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Tags
list
608523
1
608636
null
2
27
Suppose we have two categorical random variables $X$ and $Y$, with both $k$ levels. We assume $Y$ is generated causally from $X$ ($X \to Y$). We also assume causal Markovian is satisfied, which means $X$ and $Y$ are probabilistically dependent. My question is: - Is there always a way to re-discretize $Y$ into a new va...
Can we preserve dependence in discretization?
CC BY-SA 4.0
null
2023-03-06T12:57:08.157
2023-03-07T13:22:59.153
2023-03-07T13:22:03.123
345167
345167
[ "causality", "discrete-data", "non-independent", "discrete-distributions" ]
608524
1
null
null
1
28
here's a pretty general question, so i do not expect to get precise answers. Instead i hope to read ideas and suggestions. I have a deployied proprietary Deep Learning model that make retail price prediction of pre-owned cars. Data are shaped like this: car characteristics, selling date and selling price and i'm receiv...
How to make a DL price prediction model aware of market fluctuations
CC BY-SA 4.0
null
2023-03-06T13:06:53.203
2023-03-09T11:49:09.883
2023-03-09T11:49:09.883
350354
350354
[ "regression", "neural-networks", "trend" ]
608525
1
608626
null
2
75
I'm trying to run a linear mixed model (in R) but my model either never seems to finish running or (with a simpler random effects structure) there is a warning about singular effects. My full model is below (this is the version that runs for ages and never completes): ``` RT_lme <- lmer(RT ~ Condition * HighLow * Corre...
Choosing Random Effects to Include in a Linear Mixed Model
CC BY-SA 4.0
null
2023-03-06T13:14:04.757
2023-03-07T12:10:55.283
2023-03-07T11:36:36.220
345611
379020
[ "r", "regression", "mixed-model", "lme4-nlme", "singular-matrix" ]
608526
2
null
606988
4
null
For Dirichlet random variates $x_1,...x_K$ with concentration parameters $\alpha_1...\alpha_K$, $$y_{i,j}=\frac{x_i}{x_i+x_j}\sim\text{Beta}(\alpha_i,\alpha_j)$$ and $$\frac{x_i}{x_j}=\frac{y_{i,j}}{1-y_{i,j}}\sim\beta'(\alpha_i,\alpha_j)$$ which is the [beta prime distibution](https://en.wikipedia.org/wiki/Beta_prime_...
null
CC BY-SA 4.0
null
2023-03-06T13:27:16.817
2023-03-08T17:16:21.080
2023-03-08T17:16:21.080
214015
214015
null
608527
1
null
null
0
32
I am trying to generate time-to-event data for two treatments, with 25 patients in each arm. I generated the survival time in the treatment arm using an exponential distribution with parameter 0.95, and in the control arm using parameter 1.0. I assumed that all patients would experience an event without censoring. The ...
Why the actual hazard ratio of the simulated time-to-event data is very different from the expected value?
CC BY-SA 4.0
null
2023-03-06T13:27:46.477
2023-03-16T10:46:41.973
null
null
364419
[ "survival", "simulation", "cox-model", "exponential-distribution", "hazard" ]
608528
1
608657
null
1
70
This is probably a straight-forward question but I can't find a straight-forward answer. The topic is new to me. I am performing parametric survival analysis, e.g. estimating a survival function from survival data and some covariates. It seems like it would be intuitive to check the residuals of the model in the same w...
residuals in parametric survival analysis
CC BY-SA 4.0
null
2023-03-06T13:40:19.623
2023-06-03T07:49:27.663
2023-06-03T07:49:27.663
121522
72174
[ "survival", "residuals", "parametric" ]
608529
1
null
null
0
32
Model framework: Suppose that the loss function is given by the Kullback-Leibler divergence (KLD) as follows: \begin{equation} \text{KL}(\Theta \parallel \hat{\Theta}) = \text{KL}\big(f(x;\Theta) \parallel f(x; \hat{\Theta})\big) = \int_{\mathcal{A}}\log\frac{f(x; \Theta)}{f(x; \hat{\Theta})}f(x; \Theta) dx, \end{equa...
Bayes estimate of mixture of exponential under the the Kullback-Leibler divergence loss function
CC BY-SA 4.0
null
2023-03-06T13:44:08.053
2023-03-06T13:44:08.053
null
null
351356
[ "bayesian", "estimation", "loss-functions", "kullback-leibler", "mixture-distribution" ]
608530
1
null
null
2
20
In the introduction of this paper [Bifurcations in a predator–prey model with general logistic growth and exponential fading memory](https://doi.org/10.1016/j.apm.2016.12.003) The authors claim [](https://i.stack.imgur.com/HKeYF.png) I didn't know that this model was well known. Can anyone point to a general reference ...
Who formulated this Generalized Lotka-Volterra model?
CC BY-SA 4.0
null
2023-03-06T13:45:17.430
2023-03-06T14:00:23.017
2023-03-06T14:00:23.017
382497
382497
[ "references", "growth-model", "differential-equations" ]
608531
1
608532
null
3
53
Suppose we have two discrete random variables $X$ and $Y$, both of which take values from $\{1,2,...,k\}$. $Y$ is generated from $X$ via a transition probability matrix (also known as the [stochastic matrix](https://en.wikipedia.org/wiki/Stochastic_matrix)), which is defined as: $$P:=[P_{ij}]_{k \times k}$$ with $P_{ij...
What kind of transition probability matrix indicates dependence/independence?
CC BY-SA 4.0
null
2023-03-06T13:50:27.880
2023-03-06T14:19:15.860
null
null
345167
[ "probability", "stochastic-processes", "markov-process", "discrete-data", "discrete-distributions" ]
608532
2
null
608531
4
null
Since the sample space of both $X$ and $Y$ is finite, the independence boils down to finite number of constraints namely $P_{ij}$ as defined in the question should only depend on $j$ or in other words every row of $P$ should be the same (the distribution of $X$). It can be seen easily (for eg. using law of total probab...
null
CC BY-SA 4.0
null
2023-03-06T14:19:15.860
2023-03-06T14:19:15.860
null
null
342327
null
608535
2
null
608273
4
null
It's somewhat easy to present results when using a log transformation and traditional tests of the mean like anova, because the results are essentially on the geometric means of the data. That is, results could be presented as "The geometric means of Group A and Group B were statistically different.". And then back-t...
null
CC BY-SA 4.0
null
2023-03-06T14:43:02.730
2023-03-06T14:43:02.730
null
null
166526
null
608536
1
null
null
0
22
Assume that a device is traveling at a constant expected speed $\mu$, subject to random variation with standard deviation $\sigma$, for a measurement period of duration $t$. Then the expected travel distance will be $\mu t$ over duration $t$. I am only able to measure the distance that the device has traveled and not i...
