All Questions

0
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0answers
10 views

Given m n-dimensional vectors, how to create a vector perpendicular to all of them?

Given $m$ vectors, $x_1$, $x_2$, ... $x_m$ with all $x_i \,\, \epsilon \,\, \mathcal{R}^n$, $i=1,2... m$ and $m < n$. How to sample a vector $x_{m+1}$ perpendicular to all the vectors $x_1$, $...
0
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0answers
7 views

ABC, compute Bayes factor from posteriors

I am pretty new to ABC stuff so I may be saying dumb things. My question is: I ran an ABC with two models $M_1$ and $M_2$ and now I have an approximation of the posterior distribution for both model. ...
0
votes
0answers
4 views

Confusion about order of cointegration

I know that my question may sound naive, but I haven't found any clear answer so far. It is generally accepted that when it comes to cointegration testing between two variables, one should test if ...
1
vote
0answers
8 views

Average time series forecast errors from cross-validation with rolling origin

I'm calculating the MAPE and RMSE over a rolling origin cross-validation with fixed forecast interval for several models. For example, for a daily series with 3 years, I'm training my model with 2 ...
0
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0answers
11 views

Are there kernel functions available for categorical variables where matches between different variables would also raise the similarity?

For my master thesis I have to apply bayesian optimization on the development of modular endolysins. This endolysin consists of 3 building blocks that are linked together (variables). Each of these ...
0
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0answers
14 views

optimization algorithm [on hold]

optimization algorithm which having lot of constraints and the output should be binary either zero or one. The algorithm should satisfy linear and non linear constraints.Which one is better other than ...
2
votes
2answers
34 views

Does an inequality hold as an expectation over a probability distribution?

Suppose I have to functions $f(x)$ and $g(x)$ such that $$ f(x) \leq g(x) \quad \forall x. $$ For a distribution $\pi(x)$ on $x$, is it necessarily true that $$ E_\pi[f(x)] \leq E_\pi[g(x)]? $$ My ...
1
vote
1answer
29 views

Is this a reasonable coarse test for normality?

I'm interested in assessing if the marginalized posterior of a parameter obtained through a Bayesian MCMC process is "more or less normal". I use quotation marks because I'm not trying to asses for ...
0
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0answers
11 views

SURE is the best instrument for the analysis of simultaneous equation model?

I would want to make a study about the influence of some regressors in the evaluation of the effects of increment of subsidy in an economic sector. I would use SURE (Seemingly UnRelated Equations ...
0
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0answers
17 views

Relation between the AIC and the Kullback-Leibler Divergence

I am searching a formal derivation of the Akaike Information Criterion from the Kullback-Leibler Divergence. Can you show me one, or point me toward a book/article in which this is done? Here I set ...
1
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0answers
12 views

How to find posterior of global parameter over many datasets? Is my method valid?

Let us say I have 100 objects, and for each one I have a dataset with 50 data points. Each object's dataset can be modelled with 2 free parameters, let's say P1 and P2. On top of this, there's a ...
0
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0answers
13 views

Determining variance of UMVUE

Let $X_1,...,X_n$ be iid with pdf given by $f(x;\theta)=\frac{log\theta}{\theta^{x-1}}I(x>1)$. My task is to determine if the $\mu=E[X]=1+\frac{1}{log\theta}$ can be estimated efficiently, i.e. if ...
0
votes
0answers
14 views

How would I figure out - TSS of Y, Yi and XiYi from the following information?

I came across an analogous question when revising and have no clue how to approach it. The Given information is ΣXi= 20, ΣYi=40 Σ(Xi-x̅)²= 40, Σ(Xi-x̅)(Yi-nȳ)=20 and n=20. The question requires ...
0
votes
1answer
26 views

Mean of an ARMA(1,1) model

Let $X_t$ be a weak stationary process ARMA(1,1) $X_t=c+\phi X_{\left(t-1\right)}+\theta\varepsilon_{\left(t-1\right)}+\varepsilon_t$ $\varepsilon_t$ ~ $WN\left(0,\sigma^2\right)$ The estimated ...
0
votes
0answers
11 views

Description of the Cotton data in R package agricolae [on hold]

