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For a given data matrix $A$ (with variables in columns and data points in rows), it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical solution of ordinary least squares. Or, for PCA, its eigenvectors are the principal components of the data.
I understand how... |
"Big data" is everywhere in the media. Everybody says that "big data" is the big thing for 2012, e.g. KDNuggets poll on hot topics for 2012. However, I have deep concerns here. With big data, everybody seems to be happy just to get anything out. But aren't we violating all classic statistical principles such as hypothe... |
I have failure data for an experience over $T$ years: at the beginning of each year I have $n_t$ subjects and $d_t$ of these subjects experience a "failure" at the end of the year.
Now if I assume that the trials are iid Binomial and the probability of failure $p$ is homogenous (i.e. constant over time), the ML esti... |
Next week we have an intern from a local school in the house. The concept behind his short internship is to get an idea how the real world works and what certain jobs deal with, how the daily work looks like etc.
Now I wondered, what one can tell/show/demonstrate such a young kid about Statistics and Machine Learning s... |
Does anyone know a way to calculate the effect size of a Fisher's exact test? Does that even make sense?
|
I want to identify bad responses in the data we get from our vendors. To assess the quality of the data, what statistical tests can i apply to identify bad respondents?
I performed Discriminant analysis to identify the % similarity of responses among surveys completed by a particular interviewer. How can i further auth... |
This thread offers some good information on the calculation of linear regression prediction intervals and includes a link to some practical notes. At the end of the link the author claims that, in case of multiple linear regression, we should consider the joint region of the predictor variables.
How should MLR predicti... |
What is wrong with the following sentence:
The Central Limit Theorem implies that, as the sample size grows, the error distribution approaches normality.
Am I correct by saying that it should in stead state the MEAN of the sample error approaches zero as sample size grows?
|
I have about 3 hours worth of 3-axis accelerometer, gyroscope and compass data taken at subsecond intervals. I'm fully aware that this data needs to be filtered and that there are a shedload of methods for filtering it (FFT, ARMA, et al). How can I tell from my data or a plot thereof, which is the "best" filter to use?... |
I calculated a sequence of multi-level models with stata (xtmixed). I have a sample of 800 kids in 46 classes and I want to explain their individual level of prejudice by the proportion of fully prejudiced respondents in the class. This is based on a three categorical index, the level of prejudice is measured by a prin... |
While I was reading about Bayesian networks, I run into "Markov blanket" term and got severely confused with its independency in a Bayesian network graph.
Markov blanket briefly says that every node is only dependent on its parents, children and children's parents [it is gray area for node A in the picture].
What is... |
Let $X\,$ be a non-negative r.v. with known pdf $f(x|\theta)$ but with a single unknown parameter $\theta$. Suppose that the mean $\mu$ can be used to uniquely determine the value of $\theta$, i.e. if given the value of $\mu$, then the value of $\theta$ can be calculated directly. Thus, an alternative way of writing th... |
I am a linguist trying to decide on the appropriate statistical test for some data, and I'm a bit at sea.
The data relates to how often participants in bilingual conversations use words from the other language (codeswitches, in the jargon). I want to compare the variance (number of codeswitches) between participants i... |
i'm using Kevin Murphy's HMM Toolbox.
But i have a problem in understanding the results.
My problem is to classify some sequences with Hidden Markov Model.
I'm using a (test) dataset build with random sequences of symbol '1' '3' '6'.
this one is my training dataset:
data = [ 1 1 1 3 6;
1 1 3 ... |
we're looking for any software/framework that is able to analyse the financial flux?
Some preliminaries. We've been asked by one of our customer to find or develop the software that would solve some their problems. The firm selling a lot of small staff (food elements for animals) in enormous quantity. The problem is to... |
I am quite new to Statistics, so please do not flame me for such a simple question.
I made a controlled experiment and successfully gathered the data. 41 persons participated. They made a questionnaire and a game. From both of them, they obtained a single, discrete score.