Detection limit for a drop in speed, due to stopping between measurements
CC BY-SA 4.0
null
2023-03-06T14:46:20.437
2023-03-06T15:02:18.430
2023-03-06T15:02:18.430
36229
36229
[ "hypothesis-testing", "likelihood-ratio", "measurement", "bayes-factors" ]
608537
2
null
561483
0
null
# 1) WSS processes Here is the definition of cyclic autocorrelation function from Wikipedia: $$ R_x^{n/T_0}(\tau) = \frac{1}{T_0} \int_{-T_0/2}^{T_0/2} R_x(t,\tau)e^{-j2\pi\frac{n}{T_0}t} \mathrm{d}t. $$ We can evaluate this quantity for a WSS process ($R_x^0(\tau)\ne 0$) for the special case of $n/T_0 = 0$ and get ...
null
CC BY-SA 4.0
null
2023-03-06T14:59:40.930
2023-03-06T14:59:40.930
null
null
375862
null
608539
2
null
608515
2
null
This is not true. Set the probability space $(\Omega, \mathscr{F}, P)$ to be $((0, 1], \mathscr{B}, \lambda)$ and define $X_n = \sqrt{n}I_{(0, n^{-1})}(x)$, $n = 1, 2, \ldots$, $X \equiv 0$, then \begin{align} E[|X_n|] = \frac{1}{\sqrt{n}} \to 0 = E[|X|] \end{align} as $n \to \infty$. Let $f(x) = x^2$, which is contin...
null
CC BY-SA 4.0
null
2023-03-06T15:09:07.797
2023-03-06T15:09:07.797
null
null
20519
null
608540
2
null
24799
0
null
There is actually [a paper](https://academic.oup.com/biomet/article/107/2/489/5715611) that connects CV and EB: E Fong, C C Holmes, On the marginal likelihood and cross-validation, Biometrika, Volume 107, Issue 2, June 2020, Pages 489–496 If I understand correctly, the paper claims that the marginal likelihood is simil...
null
CC BY-SA 4.0
null
2023-03-06T15:28:50.180
2023-03-06T15:28:50.180
null
null
348832
null
608541
1
608545
null
0
32
I just fitted a glm with the binomial family in R and to my surprise I didn't need to specify the $m_i$ values. Checking my notes, we simply assumed that $Y =_d \text{Binom}(m_i, p_i)$ where $p_i = H(x_i^T \beta)$, and thus our predictions are $\mathbb{E}[Y|X_i] = m_i p_i$. My response was binary to begin with, and to ...
In binomial regression, how do we know what is $m_i$ (number of trials in the binomial distribution)?
CC BY-SA 4.0
null
2023-03-06T15:32:32.087
2023-03-06T15:55:40.720
null
null
342779
[ "regression", "generalized-linear-model" ]
608542
1
null
null
0
14
I have this type of diagram [](https://i.stack.imgur.com/NVo6V.png) Where my main focus is the latent variable A and I want to know which factors impact the most on it. To make things more clear I will describe some made-up context that fits this situation. Imagine that A is a concentration of a compound in solvent A, ...
How to specify this diagram type in lavaan
CC BY-SA 4.0
null
2023-03-06T15:35:28.040
2023-03-06T15:35:28.040
null
null
382508
[ "r", "python", "structural-equation-modeling", "latent-variable", "lavaan" ]
608543
2
null
608503
1
null
> Because I have found outliers in my dataset (both in terms of Mahalonobis distance and generalized Cook's distance These were calculated by treating your 6-point Likert scale as a continuum, right? So 1 means 1, 2 means 2, ... > Because of the ordinal nature of the data, I am using ULS instead of ML, and the ord...
null
CC BY-SA 4.0
null
2023-03-06T15:40:54.973
2023-03-06T15:40:54.973
null
null
335062
null
608544
1
null
null
0
27
In R I have fitted a logistic model for polygenic risk scores in cases and controls as well as a number of covariates : ``` model <- glm(phenotype~prs+var1+var2+var3...var10, family=binomial(link='logit')data=data.prs) ``` The PRS column have values from around -0.1 to 0.2 The summary of my model looks like this: [](h...
Way of making odds ratios more manageable from logistic regression
CC BY-SA 4.0
null
2023-03-06T15:46:48.417
2023-03-06T15:46:48.417
null
null
300090
[ "r", "regression", "logistic" ]
608545
2
null
608541
1
null
I think this is what is happening. From [the documentation](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/family): > For the binomial and quasibinomial families the response can be specified in one of three ways: ... As a numerical vector with values between 0 and 1, interpreted as the proportio...
null
CC BY-SA 4.0
null
2023-03-06T15:50:23.650
2023-03-06T15:55:40.720
2023-03-06T15:55:40.720
22311
22311
null
608547
1
null
null
0
13
I am trying to fit an Arima model to the following time series of yearly incidence data from an infectious disease which presents a cyclical behaviour, meaning outbreaks in a non-predictable manner. The log-transformed time series is stationary based on KPSS test (function unitroot_kpss in fpp3 package). Using the ARIM...
Arima model for infectious disease with random outbreaks (cyclic behaviour)
CC BY-SA 4.0
null
2023-03-06T15:59:03.563
2023-03-06T15:59:03.563
null
null
25032
[ "forecasting", "arima" ]
608548
1
null
null
1
25
I have data where people are given a limited number of tokens (1 - 10) which they can assign across five different items. The number of tokens they allocate to an item represents the importance of that item to them over the others. In other words they have to make make more trade-offs if they are given fewer tokens to ...
What kind of regression for predicting limited resource allocation across items
CC BY-SA 4.0
null
2023-03-06T15:59:06.163
2023-03-07T09:17:21.403
2023-03-07T09:17:21.403
282624
282624
[ "regression", "statistical-significance", "multinomial-logit", "choice-modeling" ]
608549
1
null
null
1
30
dataset is a time series of index values from 2015 to 2020. i would like to do see if arima is an adequate forecasting tool for this index. in a first step i am trying to figure out whether my data is stationary or needs transformation. looking at the plot i see no seasonality and a constant mean over time, however, va...
Stationarity/ADF vs. KPSS Test
CC BY-SA 4.0
null
2023-03-06T15:39:56.257
2023-03-07T17:42:05.730
2023-03-07T17:42:05.730
11887
384355
[ "r", "time-series" ]
608550
1
null
null
0
28
There exists a classical method for solving a certain computational problem related to random sampling. It is the "gold standard", so to speak. I'm working on an algorithm that aims to solve the same problem more efficiently. It relies on partitioning the data used in the classical method and processing it in parallel....
