# Questions tagged [integral]

For on-topic question related to uses of the mathematical concept of an integral, i.e. $\int_a^b f(x)\; dx$. Purely mathematical questions about integrals are better asked at math SE: https://math.stackexchange.com/

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### Confused with notations about random variable and expectation

I asked a question originally here, but my notations were confusing and I couldn't convey properly in terms of statistics. Notations in statistics is a bit new to me, because my background is mostly ...
1 vote
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### Numerical integration over a Random Forest Regression Model

I am trying to compare the accuracy of a polynomial model and a Random forest regression model in predicting a variable Y but also the integral of this variable , With the polynomial model, it is ...
54 views

### How could I evaluate $A = \int_0^1 \log\left(\theta^s(1-\theta)^{n-s}\right)p(\theta)d\theta$?

Suppose that I want to evaluate the following integral: $$A = \int_0^1 \log\left(\theta^s(1-\theta)^{n-s}\right)p(\theta)d\theta,$$ where $p(\theta)\equiv$ Beta$(ws+1, w(n-s)+1)$ and $n$, $w$, and $s$ ...
24 views

### Integral of normal likelihood and multivariate normal prior

I'm updating cluster assignments in the context of a non-parametric Bayesian mixture model. When computing the probability of starting a new cluster, in the absence of cluster parameters (and using a ...
33 views

### Expectation of squared integral over distribution

Right now, I have some function $g(x,\theta)$ where the expectation this function at a given $x$ evaluated over $\theta$ $E_\theta[g(x,\theta)]$ is known, and I want to upper bound (or compute if at ...
1 vote
43 views

### Why are Square Integrable Functions important in Statistics?

I'm reading a paper by Giles Hooker on Functional Decomposition through the use of Functional ANOVA. In the paper he defines a function: $$F(x) : \mathbb{R}^k \rightarrow \mathbb{R}$$ and explicitly ...
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434 views

### Applying Leibniz's integral rule to the Gaussian distribution's normalization condition

I'm working on problem 1.8 of Bishop's Pattern Recognition and Machine Learning and am having a hard time understanding one of the technical details in a solution that I found online. Specifically, ...
1 vote
I was reading a paper and couldn't understand the following transition. Could someone tell me where the term of $p^k (\frac{1}{2} − c′)$ comes from in the following transition? Def: Cumulative ...