The situation is the following:
I split the 41 ... |
Just want to check that I am performing my cross validation procedures right. I'm using a non-linear svm. I do a five fold cross validation (5 splits of test/train on my original training data) and for each fold, run a grid search to find the optimal parameters for that train/test pair (e.g. best parameters where model... |
Alright, I'm having an insane amount of difficulty for what seems like a simple concept. I need to generate a bunch of basis functions for a curve that underlies some simulated Poisson distributed data and then run Newton's method on it to fit the log-likelihood (Poisson regression). I understand the math behind Newton... |
Seeking a textbook or other publication describing the Mantel-Haenszel test of a $2 \times 2 \times r$ table that provides at least one numeric example. Thanks.
|
The central limit theorem states that the mean of i.i.d. variables, as $N$ goes to infinity, becomes normally distributed.
This raises two questions:
Can we deduce from this the law of large numbers? If the law of large numbers says that the mean of a sample of a random variable's values equals the true mean $\mu$ as... |
In statistical inference, there are many fundamental statistical principles, such as likelihood principle and repeated sampling principle. I am wondering whether there are any other principles? And what's the meaning of these principles? What's the difference between these principles, especially between likelihood prin... |
For an assignment (M.Sc. Epidemiology), I need to calculate a C.I. on a standardized risk difference (RD). To be more precise, I have 2 dichotomous variables, age (younger/older) and gender (m/f), thus yielding 4 stratum-specific RD estimates as regards to a certain exposure and outcome.
Any hints on how to do this wo... |
In "To Explain or to Predict?", Pr. Galit Shmueli said that sometimes a less true model can predict better than a truer model. Why is it so? When will it happen? How does it happen? Is explanation a trade-off for prediction in models?
|
In general setting of gradient descent algorithm, we have $x_{n+1} = x_{n} - \eta * gradient_{x_n}$ where $x_n$ is the current point, $\eta$ is the step size and $gradient_{x_n}$ is the gradient evaluated at $x_n$.
I have seen in some algorithm, people uses normalized gradient instead of gradient. I wanted to know wh... |
In general, what is meant by saying that the fraction $x$ of the variance in an analysis like PCA is explained by the first principal component? Can someone explain this intuitively but also give a precise mathematical definition of what "variance explained" means in terms of principal component analysis (PCA)?
For sim... |
Will software eventually make statisticians obsolete? What is done that can't be programmed into a computer?
|
I've been working for almost a year on electricity load forecasting in collaboration with some climate scientists, using temperature data obtained from models. Instead of using directly temperature values, we use the 'anomaly' from the annual average (called 'climatology'). It seems, in climate sciences, that is good p... |
I am using the homals-package in R to optimally quantify my data that contains categorical (nominal and ordinal) as well as numerical variables. My goal is to quantify the categorical variables using optimal scaling. To achieve this, I use the rank constraint rank = 1, since this "reduces homogeneity analysis to princ... |
I'm looking for common standards (file formats) for how most statistics software packages import data.
The reason is that I'm going to make an export function for a simulation software package.
The data to be exported consists of time-series of (1 or more) values for all members of a population. The population size ca... |
Say the null hypothesis is that two samples emanate from two distributions with either equal medians or equal variances. And p values are the probability that a value or more extreme comes from the original distribution given the null hypothesis holds. Therefore, why do correlations with low p-values mean that they are... |
I have a function on the unit square that's expensive to evaluate,
and want to estimate where it reaches its minimum in at most $N$ evaluations, $N$ ~ 10 say.