Hypothesis testing for two samples from discrete distributions
CC BY-SA 4.0
null
2023-03-06T16:12:21.667
2023-03-06T16:12:21.667
null
null
300849
[ "hypothesis-testing", "chi-squared-test", "kolmogorov-smirnov-test", "discrete-distributions" ]
608551
1
null
null
0
41
Suppose I've sampled $x_0,\ldots,x_{n-1}$ and want to calculate the variance of these samples. What is a good (numerically stable) algorithm for this? And does the answer change, if we impose assumptions on the correlation of the samples (like assuming that they are samples drawn from a Markov chain)? I've seen that th...
Numerically stable computation of the variance
CC BY-SA 4.0
null
2023-03-06T16:14:52.867
2023-03-06T17:00:58.863
null
null
222528
[ "variance", "references", "markov-chain-montecarlo", "markov-process" ]
608552
1
null
null
0
8
I need to find the best variance estimator of my parameter $\theta$ using complex sampling data. My survey data with dimension N are drawn with a two-stages stratified sampling. I thus began from my dataset, I draw 1000 samples with dimension $n<N$ replicating the original sampling scheme and I estimate for each sample...
Compare variance estimators in complex sampling designs by simulations
CC BY-SA 4.0
null
2023-03-06T16:18:55.430
2023-03-06T16:51:44.617
2023-03-06T16:51:44.617
382514
382514
[ "variance", "simulation", "monte-carlo", "estimators", "weighted-sampling" ]
608554
1
null
null
1
7
If we have a fully connected MRF with three random variables $a, b, c$, what probablistic assumption would we make if we break the joint potential of the three by pairwise potentials? $$ \phi(a,b,c) = \phi(a,b)\phi(b,c)\phi(a,c). $$
What type of probabilistic assumption do we make in a MRF if we break a clique by pairwise potentials?
CC BY-SA 4.0
null
2023-03-06T16:23:02.100
2023-03-06T16:23:02.100
null
null
382515
[ "conditional-probability", "graphical-model", "markov-random-field" ]
608557
2
null
608297
4
null
I tend to have data with inherent structure, such as multiple samples per patient, multiple measurements per sample and the like. In that situation, the statistically independent unit is typically the patient rather than the row of the data matrix. (In some cases, independence is even more complicated, with multiple to...
null
CC BY-SA 4.0
null
2023-03-06T17:30:36.057
2023-03-10T21:33:40.393
2023-03-10T21:33:40.393
4598
4598
null
608558
1
null
null
1
19
Given two probability densities $p(x)$ and $p(y)$, define the dot-product of their log-likelihood gradients, also sometimes known as "scores", $\langle \nabla_x \log p(x), \nabla_y \log p(y) \rangle $. I was wondering if this pops up in a specific definition of a distance measure between distributions, is there a conne...
Dot-product of log-likelihood gradients ("scores")
CC BY-SA 4.0
null
2023-03-06T17:31:22.737
2023-03-06T17:31:22.737
null
null
133692
[ "machine-learning", "probability", "distributions", "distance" ]
608559
1
608562
null
1
39
To start I'll say I am relatively new to data analytics. How is this data set distributed? I'm debating whether I can use the Mann-Whitney test on it along with gender (M/F). I've been assuming it's very highly skewed but a couple of things are making me question whether it is considered skewed: - The means and median...
How would you describe the distribution of this data?
CC BY-SA 4.0
null
2023-03-06T17:32:49.033
2023-03-06T18:01:02.340
null
null
382520
[ "hypothesis-testing", "mathematical-statistics", "statistical-significance" ]
608561
1
null
null
2
150
$$ \newcommand{\pset}[1]{2^{#1}} \newcommand{\NN}{\mathbb{N}} \newcommand{\PP}{\mathbf{P}} \newcommand{\OO}{\Omega} \newcommand{\oo}{\omega} \newcommand{\sal}{$\sigma$-algebra\xspace} % Sigma algebra \newcommand{\sals}{$\sigma$-algebras\xspace} % Sigma algebras (plural) $$ Background: I'm tr...
Help with rigorous derivation of multinomial distribution
CC BY-SA 4.0
null
2023-03-06T17:43:25.687
2023-03-11T23:17:30.497
2023-03-07T01:01:33.840
173082
273784
[ "probability", "distributions", "mathematical-statistics", "multinomial-distribution" ]
608562
2
null
608559
1
null
First, you should use a more descriptive title, if possible. You have ordinal data (scores between 1 and 10?), where the data is mostly saturating the scale (getting the top value). Your data seems skewed, because one tail is longer than the other, but I think that the actual issue with your data is that most of it is ...
null
CC BY-SA 4.0
null
2023-03-06T18:01:02.340
2023-03-06T18:01:02.340
null
null
134438
null
608563
1
null
null
1
17
The data I have is essentially the number of times two students were seen together. So student 1 and 3 were seen the most amount of times together, then 2 and 3, then 1 and 2. The correlation matrix looks like this: [1](https://i.stack.imgur.com/Q6ZRe.jpg) [2] [3] [1](https://i.stack.imgur.com/Q6ZRe.jpg) 0 0.4 0.7 [2...
I want to conduct some test on a large correlation matrix in r
CC BY-SA 4.0
null
2023-03-06T18:22:58.290
2023-03-06T18:22:58.290
null
null
382528
[ "fisher-transform" ]
608564
1
null
null
4
67
In Lemma 1 of [these lecture notes](https://ocw.mit.edu/courses/14-382-econometrics-spring-2017/resources/mit14_382s17_lec1/), Chernozhukov and Fernández-Val write that partialing out with the Frisch-Waugh-Lovell theorem has an "adaptivity" property. Namely, suppose we regress $Y$ on $D$ and $W$ and partial out $W$. Th...
Why does the "infeasible" Waugh-Frisch-Lovell estimator agree with the usual one?
CC BY-SA 4.0
null
2023-03-06T18:26:56.633
2023-03-07T16:45:09.667
null
null
382529
[ "regression", "asymptotics" ]
608565
2
null
608111
4
null
- That looks curved to me. No, it is not wiggling all over the place, but there is curvature upon visual inspection. - A highly significant p-value despite only modest curvature can be interpreted just like any other hypothesis test that catches a modest effect. I will venture a guess that you have a fairly large sa...
null
CC BY-SA 4.0
null
2023-03-06T18:31:52.807
2023-03-06T19:12:56.943
2023-03-06T19:12:56.943
247274
247274
null
608566
2
null
582236
1
null
I think that the article ["Evaluating the density of ratios of noncentral quadratic forms in normal variables"](https://%20https://www.sciencedirect.com/science/article/pii/S0167947308005070) may be what you are looking for, although there doesn't seem to be a nice tidy expression there. In Proposition 1 in the paper, ...
null
CC BY-SA 4.0
null
2023-03-06T18:33:58.323
2023-03-16T14:17:08.903
2023-03-16T14:17:08.903
134438
134438
null
608567
2
null
581493
1
null
I'm going to break ranks with others complaining that you can't fit a continuous distribution to a discrete valued sample. We actually do this all the time, and it's an interesting problem in statistical computing and asymptotics to consider what happens when the distributional assumptions aren't exactly met. So... you...
null
CC BY-SA 4.0
null
2023-03-06T18:34:58.940
2023-03-06T18:46:12.420
2023-03-06T18:46:12.420
8013
8013
null
608568
1
null
null
0
44
I have been working to try to get means adjusted for covariates. I've seen examples such as [this](https://stats.stackexchange.com/questions/567116/calculate-covariate-adjusted-means-and-95cis-for-treatment-and-control-group-se) one, but I haven't seen an example that has Dr. Lumley's `survey` package in R. The code I ...
