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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28 views

Making one-sided conclusions from two-sided tests

I'm reading Montgomery's Design and Analysis of Experiments. On page 39, he rejected a two-sided $t$-test against the null hypothesis that modified formulation of some cement mortar doesn't change its ...
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Confidence interval for success failure ratio?

I need to report the ratio of success to failure with a confidence interval. Assume I have a list of success and failures in the following form: $X = [1,0,0,0,0,1,1,1,1,0,0]$ I need to calculate the ...
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86 views

Forecasting: Linear vs. Exponential vs. ARIMA

I have tried forecasting next 13 years data point by using past 20 years data (1998-2010) available in the following graphs. I used three models to compare- linear regression, exponential regression, ...
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z scores in spatial statistics [on hold]

I have a map of employment rates for all census tracts in a city. Is it OK to calculate z scores for the employment rates given that there may be spatial autocorrelation present and my observations ...
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3answers
64 views

Finding minimum/maximum peaks in a n-modal distribution

I have distributions that show n-modal behavior. I need to find the values of the largest and smallest modes. For example, in the histogram below I need to find the values representing the yellow ...
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1answer
17 views

What defines a correct / incorrect model in Bayesian inference when it comes to independence

This might be a very broad question but I'm wondering whether we can say a model of Bayesian inference is "correct" or not about assuming independence. For example, suppose there are $N$ coins each ...
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40 views

Borrowing observations for prior probability in Bayesian Inference

For the purposes of Bayesian Inference, is it assumed that the historical observations used for the prior probability values must be from the exact entity for which you are looking to calculate the ...
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13 views

Bayesian inference out of partial information - Dirichlet example

Suppose we have two coins $X_1$ and $X_2$. They are possibly biased and correlated coins. The heads probability of each coins is denoted by $p_1$ and $p_2$ which we don't know at the beginning. The ...
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Multiple Linear Regression Zero Conditional Mean Assumption

Greene [1] and Wooldridge [2] 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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When should one do class rebalancing? [duplicate]

Does anybody know a source when class rebalancing should be considered? Say one has a very small dataset. About 70 observations. When would class rebalancing make sense? When the 0/1 ratio is 70/30, ...
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1answer
50 views

Complete statistics for $f_X(x) = e^{-(x - \mu)} I_{\mu, \infty}(x)$

I am studying parametric statistical inference. One of the self study I have to find a sufficient, minimal and complete statistic for the $\mu$ parameter of the following p.d.f. $$ f_X(x \mid \mu) = e^...
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12 views

compare 2 different sized multivariate samples

I have a two data tables like below. The dataset1 represents failed candidates. The dataset2 represents the successful candidates. I want to know, by applying some inference statistics which var (...
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1answer
26 views

How does graphical model of a GP look like?

I'm trying to understand the difference between GP and Markov process. I couldn't find answers on the internet. I figured that graphical models can tell the difference, hence my question.
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41 views

Bayes formula alternate expression using alpha

I know that Bayes theorem is: Posterior = Likelihood * Prior / Evidence However, I am confused about the above notation in the picture. How do we get to the above three notation? How does ...
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13 views

How to correctly state a multiple-comparison hypothesis pair

I need to compare multiple treatments over a predefined set of benchmark instances. However, I'm facing some difficulties on how to correctly state my hypothesis pair. I want to verify if there are ...
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1answer
105 views

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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15 views

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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2answers
38 views

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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118 views

Estimate probability of selecting the same card more than once

Suppose I have a deck of N=1,000 cards where each card is a unique number from 1 to 1,000. Draw 1: draw n=10 cards at random. Put them back Draw 2: draw n=10 cards at random. Put them back ... ...
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25 views

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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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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1answer
55 views

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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302 views

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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1answer
30 views

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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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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1answer
35 views

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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83 views

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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1answer
19 views

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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17 views

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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32 views

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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30 views

Recommended textbooks for student majoring in applied statistics [duplicate]

I am currently a second year science student double majoring in biochemistry and applied statistics. The stats course im doing this semester (Statistical Theory) is focused on joint probability ...
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1answer
208 views

Understanding how the determinant of the multidimensional normal likelihood can overrule the prior probability