Assuming a model of the form paraboloid + noise,
$ \qquad \text{f}( x; x_{min}, a, c, \sigma )
\approx a (x - x_{min})^2 + c + \mathcal{N}( 0, \sigma^2 ) $
what'... |
I am interested in using quantile regression for some of my models, but would like to have some clarifications on what can I achieve using this methodology. I understand I can obtain a more robust analysis of IV/DV relationship, especially when faced with outliers and heteroscedasticity, but in my case the focus is on ... |
From what I understand, the lognormal probability density function in base-10 is mathematically defined thus:
$$
p(x; \mu, \sigma) = \frac{log_{10}(e)}{x \sigma \sqrt{2 \pi}} e^{-\frac{(log_{10}(x) - \mu)^2}{2 \sigma^2}}
$$
As any PDF is bound to be, this function is normalised - that is, integrated over all $x$ (I i... |
Does anyone know of any method for deciding when a genetic algorithm is done? In MCMC (e.g, BUGS), several chains are started at different, random points. When they all look the same, it is done. Has this approach ever been tried with GA? Any other ideas?
|
I have a question. Here it is guys.
How do you use R from the command line?
|
I would like to generate conditional correlated random variables. I have a correlation matrix between normal variables, and these variables are modeled through SDEs.
What are the algorithms to generate such random values? One example I found is;
http://www.mathworks.com/help/toolbox/econ/interpolate.html
|
I read on this site that apparently the Kinect uses the random forests algorithm for machine learning in some way. Can anyone explain what it uses random forests for, and how their approach works?
|
I am a beginner to time-series analysis. I have the model below; y is sales of product and x is tweet-rate:
$y_t=ay_{t-1}+by_{t-2}+...+cy_{t-m}+dx_t+ex_{t-1}+...+fx_{t-n}$
What is this model called? I guess it's called an AR model but I am not
sure since the dependent variable y is on R.H.S as well.
How do I fix the ... |
Say you have a random variable $X$ (e.g., kilometers driven). Getting its variance is straightforward. But what if you want to say, $A$ percent of the variance in $X$ is due to $\text{Var}(X)$ for female drivers and $B$ percent is the rest, that is, $\text{Var}(X)$ for male drivers? $A + B$ should be 100 percent.
Is th... |
I have a ton of univariate samples ($x_i \in \mathbb{R}^+$). I'd like an automated method to check for outliers and identify the outliers, if any are present. A reasonable model for the distribution of the non-outliers is a mixture of Gaussians. The number of Gaussians in the mixture and their parameters are not kno... |
I've been reading about the star schema (or dimensional) database structure, which puts all measurements main in 'facts' table, and all context for those measurements in 'dimension' table linked to the facts table (I'm doing a horrible job explaining this), so that you can query any measurement by conditioning on the d... |
I am looking at following books:
Statistical Models (Cambridge Series in Statistical and Probabilistic
Mathematics) - A. C. Davison
Essentials of Statistical Inference (Cambridge Series in Statistical
and Probabilistic Mathematics) - G. A. Young
Asymptotic Statistics (Cambridge Series in Statistical and
Probabilistic ... |
I'm going to teach classes on Physics Laboratory on First year of Bachelor studies. In most of the excercises during data analysis students will have to fit a line to measurements they have taken.
I need formulas that fit data to the model:
$$
y_i = Ax_i + B + \epsilon_i
$$
Where $\epsilon_i$ is error for point... |
I've recently run into an interesting and rather odd problem with cross validating a multiclass SVM that I can't figure out. Basically, I have a timeseries to predict and have created a dataset of what I believe are relevant predictors (also timeseries). I've done some preprocessing (reduced the example size of the dat... |
I have some questions about the notations used in Section 9.2 Lack of Inherent Superiority of Any Classifier in Duda, Hart and Stork's Pattern Classification. First let me quote some relevant text from the book:
For simplicity consider a two-category problem, where the training set $D$ consists of patterns $x^i$ a... |
This looks like a similar question and didn't get many responses.
Omitting tests such as Cook's D, and just looking at residuals as a group, I am interested in how others use residuals when assessing goodness-of-fit. I use the raw residuals:
in a QQ-plot, for assessing normality
in a scatterplot of $y$ versus residual... |
In classification and regression tasks, we try to learn from a training data set a function mapping a independent variable $X$ to a dependent variable $Y$.