Means adjusted for covariates
CC BY-SA 4.0
null
2023-03-06T19:37:45.897
2023-03-06T19:37:45.897
null
null
254436
[ "r", "survey", "geometric-mean" ]
608569
2
null
608514
3
null
A common approach is to look at the standardized residuals (a.k.a. Pearson residuals), or to the adjusted standardized residuals. See Donald Sharpe's paper "[Chi-Square Test is Statistically Significant: Now What?](https://doi.org/10.7275/tbfa-x148)" (2015), that is a short review of residual analysis and other methods...
null
CC BY-SA 4.0
null
2023-03-06T19:53:45.980
2023-03-06T19:53:45.980
null
null
164936
null
608570
2
null
594060
1
null
I think your professor means that $e^x$ cannot be approximated by a single layer of ReLU globally (on the entire $\mathbb{R}$), which seems correct because whatever the output of a single layer of ReLU is, it grows linearly, not exponentially. Meaning that the output of your network cannot be equal to a function that g...
null
CC BY-SA 4.0
null
2023-03-06T19:58:37.373
2023-03-06T19:58:37.373
null
null
214510
null
608572
1
608581
null
1
37
After an ANOVA in R, do you know if it is possible to get the group differences using Bonferroni correction ? If I use the iris dataset ``` a<-aov(iris$Sepal.Width~iris$Species, data=iris) ``` When I run a TukeyHSD, I get the group differences directly ``` TukeyHSD(a) Tukey multiple comparisons of means 95% fami...
How to get the group differences after Bonferroni correction in multiple comparison?
CC BY-SA 4.0
null
2023-03-06T20:15:51.147
2023-03-06T23:13:14.107
null
null
261354
[ "r", "anova", "post-hoc", "bonferroni", "tukey-hsd-test" ]
608574
2
null
608478
2
null
What you are looking at is the [law of total probability](https://en.wikipedia.org/wiki/Law_of_total_probability), [law of total expectation](https://en.wikipedia.org/wiki/Law_of_total_expectation), etc. These laws follow directly from the definition of conditional probability and conditional probability densities. I...
null
CC BY-SA 4.0
null
2023-03-06T21:59:14.877
2023-03-06T21:59:14.877
null
null
173082
null
608575
1
null
null
0
25
I have 2 questions. - How can I calculate the probability of getting a specific sequence of heads vs tails? - If I have a given sequence of tosses, how can I use this information to help me guess the next flip? Let's suppose that I have a fair, 2 sided coin. My attempts for 1: Let's suppose I want to know what th...
Conditional probablity for a given seqeunce
CC BY-SA 4.0
null
2023-03-06T22:09:55.157
2023-03-06T22:09:55.157
null
null
382535
[ "probability" ]
608578
2
null
608394
1
null
It doesn't make sense to use $f(x)=\frac{1}{2\pi}\int \exp(-\mathrm itx) \varphi_X(t)~\mathrm dt$ when $\int|\varphi_X(t) |~\mathrm dt=\infty, $ for the former is true if $\int|\varphi_X(t) |~\mathrm dt<\infty.$ The general inversion formula (assuming $a,~b\in \mathcal C(\mathrm F) ;~a<b$) is $$ \mathrm F(b) - \mathrm ...
null
CC BY-SA 4.0
null
2023-03-06T22:57:34.027
2023-03-07T03:02:29.780
2023-03-07T03:02:29.780
362671
362671
null
608579
2
null
606983
0
null
Based on your reference I believe that you are estimating the vector $\boldsymbol{\beta}$ of size $p_n$ with a posterior distribution based on the observation of the vector $\mathbf{Y}$ of size $n$ in the model $$\mathbf{Y} = \mathbf{X} \boldsymbol{\beta} + \boldsymbol{\epsilon}$$ where $\mathbf{X}$ is a fixed regress...
null
CC BY-SA 4.0
null
2023-03-06T23:02:04.947
2023-03-08T09:15:32.070
2023-03-08T09:15:32.070
164061
164061
null
608580
1
null
null
0
26
Why is the value of MSE in cross-validation is always less than 1 in the MSE values of the hidden nodes selected by the MLP function. [](https://i.stack.imgur.com/Lbcp9.png) This is the result of the code ``` fit2 <- mlp(fit, auto.hd.type = "cv") fit2$MSEH ``` The values of my input have a mean of 9000. Further, the M...
MSE on cross validation of MLP
CC BY-SA 4.0
null
2023-03-06T23:05:33.293
2023-03-06T23:05:33.293
null
null
367146
[ "time-series" ]
608581
2
null
608572
1
null
This can be done using the `emmeans` package, which allows easy working with contrasts. We can get specify a bonferroni-adjusted pairwise series of tests by ``` fit <- aov(Sepal.Width ~ Species, data = iris) fit_em_bonf <- emmeans::emmeans( fit, specs = pairwise ~ Species, adjust = "bonf" ) ``` and then extrac...
null
CC BY-SA 4.0
null
2023-03-06T23:13:14.107
2023-03-06T23:13:14.107
null
null
335519
null
608582
1
null
null
2
62
I am trying to calculate the odds ratio using the epitools package. The counts in 2 cells of my 2x2 table are $< 10$ so I keep receiving the following error "Error in chisq.test(xx, correct = correction) : (converted from warning) Chi-squared approximation may be incorrect". I tried defining the method as "fisher" and ...
Epitools oddsratio error in chisq.test
CC BY-SA 4.0
null
2023-03-06T23:22:11.597
2023-03-09T16:17:22.893
2023-03-09T15:32:11.490
11887
382539
[ "chi-squared-test", "odds-ratio", "epidemiology" ]
608583
1
null
null
0
20
In my problem, I have a condition in which I need to compute the joint distribution of two dependent distributions. The first distribution is normal and the second one is beta distribution. How can I get the joint distribution function of these two distributions? Any help would be appreciated. Update Actually, I am tes...