I am trying to use the cotton data in the agricolae package in R but the package documentation does not provide enough description of the dataset especially details concerning the variables "lineage" ...
1
vote
1answer
20 views

using decision tree to describe high dimensional data

I have a dataset with 6 numeric columns and one dichotomous factor contain yes and no. I would like to understand when yes is more likely given the 6 numeric columns. I intend to use a decision tree (...
0
votes
1answer
22 views

A different proof for KL divergence non-negativity

KL divergence's non-negativity can be proved in many ways. One could use the inequality $\log x \leq x - 1$ as a main step in the proof, another one could leverage the property of concave of the ...
2
votes
0answers
16 views

Interpreting the estimate of an ordered factor in regression

I have an output from a lm() object that has ordered factors. ...
0
votes
0answers
16 views

Plot a regression equation with mean standard error [on hold]

I would like to plot values from the image from a model regression, with R. eqn = function(x){ZZZ} curve(eqn, from=0, to=50, n=100)
1
vote
1answer
33 views

Which statistical test to use? Not really paired, not entirely unpaired

I am setting up an experiment where I would like to determine whether there exists a difference between the participants' average self reported mental effort in some condition A and condition B. The ...
0
votes
0answers
22 views

Evaluating goodness of fit for Bernoulli glm

I am trying to fit a model estimating the success probability of the Bernoulli distributed random variable with the logistic link function. However, I am stuck with testing the goodness of fit of my ...
0
votes
1answer
25 views

Question about making prediction with only two variables

I have a data set with only two variables, student id and book id. I have train and test sets and I will make prediction about what book student will get next time. Should I attach dummy variables to ...
1
vote
1answer
19 views

Is there an upper bound on number of logistic regression responses that yield infinite estimates

Suppose a logistic regression problem has N observations of {0, 1} and that there are p parameters. Also assume the design matrix, X, is full rank with p < N. We know that there will be certain ...
0
votes
0answers
8 views

Variable as confounding if it influences other factors in opposite directions?

I examine the relationship between population density (PD) and the insurance density (ID) taking into account different market exploitations (ME) of an insurance company in municipalities. The ...
0
votes
0answers
9 views

MANOVA - Can I use DV's with different scales?

Maybe it is a dumb question, but I'm not finding any reference that specifically answer to this question. Is it possible to use two DV with different scales in a MANOVA or do I need to standardize? If ...
1
vote
0answers
14 views

Correction for the number of factors in multi-way ANOVA

QUESTION: Should we do multiple comparisons correction for the number of effects (main effects and interactions) in multi-way ANOVA? I might have failed to find a relevant question, but mostly ...
0
votes
0answers
7 views

Is it mandatory to supply expected values using SARIMA in python?

I went through several examples on the internet discussing time series models. All of them take the dataset, divide it into train and test subsets, then make predictions. On those lines, I have built ...
1
vote
1answer
56 views

Converting MA(1) to AR(p)

While it is $MA(1)$ process there is no dependence between $u(t)$ and $u(t-1)$ i.e $$u(t)=v(t)+Q(1)v(t-1)$$ but when i converted it to AR process i get $u$’s that is dependent on the other $u$’s i.e. $...
0
votes
1answer
26 views

differences between conditional probability and dependency

Sometimes, I read articles about conditional probabilities and other articles about conditional dependency. My question what is the main differences between them? For example, "https://en.wikipedia....
0
votes
1answer
17 views

Question regarding posterior and prior distribution relation

I am currently reading the book Machine Learning and Pattern regocnition by Bishop. They state in (1) or (1.66) in the book (relating how to derive regularized SSE with posterior and prior ...
1
vote
0answers
12 views

Quantile regression line formulation

I want to apply a quantile regression model to my data, and of course would like to understand at least in principle what quantile regression does to my data. Now I understand the basic concept and I ...
0
votes
1answer
17 views

Consequences of unbalanced subgroups of categorical variables in logistic regression?

I have a dataset of around 120000 (120K) unique individuals. I am fitting a binary logistic regression, where I have around 150 variables to choose from. For the categorical variables, some are very ...
0
votes
1answer
27 views

Lag regression independent variables in dynamic panel: which Explanation of the signs? [Resolved]

In the famous paper " Richard Blundell & Stephen Bond (2000): GMM Estimation with persistent panel data: an application to production functions, Econometric Reviews, 19:3, 321-34" the authors ...
2
votes
1answer
66 views

Gaussian Mixture: is this plot right?