When evaluating the error rate of a learning algorithm in classification or regression
in theory, there are usually assumptions on the true relation
between indepe... |
Could an inappropriate link function contribute to non-uniform residuals in a GLM, or could that only be caused by an inappropriate error structure?
|
I don't know much about stats so I'm looking for a starting point here. Any resources or insights would be helpful.
I'm conducting an e-learning experiment, in which students watch videos and then complete a survey which measures cognitive load and user satisfaction, and afterwards they complete a short assessment to t... |
How would I use the output of a principal components analysis (PCA) in a generalized linear model (GLM), assuming the PCA is used for variable selection for the GLM?
Clarification: I want to use PCA to avoid using correlated variables in the GLM. However, PCA gives me output like .2*variable1+.5*variable3 etc. I'm use... |
Consider the following pmf for a discrete random variable $X$: $f(x) = x/15$ when $x = 1, 2, 3, 4, 5$, and $f(x)= 0$ for all other values of $x$. What is $f(3)$? (I.e., the PMF evaluated at 3)
|
We have some data represented as follows: on each row there are 10 observable effects, and 3 non-observable causes out of 8 that were guessed by scholars. Effects are real numbers, and causes are discrete categories.
We want to train a system that would accept observed effects, and guess three most likely causes.
So ho... |
Is there a good reference (book if exists) about mathematical statistics of dependent random variables? Something along the lines of Casella and Berger's textbook, but for dependent samples.
I'm not interested in a specific application, just theory, of course assuming independence sometimes seems to be good enough, bu... |
Lets say I have a linear regression with two numeric explanatory variables: A and B.
Consider the following scenarios:
A and B are both insignificant
A is significant, B is insignificant; or the other way around
A and B are both significant
Now, my question:
In which scenarios is it possible (or should we differentia... |
This question follows my previous one.
I will now provide my data in order to help you help me :)
As previously said, I have N=42 from a controlled experiment.
People made a questionnaire assessing their mood and then played a videogame. They obtained a score from the game.
According to the questionnaire score, they m... |
Which distribution fits the following data? Data are generated by the process:
$X_t, \, t=\{1,2,3,\ldots,n\}$ is equal 1 with probability $p$, and 0 with probability $(1-p)$ for each $t$.
What is the distribution of gaps between each occurrence of 1?
Example series: $0,0,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1$ gives gaps $2,0,1... |
I have a list of 6,500 or so medical treatments, of which I have classified 700 or so as involving a physician or not. I am interested in both the specific question of how to calculate whether 700 observations is sufficient, and the general question about how one does power calculations in text mining.
A typical treat... |
Possible Duplicate:
Incremental or Online or Single pass or Data Stream Clustering refers to the same thing?
Incremental clustering algorithms
Online clustering algorithms
Data stream clustering algorithms
Single pass clustering algorithms
Are the following expressions related ? does some of them include others ? ... |
I received the following message in SAS:
Measures of association between the observed and predicted values were not calculated
because the mean scored predicted probabilities are indistinguishable when they are
classified into intervals of length 0.008.
|
Suppose we seek to approximate an arbitrary distribution $p_1(x)$ by a normal
$p_2(x) \sim \mathcal N(\mu, \Sigma)$. How can I show that the values that lead to the smallest Kullback–Leibler
divergence are:
$$
\mu_1 = \mathbb E_1[X]
$$
and
$$
\Sigma_1 = \mathbb E_1[(X − \mu)(X − \mu)^T],
$$
where the notation $\mat... |
I would like to know, or have references on, analysis process most of statistical data analysts go through for each data analysis project.