How can I combine and get cdf of joint distribution of normal and beta distributions on the same set of data?
CC BY-SA 4.0
null
2023-03-06T23:26:02.393
2023-03-06T23:26:02.393
null
null
365295
[ "wilcoxon-mann-whitney-test", "joint-distribution", "kolmogorov-smirnov-test" ]
608584
1
null
null
5
635
I am reading [this article](https://towardsdatascience.com/horseshoe-priors-f97672b4f7cb) about the horseshoe prior and how it is better than lasso and ridge priors. The author makes several points that I don't understand. One of them is "The ideal prior distribution will put a probability mass on zero to reduce varian...
How does an ideal prior distribution needs a probability mass on zero to reduce variance, and have fat tails to reduce bias?
CC BY-SA 4.0
null
2023-03-06T23:32:25.283
2023-03-08T09:38:39.630
2023-03-07T08:16:55.283
53690
362604
[ "regression", "bayesian", "prior" ]
608585
2
null
608561
6
null
Even under the rigorous measure-theoretic framework, your proof is overly verbose, probably due to that you confused the underlying probability space $(\Omega, \mathscr{F}, P)$, where $X_1, X_2, \ldots, X_n$ and $Y = (Y_1, \ldots, Y_m)$ are defined, with their image space $(\mathbb{R}^1, \mathscr{R}^1)$. In particular...
null
CC BY-SA 4.0
null
2023-03-06T23:49:01.043
2023-03-07T12:21:20.927
2023-03-07T12:21:20.927
20519
20519
null
608586
2
null
608584
6
null
The idea is that you want your regularisation procedure to set small parameter estimates to zero and leave large estimates unchanged. Now, lasso does zero out small estimates (ridge doesn't even do that), but both lasso and ridge shrink large estimates towards zero, which is a significant source of bias in the two proc...
null
CC BY-SA 4.0
null
2023-03-06T23:56:19.037
2023-03-06T23:56:19.037
null
null
335519
null
608587
2
null
608584
6
null
### Probability mass at zero > How does the normal distribution have a zero probability mass at zero? The normal distribution has a non zero density at zero but the probability (mass) is zero $P[X=0] = 0$. By placing a probability mass at zero the prior is expressing more strongly the believe that a parameter is ...
null
CC BY-SA 4.0
null
2023-03-06T23:56:24.470
2023-03-08T09:38:39.630
2023-03-08T09:38:39.630
362671
164061
null
608588
1
null
null
0
20
I am reading [Inference on Counterfactual Distributions](https://arxiv.org/pdf/0904.0951.pdf) and my knowledge of distribution functions is rusty. > Suppose we would like to analyze the wage differences between men and women. Let 0 denote the population of men and 1 the population of women. $Y_j$ denotes wages and $X_...
Integrating a conditional CDF WRT another distribution with nested support
CC BY-SA 4.0
null
2023-03-07T00:11:05.217
2023-03-07T00:11:05.217
null
null
382540
[ "probability", "distributions", "conditional-probability" ]
608589
2
null
608584
9
null
#### The MAP estimator can have non-zero probability mass at a point (even if the posterior distribution is always continuous) The linked article is actually a bit misleading on this point, since even under the stipulated model all the relevant distributions are still continuous, so there is still zero probability m...
null
CC BY-SA 4.0
null
2023-03-07T00:22:37.470
2023-03-07T21:23:25.287
2023-03-07T21:23:25.287
173082
173082
null
608590
1
null
null
1
22
I am using `lagsarlm` in spdep package in `r` to estimate a spatial Durbin (mixed) model by ``` m1 <- lagsarlm(f, data = d, wlist, type = "mixed") ``` and using predict function ``` pred <- predict(m1,newdata = d, listw = wlist) ``` with the original data and spatial weight list to estimate the dependent variable. Th...
predict return different values from fitted.value
CC BY-SA 4.0
null
2023-03-07T00:53:30.703
2023-03-08T00:59:36.813
2023-03-08T00:59:36.813
382545
382545
[ "r", "spatial-correlation" ]
608591
1
null
null
2
81
I have fitted gam for a generated data with binomial responses. The problem is, many times while running this gam with different bootstrap samples, error occurred.
Why does using "REML" in mgcv give error for generalized additive models?
CC BY-SA 4.0
null
2023-03-07T00:53:58.060
2023-03-23T06:25:31.760
2023-03-23T06:25:31.760
null
null
[ "convergence", "aic", "generalized-additive-model", "mgcv", "reml" ]
608592
2
null
608561
4
null
#### Your present attempted proof is question-begging Firstly, well done on your initial attempt. You appear to have a basic idea of how you would like to proceed, and you are making an attempt to set this out rigorously, which is no easy task. I see a couple of problems with your proof. The first problem is that ...
null
CC BY-SA 4.0
null
2023-03-07T00:57:36.263
2023-03-11T23:17:30.497
2023-03-11T23:17:30.497
173082
173082
null
608593
2
null
608582
0
null
The issue is that `oddsratio`, `oddsratio.fisher` and `oddsratio.small` all calculate a "regular" chi-squared statistic for reporting each time: you can see this in the example output for `oddsratio.fisher(mat)` below (the `$p.value` table, `chi.square` column). So each of these variants of oddsratio is triggering the ...
null
CC BY-SA 4.0
null
2023-03-07T01:04:49.567
2023-03-09T15:32:37.773
2023-03-09T15:32:37.773
11887
16974
null
608594
2
null
608249
1
null
Standardizing the coefficients may help. Also could try using canopy cover as the dependent variable and adding a grass and forb counts as independent variables and just use a linear model rather than poisson.
null
CC BY-SA 4.0
null
2023-03-07T01:27:10.130
2023-03-07T01:27:10.130
null
null
382547
null
608595
2
null
605619
0
null
You may find the answer quite intuitive. Consider the sketch below. As cosine similarity deals with the angle between $\bf{X}$ and $\bf{w}$, the question boils down to projecting $\bf{X}$ on a sphere passing through the center of the distribution of $\bf{X}$, that is, through $E[\bf{X}]$. From the symmetry of the distr...
null
CC BY-SA 4.0
null
2023-03-07T01:43:29.787
2023-03-07T01:43:29.787
null
null
382548
null
608596
1
616605
null
0
34
I am currently reading up on RealNVP, which has the following transformations according [Lilian Weng](https://lilianweng.github.io/posts/2018-10-13-flow-models/): $$ \begin{aligned} \mathbf{y}_{1:d} &= \mathbf{x}_{1:d} \\ \mathbf{y}_{d+1:D} &= \mathbf{x}_{d+1:D} \odot \exp({s(\mathbf{x}_{1:d})}) + t(\mathbf{x}_{1:d}) ...