I'm studying about Gaussian Mixtures and I decided to play around with it in Python, but I'm not entirely sure if I understand it fully. I generated some data, and then calculated the Gaussian ...
2
votes
1answer
31 views

Which random effects to include in a mixed effects model?

I am analyzing data from a perceptual decision making experiment (10 participants, 1800 trials each). Participants made perceptual decisions (3 possible responses) and then rated their confidence on a ...
3
votes
1answer
29 views

Predictability of a time series

Say we are given a time series $(x_t)_{t \in P}$ where $P$ is the index set of past observations (train set). Imagine that we have built a model for our data and now want to assess predictability of ...
1
vote
1answer
23 views

Derivation of Perceptron weight update formula

I've started out studying Machine Learning and am currently reading up about how a single perceptron works. From the wikipedia page, my understanding is as follows: suppose we have an input sample $\...
0
votes
0answers
12 views

VineCopula package conditional probability

Suppose I have 3 variables, $U_1, U_2, U_3$. Suppose further that I fit R or CVine copula. Then, to find the conditional probability $U_1 \leq u_1|U_2=u_2,U_3=u_3$, the package suggests using ...
1
vote
1answer
11 views

Clustering with constraint on minimum size of cluster

I have dataset of $n$ objects, I want to cluster them according to correlation and I want to divide the dataset into groups of similar objects of sizes not less than 50 - because I use clustering for ...
0
votes
0answers
18 views

System of equations for quadratic programming with inequality constraints [on hold]

Through the problem can be written for GLMs as well as for other more complex settings in terms of objective function and constraints, for easy of presentation, I present the problem using a simple ...
0
votes
0answers
66 views

Posterior distribution of mixture models

In the context of mixture models in bayesian inference, one can assume that the general form of the joint posterior for a mixture model of $k$ components is $$ \begin{equation} p( \boldsymbol{\...
0
votes
0answers
8 views

Applying logit model on another data set

I have a following situation: I am testing a probability of harvesting in one forest - no previous harvesting data available. I have found an article about harvesting model - logit model done in a ...
1
vote
2answers
23 views

Denoting random variable $\theta$ with capital $\Theta$?

It is common practice to denote random variables with a capital letter $X$ and the realization with a small $x$. But how about in Bayesian statistics? The parameter $\theta$ is a RV, so shouldn't it ...
1
vote
1answer
19 views

Asking for inspiration

I am a teacher. I want to create a system where my students will take exams online and I will predict their chances of getting a certain marks in the final exam. Is there any mathematical model where ...
1
vote
0answers
13 views

Performing random forest on spatio-temporal rasters

We are trying to train a random forest model on land-use and meteorological variables to predict daily concentrations of air pollution at a 1km resolution. Our input data consists of 1km raster stacks ...
0
votes
0answers
19 views

How to deal with auto-correlation in generalized linear modelling?

I've built a generalized linear model by using glm.nb function (my response is a count type of data) using a single predictor. The model summary is given below. <...
1
vote
0answers
25 views

Training a neural network with partial labeling

I want to train a neural network that is part of a multi-armed bandit problem. For each data sample, I have some features representing the context of the sample and there are x neurons in the output ...
0
votes
1answer
15 views

Feature selection by lasso in two samples compared to one joint sample

Let's say you have two sets of features $X_1$ and $X_2$ together with a response variable $Y$. I wonder whether the two following procedures are identical asymptotically (or in finite samples) in ...
0
votes
0answers
7 views

How to handle varying sample size in a panel study?

Our panel study has an initial sample size of 17 and increased to 25 in the second data collection. How can be avoid bias in the data analysis? Method: We used a survey form with 23 likert-scale ...
0
votes
0answers
13 views

Accelerated Projected SGD under box constraints

Are there generalizations of ADAM or Adagrad algorithm that allow box constraints for the parameters to be incorporated in the gradient descent step? Is it valid to simply run the algorithm as usual ...

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