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1 vote

Consecutive coin flips, what is the appropriate statistical test for this word problem?

Heads to win, 1000 people flip coins, after 10 flips there is a winner every time No, this is not true. It is not every time. As you computed the probability for one or more winners is $100\% - 36.8\%...
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1 vote

Statistical Models that "Exploit" Distributional Knowledge of the Predictor Variables

In regression models, by definition, we are interested in the conditional distribution of the response variable $Y$ given the observed predictors (covariates) $X$. Namely, if the joint distribution ...
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2 votes

Conditioning of join gaussian over a line

Let $X$ and $Y$ be jointly normal random variables with means $\mu_X, \mu_Y$, and covariance matrix $\Sigma$. (We do not need that $X$ and $Y$ are independent, although it does simplify some ...
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2 votes

Conditioning of join gaussian over a line

A bivariate normal density can be likened to a piece of bologna (or did I mean to write baloney?) about which Americans often say "No matter how you slice it, it is still bologna". The ...
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-3 votes

Logistics model on variable with values 1, 2, 3?

You could try that binary transformation, directly or as suggested by @david. However, data transformation could change the odds. For example, if you have $n_{f_0} = 25$, $n_{f_1} = 25$, $n_{f_2} = 25$...
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6 votes
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Sample uniformly from unit square conditioned on sum and product

Let's solve a generalization, so that we can obtain both solutions at once. Let $h:[0,1]^2\to\mathbb{R}$ be differentiable with derivative $\nabla h=(D_1h, D_2h).$ To avoid technical complications in ...
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3 votes
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How do you get P(A|C) from P(A, B|C)?

Ignore the conditioning on $C$ for a moment. How does one in general get a marginal distribution $P(A)$ from a joint distribution $P(A,B)$? One "integrates out" the dependence on $P(B)$, ...
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1 vote
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Expectation of transition in a Markov process

This is a peculiar property of your transition matrix, but it doesn't have to be that way. If your system satisfies $\pi_A P(B|A) = \pi_B P(A|B)$ for all states $A$ and $B$, your system is said to ...
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  • 2,843
2 votes

Conditional exponential family implies joint exponential family

Let us assume that the conditional density writes as $(j=1,\ldots,d)$ $$p_j(x_j|x_{-j})= h_j(x_j)\exp\{A_j(x_j)^\text TB_j(\theta_j,x_{-j})-C_j(\theta,x_{-j})\}$$ where the various functions are ...
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1 vote

How to quantify the asymmetry of a probabilistic dependency?

I think this is quite an interesting idea, and worth pursuing. For the most part, we tend to formulate statistical and probabilistic quantities based on what we want them to do, so you will also need ...
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