Normalizing Flows Invertibility
CC BY-SA 4.0
null
2023-03-07T02:22:29.203
2023-05-22T17:50:46.887
null
null
269616
[ "probability", "neural-networks", "mathematical-statistics", "generative-models", "normalizing-flow" ]
608597
1
null
null
0
15
i have trained a small bayesian neural network by splitting a dataset in the usual training and test dataset. Now i also have an analytical model whose parameters needs to be estimated by mcmc methods on the same dataset. i would like to compare the quality of the predictions. should i split the dataset into test and ...
comparing the performance of a neural network with the prediction of an analytical model: question on the test dataset
CC BY-SA 4.0
null
2023-03-07T02:42:27.657
2023-03-07T02:42:27.657
null
null
275569
[ "regression", "bayesian", "model-comparison" ]
608598
1
null
null
1
11
I have a phylogentic tree of samples, and some samples belong to either of two groups. I'm trying to show that the mean pairwise distance of samples in one group is larger than the one from the other group. I computed the pairwise genetic distance of all samples in a tree using cophenetic.phylo and obtaining the mean p...
Distribution of genetic distances in a phylogenetic tree
CC BY-SA 4.0
null
2023-03-07T02:45:21.813
2023-03-07T02:45:21.813
null
null
8089
[ "distributions", "phylogeny" ]
608599
1
608647
null
2
48
I am trying to create a database with a dichotomized dependent variables and a bunch of binary (1/0) independent variables. I'd like to pre-set some associations between the independent variables and the outcome. Doing so is relatively easy - after generating the random binary covariates, I run a binomial function to p...
switching from probability to classification while maintaining exact ORs
CC BY-SA 4.0
null
2023-03-07T03:33:19.103
2023-03-07T14:53:36.133
2023-03-07T14:24:21.453
292896
292896
[ "machine-learning", "logistic", "simulation", "odds-ratio" ]
608600
1
608618
null
3
26
In Causality - Models, Reasoning, And Inference by Pearl, definition 2.3.3 reads as follows - > One latent structure $L$ = $\langle D,O \rangle$ is preferred to another $L^{'}$ = $\langle D^{'},O \rangle$ (written $L \preceq L^{'}$) if and only if $D^{'}$ can mimic $D$ over $O$ - that is, if and only if for every $\Th...
In what sense is one latent causal structure "preferred to" another? Definition 2.3.3 from Causality by Pearl
CC BY-SA 4.0
null
2023-03-07T03:40:24.743
2023-03-07T10:03:47.627
null
null
331772
[ "causality", "graphical-model", "bayesian-network", "causal-diagram" ]
608601
2
null
157582
0
null
Here is a simulation to demonstrate that @soakley's confidence interval works for a normally distributed random variable. - It takes $10^4$ values of $\mu$ in $[-10,10]$ and of $\sigma$ in $[0,10]$ and - for each of those pairs, it generates $10^6$ single observations $x$ and - sees what proportion of the correspon...
null
CC BY-SA 4.0
null
2023-03-07T03:43:28.657
2023-03-07T03:48:53.750
2023-03-07T03:48:53.750
2958
2958
null
608602
1
null
null
0
8
I've been asked to obtain a suitable differential equation describing the concentration profile of the oxygen gas in the wastewater column. Things I know so far: - Wastewater is stored in a large cuboidal tank, which is in contact with oxygen gas - Oxygen diffuses into the water isothermally - Height of wastewater i...
Am I missing a generation/consumption/accumulation term in this mass balance?
CC BY-SA 4.0
null
2023-03-07T04:51:11.673
2023-03-07T04:51:11.673
null
null
382554
[ "modeling" ]
608604
1
null
null
1
14
I am doing a Before/After analysis, which is aiming at evaluating the effect of a change. Assume I have made a change at the beginning of June-2022, and I want to evaluate the effect of the change based on a one-month interval. This results in two time series, related to two distinct months, i.e., the first one is for ...
How to apply a seasonal index into an eCDF?
CC BY-SA 4.0
null
2023-03-07T04:57:32.647
2023-03-07T23:57:55.030
2023-03-07T23:57:55.030
371243
371243
[ "time-series", "seasonality", "empirical-cumulative-distr-fn", "wasserstein" ]
608605
1
null
null
1
21
In [https://www.jmlr.org/papers/volume9/zhang08a/zhang08a.pdf](https://www.jmlr.org/papers/volume9/zhang08a/zhang08a.pdf), a Maximal Ancestral Graph (MAG) is defined as: ``` a mixed-edge graph that: i) does not contain any directed or almost directed cycles (ancestral) and ii) there is no inducing path between any tw...
Does a PAG (partial ancestral graph) have almost directed cycles with circular endpoints?
CC BY-SA 4.0
null
2023-03-07T04:59:30.787
2023-03-08T00:51:44.913
2023-03-08T00:51:44.913
106439
106439
[ "causality", "graphical-model", "causal-diagram" ]
608606
1
null
null
0
27
I am recently encountering a challenge with BTYD, specifically with Pareto-NBD model. See, from the papers that I read from Faders, there are few assumptions using this model, and the first and foremost is: i) Customers go through two stages in their “lifetime” with a specific firm: they are “alive” for some period of ...
BTYD prior model tweaking
CC BY-SA 4.0
null
2023-03-07T05:00:34.577
2023-03-07T05:00:34.577
null
null
382556
[ "customer-lifetime-value" ]
608607
2
null
608347
1
null
I was able to achieve my goal by using entropy. Since I want the distribution to be seen uniformly on a larger scale, I used binning and then calculated the entropy. I used this approach with multiple bin sizes together.
null
CC BY-SA 4.0
null
2023-03-07T05:07:08.200
2023-03-07T05:07:08.200
null
null
319408
null
608608
1
null
null
4
277
I'm trying to plan a study based on previous data and I need to know the sample size required for a given effect size. Previous data looks like this: |Rating |1 |2 |3 | |------|-|-|-| |control |0 |20 |11 | |treatment |6 |14 |12 | where these are counts of the number of samples given a particular ranking at some ti...
Question about sample size indicated from power analysis for chi-square analysis in Python
CC BY-SA 4.0
null
2023-03-07T05:35:54.470
2023-03-07T15:12:14.937
2023-03-07T08:28:12.777
164936
367293
[ "mathematical-statistics", "statistical-significance", "python", "statistical-power" ]
608609
1
608791
null
2
168
I've been asked to fit a ZeroInflatedPoisson model on a dataset to predict Y (count data) for an assignment. First, I did this manually: - Create a binary variable (Y_IND) based on Y where Y_IND = 0 if Y = 0, and 1 if Y >=1. - Fit a statsmodels Logistic Regression model using X variables to predict the binary variabl...