I am doing Bayesian inference. I have a normal prior probability distribution of some theoretical parameter $\theta$ and I am trying to update my knowledge of $\theta$ using some data $D$ and a model $...
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23 views

Interpreting predictive models in the presence of omitted variables

Suppose the best predictive model from a set of possible models is a univariable model, due to lots of moderate correlations with other variables for example. However, if I use this model for ...
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27 views

I was doing this course ' Bayesian Methods for machine learning' on coursera and I got stuck on few conditional statements expansion and manipulation

I have doubt in three conditional expansions : How is P(w,y|x) = P(y|w,x).P(w) ? How is P(w|y,x) = P(y,w|x)/P(y|x) ? How is <...
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1answer
49 views

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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28 views

Expectation of exponential family distributions

Is there a closed form of the following marginal (one dimensional data) $\pi(\theta|y) = \mathbb{E}_{x \sim \pi_R(x|y)} \pi(\theta|x)$, where both $\pi, \pi_R$ are exponential family distributions?
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1answer
43 views

Statistics help! Reporting ANOVA results!

I am new to statistics and I need some help in understanding how to report the data of some tests I am running on R, I hope this is the right place! I have a dataset: ...
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1answer
62 views

Treating missing data in making Bayesian inference

Suppose we have two biased coins $X_1,X_2$ that are possibly correlated to each other. In each round, when both the coins are tossed, there can be four possible outcomes: $(HH,HT,TH,TT).$ Let's ...
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1answer
45 views

Time series explaining the trend

I'm very new to time series analysis and I've been tasked with trying to make sense of some data and was hoping you smart folks out there could provide some guidance. I have some data relating to ...
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2answers
57 views

Relationship between mean and variance of samples

I am thinking about the relationship between sample mean and variance in an example. If we want to look at the average goals per month for a soccer team. And we have mean and variance of goals for ...
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1answer
54 views

Bayesian inference about means, observing only the sum of two random variables

I have: $X \sim \mathcal{N}(\mu_x, \sigma_x^2)$ and $Y \sim \mathcal{N}(\mu_y, \sigma_y^2)$. $X$ and $Y$ are independent. $\mu_x$ and $\mu_y$ are not known and I want to learn about them (Bayesian ...
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1answer
37 views

If a distribution’s scale parameter cannot equal 1, is it part of a scale family?

In general if $f$ is a scale family we have that if $X\sim f(x\mid\lambda)$ then $\frac{X}{\lambda}\sim f(x\mid 1)$. However what if $f$ has the constraint that its scale parameter $\lambda \in (1, \...
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Help with Old exam questions on Bayesian Inference Problem [closed]

I've been trying to teach myself bayesian inference and I found a question sheet online ---> https://math.mit.edu/~dav/05.dir/ps6.pdf. I was attempting to solve question 4 but I'm not sure the method ...
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31 views

Is bootstrapping appropriate for this scenario?

There are 2 binary classification models (Denoted modelA and modelB) that we built with different approaches, both of which are expected to output the probability of possitive outcome. There's a ...
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44 views

Motivations for experiment design in statistical learning?

My interests in statistics centre around statistical learning, including Bayesian inference, inference in combinatorial spaces, Monte Carlo methods, Markov decision processes, modeling stochastic ...
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30 views

fit a model to data

I want to fit a model to a data set, however each point is actually a distribution (i.e. I have the samples for each distribution). In an ideal world, I would assume that the distributions are ...
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inferential approach for estimating error rate on classified population

I am looking mainly for ideas and approaches which I could not find by just Googling. I created a classification model to predict about 175 unique classes from text features. I trained the model on ...
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17 views

Any research on learning Bayesian network structure with a limit on the parent set size?

Learning a maximum-scored Bayesian network structure with bounded treewidth is rather popular in recent years, as stated in the paper A survey on Bayesian network structure learning from data in 2019. ...
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4answers
107 views

Bayesian Hypothesis Tests with continuous priors

I am new to the Bayesian world, and I'm trying to understand how hypotheses tests are performed here (as opposed to the frequentist framework). I am aware that likelihoods, priors and posteriors can ...