# Questions tagged [inference]

Drawing conclusions about population parameters from sample data. See https://en.wikipedia.org/wiki/Inference and https://en.wikipedia.org/wiki/Statistical_inference

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### Multiple Linear Regression Zero Conditional Mean Assumption

Greene  and Wooldridge  emphasize that in the standard multiple linear regression model $${\bf y}=X{\bf b}+{\bf e}$$ a key assumption is that $$E[{\bf e}|X]=E[{\bf e}].$$ Or, in other words, $X$...
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### Sequential Inference And Evidence (Jaynes 2003): Is it valid? Is it used?

Exploring the work of ET Jaynes, Probability Theory (11th Printing 2013) has led to consideration of the technique he identifies as Sequential Inference (p. 96); where the evidence, in decibels, ...
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### How is MAP 'not invariant to reparametrization'? [duplicate]

I was watching a lecture on coursera on 'Bayesian Methods on Machine Learning' and I came across a statement that: MAP(Maximum a posteriori) is not invariant to reparametrization. I didn't quite ...
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### Random forest “out-of-bag” ensemble

I am using the R package RandomForestSRC for random forest applications. In the manual for the main function (rfsrc) they mention a setting called ...
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### What is the problem in the Neyman-Scott problem?

Let $Y_{ij} \stackrel{d}{=} N(\mu_i, \sigma^2)$ for $i\in \{1,\ldots,n\}, j\in\{1,2\}$. Also assume $Y_{i1}$ independant of $Y_{i2}$. The parameter of interest is $\sigma^2$. Setting up the ...
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### Understanding Product of individual PDF for Joint PDF

Let's say that we make multiple noisy observation from a sensor node where $h$ is the parameter we want to deduce and $v$ is the noise. $$y[k] = h + v , k=[0,1,..n]$$ Question: The PDF for each ...
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### Coefficient estimate of multiple interaction terms in regression model

I am trying to estimate coefficient of a regression model with two interaction terms. I would appreciate any help. I will try to recreate my model then ask the question. ...
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### How to do inference over two steps in a graphical model simultaneously?

I have observed data $D$ about a physical object described by $M$. I would like to determine the posterior distribution of $M$ given $D$, or $p(M|D)$. Now I can't infer this directly because unknown ...
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### Sufficient statistics for $\mu_1 - \mu_2$

If $X_1, ..., X_n$ is a random sample from $X \sim N(\mu_1, \sigma^2)$ and $Y_1,..., Y_n$ is a random sample from $Y \sim N(\mu_2, \sigma^2),$ if the samples are independent and $\sigma^2$ is known,...
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### Does it make sense to infer a rate (as a probability distribution or upper limits) for a Poisson process if there are “no events”

I have an inhomogeneous Poisson process with a rate $\lambda (\mathbf{t})$ defined on some parameters $\mathbf{t}$. I am trying to infer $\lambda (\mathbf{t})$ from some data, which are events (really ...
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### Verifying whether $X$ is a complete statistic

The pmf of $X$ is as follows: $X = -1 \rightarrow p(x)= \theta$ $X = 0 \rightarrow p(x)= \theta^2$ $X = 1 \rightarrow p(x)= 1-\theta-\theta^2$ I know that to show whether $X$ is complete it is ...
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### Statistical differences between two sets of predicted values [closed]

I have a few distinct groups and each group has units within them. Each unit has time series data to which I fit an exponential model and predict the time when it hits a certain threshold. I have such ...
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### Does order of events matter in Bayesian update?

I'm wondering whether the order of events can lead to different Bayesian update. For example, consider a coin-tossing problem with unknown $p$, the probability of Head. Initially, $p$ is known to ...
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### How to exclude events with low data (eg. threshold, outliers)

I have this data set and I want to filter only "Event" with a good conversion rate. We can say that good are those that have a higher than average conversion (but maybe you have better ideas). ...
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### How do I find the expected values and covariance matrix of the order statistics of iid random variables sampled from the standard normal distribution?

Recently I was trying to learn more about Normality tests and came to know about Shapiro-Wilk test for Normality. I understood most part of it but one thing I didn't understand is that how do I find ...
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### Bayesian Network: Calculate probabillity of child node given all probabillity tables

I have a Question about Bayesian Networks. I have a network with many parent nodes and one child node. I have the probabilities for the parents and for the child. The child node is binary, so there ...
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### Bayesian update for Beta distribution

I'm wondering how to find a posterior of a beta distribution when the "new information" is not an outcome of a binomial trial. Let $p$ be the probability of Head of a (biased) coin toss. As usual in ...
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### How to convert cohen's h to a percent difference in groups in R?

I'm trying to calculate the minimum detectable effect in an experiment after n samples. I'm able to use the pwr package like this to compute the minimum ...
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### Rate of convergence of gradient descent inference in likelihood maximization

I am reading this classic paper on convergence properties of EM for Gaussian Mixture Models. In section 5, the authors compare EM with a gradient based inference approach. The gradient approach ...
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### Hypothesis test for the difference of two means, should I consider annualized or monthly returns?

I have 10 years monthly returns. I calculated annualized return multiplying the mean return over the period for 12. Then I calculated the excess returns as difference between the annualized mean ...
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### Using hold-out method for validation set: How to choose a DL model with model selection?

After >170 deep learning experiments were I did a (almost) full factorial design with >15 factors. I cannot measure performance with cross validation because that would require to much training of ...
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### How to perform joint inference on multivariate normal variables?

Suppose I have the following model: \begin{aligned} \text C &\sim \mathcal N \left(\mu, \delta^2\right) \\ \forall i: \text L_i | \text C = c &\sim \mathcal N \left(c, \lambda_i^2 \right) \\...
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### Conducting “inference” on Titanic data set (and other non-random/“population-encompassing” data sets alike)

Presume I'm given a data set like Titanic, where the data on all the passengers is available (hence "population-encompassing" in the title). Then, by inertia, I proceed to conduct statistical ...
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### Implications of current debate on statistical significance

In the past few years, various scholars have raised a detrimental problem of scientific hypothesis testing, dubbed "researcher degree of freedom," meaning that scientists have numerous choices to make ...