Statsmodels ZeroInflatedPoisson - Unable To Converge
CC BY-SA 4.0
null
2023-03-07T06:06:24.167
2023-03-08T18:05:00.970
null
null
336714
[ "logistic", "poisson-regression", "zero-inflation", "statsmodels" ]
608610
1
null
null
0
51
For $X_1,\dots, X_n$ iid sample from $X\sim Bernoulli(p)$. I try to verity that the estimator $\hat{p}=\bar{X}$ (sample mean) is the UMVUE for unknown parameter $p$. I know that $\hat{p}$ is unbiased. I try to show that $Var[\hat{p}]=CRLB$ (Cramer-Rao lower bound), which is $$ CRLB=\frac{[I'(\theta)]^2}{nI(\theta)}, $...
Which Fisher information should I use for Cramer-Rao lower bound?
CC BY-SA 4.0
null
2023-03-07T07:59:47.757
2023-03-07T09:43:52.993
2023-03-07T09:43:52.993
362671
334918
[ "mathematical-statistics", "estimation", "inference", "likelihood", "cramer-rao" ]
608611
1
null
null
1
45
I have a very specific work-related question which I would like a second opinion on. We have a device that can be powered via battery and AC mains. We have identified a specific failure mode where suddenly, the battery cannot provide power to the device. Let's call this event P(F). In order to pose a risk to the user, ...
Probability of failure event?
CC BY-SA 4.0
null
2023-03-07T08:09:29.023
2023-03-07T08:09:29.023
null
null
382568
[ "probability" ]
608612
2
null
608608
4
null
The boundary for what is "just statistically significant" (i.e. the p-value is just below some "significance threshold" such as 0.05) is, if everything you observe is the true state of nature, around the point where you would have 50% power with that sample size. This is rather obvious, when you think about it: If what...
null
CC BY-SA 4.0
null
2023-03-07T08:12:29.010
2023-03-07T08:12:29.010
null
null
86652
null
608614
2
null
608608
5
null
As you don't provide a lot of details about the goal of your study, from the outside it looks a bit like your null hypothesis may be ill-defined: - why using a chi-squared test, when the variable Rating probably has an order? Don't you want to know if the treatment tend to increase or decrease the rating? The approach...
null
CC BY-SA 4.0
null
2023-03-07T09:01:30.783
2023-03-07T15:12:14.937
2023-03-07T15:12:14.937
164936
164936
null
608615
2
null
135739
0
null
My 2p since this question has resurfaced to the top after few years with no answer... In my opinion, it pays off to invest in a workflow manager. I'm very happy with [snakemake](https://snakemake.github.io/) and it's been a game-changer after having spent quite some time hacking together README files, bash scripts, and...
null
CC BY-SA 4.0
null
2023-03-07T09:13:33.237
2023-03-07T09:18:44.830
2023-03-07T09:18:44.830
31142
31142
null
608617
2
null
608610
3
null
Cramér-Rao Lower Bound would be of the form $\operatorname{Var}_\theta(T(\mathbf X) ) \geq \mathscr I(\theta)^{-1}. $ For exponential family, $\mathscr I(\theta) =\mathbb E_\theta\left[-\partial^2_\theta \ln f(\mathbf x;\theta)\right],$ which for $X_i\overset{\text{i.i.d.}}{\sim}\mathrm{Ber}(p) $ is \begin{align}\maths...
null
CC BY-SA 4.0
null
2023-03-07T09:41:35.873
2023-03-07T09:41:35.873
null
null
362671
null
608618
2
null
608600
1
null
## Definition 2.3.3 is in essence a statement about "excess edges" or "excess dependencies" Let us for a second assume there are no hidden variables. Then, a structure $L'$ that can, with the right parametrization $\Theta'_{D'}$, mimic all probability distributions of an alternative structure $L$ (such that $P_{[O]}...
null
CC BY-SA 4.0
null
2023-03-07T10:03:47.627
2023-03-07T10:03:47.627
null
null
250702
null
608619
1
608628
null
0
31
suppose I have categorical dataset, I'm doing data pre-processing. what is the correct order of applying these 3 techniques - Train Test split - SMOTEN to over sampler the minority class - Categorical encoding of variables (a mix of one hot, label encoding and target encoding)
Order of pre-processing the dataset
CC BY-SA 4.0
null
2023-03-07T10:09:12.843
2023-03-07T11:50:28.727
null
null
376559
[ "categorical-data", "dataset", "categorical-encoding", "data-preprocessing", "smote" ]
608620
1
null
null
3
60
I would like to generate a propensity score for a continuous treatment in R, and then control for the propensity score in a structural equation model (using the lavaan package). I'm aware that the twangContinuous package can generate propensity scores for continuous treatments, but it doesn't seem there is an option fo...
How to generate a propensity score for a continuous treatment in R?
CC BY-SA 4.0
null
2023-03-07T10:15:23.290
2023-03-07T10:15:23.290
null
null
269031
[ "structural-equation-modeling", "propensity-scores", "lavaan" ]
608622
1
null
null
1
60
Using R, I m performing a backtest on a time series by using quantile regression (quantreg::rq) on a number of features. These features are selected based on a condition such as p-values <= 5%. If I run the routine multiple times, I always end up with the same betas/coefficients on the features, however p-values are un...
p-values unstable using quantreg::rq in R
CC BY-SA 4.0
null
2023-03-07T10:31:37.457
2023-03-07T11:35:47.327
null
null
382577
[ "r", "regression", "time-series", "p-value", "quantile-regression" ]
608623
2
null
608525
2
null
Your model has an overly complicated random-effects structure. I would suggest first thinking about your research question, i.e., which associations between `RT` and the variables `Condition`, `HighLow`, and `Correct` do you want to study, and translate this to the specific fixed effects terms to include in the model. ...
null
CC BY-SA 4.0
null
2023-03-07T10:56:43.323
2023-03-07T10:56:43.323
null
null
219012
null
608624
1
null
null
0
34
I am very new to analyzing and forecasting timeseries data so apologies if this question has an answer too obvious. I am trying to find the residuals between a stationarized price data and white noise ARIMA(0,0,0). ``` library(forecast) library(tseries) DJT = read.csv("DJTA.csv") DJT_ts <- ts(DJT$DJTA, start=c(2013,1)...
ARIMA(0,0,0) residuals are the same as the timeseries data
CC BY-SA 4.0
null
2023-03-07T11:04:51.730
2023-03-07T17:53:55.100
2023-03-07T17:53:55.100
53690
382583
[ "forecasting", "arima", "residuals", "white-noise" ]
608625
2
null
536308
0
null
I just met that question and found that there is a simulation study (Valente et al., 2021) proved to permutation all data before CV is correct. And, here is reason. > A theoretical insight into why the other resampling schemes result in an inflation of false positives can be gained from (Bengio and Grandvalet, 2004), ...