If I make a "list", to complete data analysis project, an analyst has to:
first collect requirements for the project,
plan/design his data analysis based on those requirements ... |
Can you suggest any quick and simple clustering analyses, for univariate real-valued data? In other words, I have $n$ real numbers, $x_1,\dots,x_n$ where $x_i \in \mathbb{R}^+$, and I want to cluster them. I don't know a priori the best number of clusters, so that's something the method would need to discover as well... |
Suppose $Y$ is an ordinal response variable with 4 levels (i.e. $Y$ can take on the values $1,2,3$ or $4$). We want to model $Y$ with $X_1, X_2$ using a proportional odds model. If $Y$ takes on the values of $1,2,3$ and $4$ an equal number of times (e.g. $Y = 1$ 4 times, $Y = 2$ 4 times, $Y = 3$ 4 times, and $Y= 4$ 4 ... |
$X_1, X_2, \ldots, X_n$ is a random sample from $\mathrm{Bernoulli}(\theta)$, $\epsilon_1, \epsilon_2, \ldots, \epsilon_n$ are independent $\mathcal N(0, \sigma^2)$, independent of $X_i$.
Define $Y_i = \theta X_i + \epsilon_i$, for $i = 1, 2, \ldots,n$. Define estimating function
$$
\psi[\theta;(X,Y)] = \sum_{i =1}^... |
I have already run a whole bunch of OLS and found the following
Regress P= B1*L+e_1, found b1<0
Regress X= B2*L+e_2, found b2>0
Regress X= B3*P+e_3, found b3<0
I want to build a case with complex causal structure, in which there are two channels that L positively affects X.
1.Reducing P increases X
2.L positively affec... |
I have a problem that I would like to investigate regarding time-series data, but as I'm inexperienced in the field of statistics, I am unsure of the best terminology to describe my problem (so I can try to investigate further myself). Any suggestions on approaches are of course welcome!
The problem can be summarised a... |
I'll try to make an example to make it easier to understand the question.
model{
constant1=(number)
constan2=(number)
for(j in 1:k){ #k defined in data
a[j] ~ dgamma(c[j],d[j])
b[j]~ dgamma(e[j], f[j])
c[j] ~ dgamma(constan1,constant2)
d[j] ~ dgamma(constan1,constant2)
e[j] ~... |
For my research I conducted a creativity test and measured the quantity of ideas subjects had. Some people are extreme outliers as they have a lot of ideas or only 1 or 2 ideas. Intuitively I wanted to 5% trim my data to obtain a more robust estimation for my regression analyses.
Is this justifyable?
Is there a paper... |
I am currently playing around with the MNIST dataset (http://yann.lecun.com/exdb/mnist/) in R. The training set size is 60000x748 and it seems to drain all my memory even when constructing simple models like logistic regression.
My question is: how do you guys usually deal with big datasets in R?
And tangent: is it fea... |
The Pearson correlation coefficient of x and y is the same, whether you compute pearson(x, y) or pearson(y, x). This suggests that doing a linear regression of y given x or x given y should be the same, but I don't think that's the case.
Can someone shed light on when the relationship is not symmetric, and how that re... |
Is there a general principle on whether one should compute pearson correlation for two random variables X and Y before taking their log transform or after? Is there a procedure to test which is more appropriate? They yield similar but different values, since log transform is non-linear. Does it depend on whether X or Y... |
Given the variables $X$ and $Y$, which are correlated, $X\ge0$, $Y\ge0$ and each follow a gamma distribution with different shape parameters, i.e.,$X\sim\Gamma(a_1,\alpha)$ and $Y\sim\Gamma(a_2,\alpha)$. I understood that the Joint PDF $f_{X,Y}(x,y)$ can be obtained by making use of the McKay's bivariate Gamma distribu... |
Method: I presented 15 participants with audiovisual clips. There were six different clips I presented, and for each clip there was emotional incongruence between visual and auditory information. The combinations were:
visual negative with auditory positive
visual negative with auditory neutral
visual positive with... |
I have my set of documents and have extracted the unique words from them, including a count of the number of times each word appears in the document. But it would seem from the documentation on the Python library I'm using, that word count within documents is immaterial, and that co-occurrence is the main thing.
Am I ... |
I have a question.
Is it better to use deviance or - 2 Log L for the likelihood ratio test? Or are they basically the same thing?
