_2)p(x=0 | \theta_2)} = \dfrac{p(0)p(x=1 | 0)}{p(0)p(x=1|0)+p(1)p(x=1|1)} = \dfrac{0.1665}{0.417} = 0.399280576 \...
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sufficient, minimal, complete

Consider a Normal $\mathcal N(\mu,1)$ sample, $x_1,\ldots,x_{2n}$. Then both $\bar X_{1:n}$ and $\bar X_{(n+1):2n}$ are complete, insufficient, and not a function of one another.
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5 votes

variance of the difference of two independent variables is the sum of variances

The relevant equation is $V(X-Y) = V(X)+V(Y)-2Cov(X,Y).$ The correlation may seem small to you, but @whuber's Comment is exactly correct. Computations in R for your apple prices: ...
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1 vote
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I have a graph which appears to be random but there seems to be a pattern hidden in it. How do I analyze it?

The plot that you made looks like using the function xcorr which computes an autocorrelation function without normalization. $$R(l) = \sum_{\forall k:0\leq k \leq ...
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I have a graph which appears to be random but there seems to be a pattern hidden in it. How do I analyze it?

If you suspect that there are periodic signals in your data, you can analyse it in the frequency domain. I would recommend you start by plotting the signal intensity using the ...
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1 vote

Logistic regression - One model trained on different groups

I would do this in one regression that includes gender as a variable and an interaction between gender ($G$) and your $X$ of interest. Then you test the coefficient on the interaction, which measures ...
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3 votes

Meaning of multiple exposures in a DAG

The problem is the same estimation procedure you used in the first case, cannot be used in the second. DAG 1: In the first case, you rely on a very special case where the average causal effect (ACE) ...
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3 votes
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Question on solution of Casella and Berger Exercise 9.10: Showing that $Q(t,\theta)$ is a pivot

In an effort to clarify the notation I have arrived at an equivalent demonstration based on the distribution functions rather than the densities. Let's see how this plays out. What I aim to achieve ...
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1 vote

Question on solution of Casella and Berger Exercise 9.10: Showing that $Q(t,\theta)$ is a pivot

In the first equation, the solution writer applied the change of variable formula to change from a density in $t$ to one in $Y = Q(t; \theta)$, as well as applying the given information about the ...
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Why is SATE different to Treatment effect (difference in means)?

You made an error in your simulation. The difference in means estimator is unbiased for the ATE. The error you made is in simulating t (i.e., $\tau$). The question ...
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Causal Inference for experiment

The validity of the post-pre estimator in the intervention group depends on there being no change in the control group. If there was change in the control group, then any changes you see in the ...
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12 votes
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Motivating use of Bayesian splines in excess mortality estimation

The death rate can't be negative (the pandemic was bad but it wasn't zombie apocalypse bad), so a natural way to enforce that is to fit an additive/linear model on the log scale (hence why the model ...
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Categorical linear-model coefficients from a pairwise competition experiment

Your experiments are very interesting! Thank you for explaining how they are set up. My answer is long but it addresses all four questions. Along the way we learn about design matrices and contrasts. ...
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0 votes

How to calculate sampling error for proportionate sampling?

I need a bit more data to help you with the sampling error, but just know its the same as standard deviation, but replace p with p^. That accounts for your standard error. "Also if I can use some ...
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2 votes
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"De-meaning" or "Differencing the mean of..." in mathematical term

It is hard to comment without context. Many terms may be ambiguous or there may be different procedures and methodologies of doing things that at first sight may be the same, but because of the "...
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