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CC BY-SA 4.0
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2023-03-07T11:22:35.157
2023-03-07T11:23:36.587
2023-03-07T11:23:36.587
382584
382584
null
608626
2
null
608525
1
null
The singular effects error is no accident and is fairly common in fitting complicated interaction models (Meteyard & Davies, 2020). This typically happens when a mixed effects model has a random effects structure specified that doesn't fit the data well. For example, there may be very little variance in the way you mod...
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CC BY-SA 4.0
null
2023-03-07T11:35:10.833
2023-03-07T12:10:55.283
2023-03-07T12:10:55.283
345611
345611
null
608627
2
null
608622
0
null
This is an example of the instability of feature selection and a drawback of the threshold-based approach that you take. There’s basically no difference between the $0.049$ and $0.0536$ p-values you give, yet your approach to feature selection treats those as dramatically different. It is typical to see instability in ...
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CC BY-SA 4.0
null
2023-03-07T11:35:47.327
2023-03-07T11:35:47.327
null
null
247274
null
608628
2
null
608619
0
null
While one hot and label encoding can be applied dataframe wise before splitting (using e.g. pandas routines), it's better to split first and build a proper pipeline which would simplify the input of the new data without extra manual steps. Target encoding should always be done after splitting, otherwise it creates a hu...
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CC BY-SA 4.0
null
2023-03-07T11:50:28.727
2023-03-07T11:50:28.727
null
null
361202
null
608629
2
null
608498
7
null
This is a consequence of the (general) fact that (auto)correlation matrices like $$ \begin{pmatrix} 1&\rho_1&\rho_2\\ \rho_1&1&\rho_1\\ \rho_2&\rho_1&1\\ \end{pmatrix} $$ are positive [semi-definite](https://stats.stackexchange.com/questions/69114/why-does-correlation-matrix-need-to-be-positive-semi-definite-and-what-d...
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CC BY-SA 4.0
null
2023-03-07T11:51:37.370
2023-03-10T07:47:38.300
2023-03-10T07:47:38.300
67799
67799
null
608630
1
null
null
0
91
I am trying to interpret an NMDS analysis. And for that I did a shepard plot. I understand that ideally the points should follow a monotonic line, which is not really the case in my example. But I do not really understand what Non-metric fit and metric fit correspond to. What can I extract from these squared-r? Does it...
Interpretation of a shepard plot for NMDS
CC BY-SA 4.0
null
2023-03-07T12:19:30.930
2023-03-07T17:51:37.453
2023-03-07T17:51:37.453
234629
234629
[ "multivariate-analysis", "dimensionality-reduction", "r-squared" ]
608632
2
null
46591
1
null
There are competing factors. One the one hand, multicollinearity inflates standard errors. On the other hand, removing a variable to remove the multicollinearity can lead to omitted-variable bias, and it is not clear that you are better-off with a narrow standard error for a biased estimate than you would be with the m...
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CC BY-SA 4.0
null
2023-03-07T12:22:25.643
2023-03-07T12:22:25.643
null
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247274
null
608633
2
null
45259
0
null
This does not make sense to me. The point of regression is to use the variation in covariates ($x$ variables) to explain the variation in some variable of interest ($y$). If you have no variability in a covariate, it isn’t helping to accomplish that goal. What you might find interesting is to fit a quantile regression ...
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CC BY-SA 4.0
null
2023-03-07T12:27:11.717
2023-03-07T12:27:11.717
null
null
247274
null
608635
2
null
608528
0
null
Survival times are sometimes modelled as $$Y_i = e^{\beta X_i} \cdot \epsilon_i$$ where the $\epsilon_i$ are exponential distributed. The term $e^{\beta X_i}$ relates to the risk and increases or decreases the mortality rate. [Cox Snell residuals](https://www.jstor.org/stable/2984505) are in this case defined as the so...
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CC BY-SA 4.0
null
2023-03-07T13:08:47.117
2023-03-07T13:08:47.117
null
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164061
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608636
2
null
608523
0
null
After some thinking, I believe the answer to my question is yes: there is always such a re-discretization as long as $k>l\geq2$. The proof is as follows: Denote the transition probability matrix from $X$ to $Y$ as $P(Y|X):=[pr(y_i|x_j)]_{i,j}$. Then, $X \not \perp Y$ means at least two columns of $P(Y|X)$ are different...
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CC BY-SA 4.0
null
2023-03-07T13:22:59.153
2023-03-07T13:22:59.153
null
null
345167
null
608638
1
null
null
0
30
With a certain rate $R$ balls fall into a box. There is no limit to the number of balls the box can hold, but each ball has a rate $\gamma$ to leave the box and when two balls hit each other they leave both the box. The rate which two balls hit each other is $\beta$. One can build a markov chain to describe this proces...
stationary distribution of a continuous time markov chain
CC BY-SA 4.0
null
2023-03-07T13:34:22.187
2023-03-07T13:34:22.187
null
null
382593
[ "probability", "distributions", "stationarity", "markov-process", "transition-matrix" ]
608639
2
null
608297
4
null
There's situations where you can bootstrap. If your sample size is large, then bootstrapping when possible is really convenient for a number of reasons: - If it works, then it works for almost any metric you can define, while frequentist analytical solutions tend to be derived for one metric at a time (bad luck if you...
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CC BY-SA 4.0
null
2023-03-07T13:59:31.650
2023-03-07T14:08:15.847
2023-03-07T14:08:15.847
86652
86652
null
608640
1
null
null
0
18
I tried to measure entropy of binary matrix like below using code at : [https://github.com/cosmoharrigan/matrix-entropy](https://github.com/cosmoharrigan/matrix-entropy) (I already saw the question : Measuring entropy/ information/ patterns of a 2d binary matrix) [](https://i.stack.imgur.com/WAPez.png) (red implies 1 a...
Measuring entropy of a binary matrix with biased probability
CC BY-SA 4.0
null
2023-03-07T14:15:23.753
2023-03-07T14:15:23.753
null
null
366997
[ "algorithms", "matrix", "entropy", "information-theory", "pattern-recognition" ]
608642
2
null
23197
1
null
`aov3` in the sasLM package in R will give the same results as SAS Type III. (Continued after output.) ``` library(sasLM) aov3(Y ~ T*B, Data) # Data is defined in question ``` giving: ``` Response : Y Df Sum Sq Mean Sq F value Pr(>F) MODEL 5 77.900 15.580 8.9029 0.02733 * T ...
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CC BY-SA 4.0
null
2023-03-07T14:27:16.660
2023-03-08T13:44:27.543
2023-03-08T13:44:27.543
4704
4704
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