SAS returns the "deviance" sometimes. But I just use the -2 Log L value for the likelihood ratio test (e.g. subtract the -2 Log L for two models to compare them). Is is that okay?
|
I am not a statistics expert but was interested in the validity of the reasoning below.
Somebody argued that many people had the letter 'J' in their initials. Can someone comment on the validity of the following approach and how it could be improved, notably what probability distribution would a list of firs tnames sor... |
I have a collection of data which is inherently the same (would expect it to follow the same distribution) where some of it is rated with one scale of ordinal ratings and the rest of the data is rated with another scale of ordinal ratings. One scale has a larger number of possible ratings than the other. So, if I wer... |
OP EDIT: There where no problem with this. The problem was with the method I was using for obtaining the PACF. Apparently it doesn't work quite well in this case (I was using the scikits/tsa python package to obtain the PACF via the YW equations). Testing the coefficients in R worked like a charm.
I'm trying to simulat... |
My company would like to use control charts (Shewhart, EWMA, or both) to detect changes to the distributions of our key business metrics. For instance, we could sample user signups each day and determine whether a change to our sales webpage has caused the mean to shift. We have two major goals:
To find out quickly wh... |
I am trying implement importance sampling of this integral
$$
\mathfrak{I} = \int\limits_{-\infty }^{\infty }{\sqrt{\left| \frac{\theta }{1-\theta } \right|}}f(\theta )\text{d}\theta
$$
where $f(\theta )\propto {{(1+{{\theta }^{2}}/5)}^{-3}}$ is a t-distribution with df=5.
I already sampled from the above distributio... |
I'm attempting to use the rpart R package, and I'm having difficulty figuring out how to determine the quality of a given tree output. For most linear models I would just examine p-values and $r^2$ values to determine whether the model performs satisfactorally. Is there a similar number for decision trees, or is the on... |
I have an error that says
The estimation algorithm did not converge after 50 iterations and the forecast was not done.
What can I do to prevent this error? Like how can I check the data before forecasting?
|
We have a collection of 40 boxes, each is one of four sizes (evenly distributed 10 of each): sizeA, sizeB, sizeC, sizeD.
Our person is presented with 1 box of each size, they must select one box from the different sizes, then the remaining three will be taken away and four new boxes of each size is presented.
I know... |
I have a 2000 SKUs, I want to identify the ARIMA process for them, what is the best way to do that?, which tools should I use?
thank you very much.
Roji
|
I need to figure out the covariance matrix of a uniform spherical distribution. But there I can't even find a closed form of the distribution. This link says it is $\frac{1}{n}\mathbf{I}$, where $\mathbf{I}$ is the $n \times n$ identity matrix. But can someone please help me derive it? Or even point to literature o... |
I am trying to work out how to propagate standard deviations in a biological experiment, but I have some difficulties.
I have the following (semi)fictitious data originating from an image analysis resulting in optical density (OD) measurements:
ds <- data.frame(
Sample = c(rep(seq(1,6),2)),
Control.OD = c(7000... |
I'm curious to know what others tend to see as a suitable naming convention for model features or variables, particularly as they relate to their use and reference in software applications.
For instance, given two inputs: age and income, we could construct features around various transformations and discretizations of ... |
I have roughly 15,000 non-independent features for each of which I have a sample size of 100. For each of these feature-sample data points, I have a value of TRUE or FALSE corresponding to some status of the feature, such that for each feature, I have 100 TRUE or FALSE values.
How can I test the "trueness" of each feat... |
I am reflecting on the discussion around this question and particularly Frank Harrell's comment that the estimate for variance in a reduced model (ie one from which a number of explanatory variables have been tested and rejected) should use Ye's Generalized Degrees of Freedom. Professor Harrell points out this will be... |
Is it possible to have two different methods of sampling from a bivariate normal distribution with a non-identity correlation matrix in such a way that one method would "consistently" result in a sample whose sample correlation matrix is closer to the correlation matrix of the distribution? I do not have a precise defi... |
Self-organizing maps are claimed to be an approach for dimensionality reduction. However, I am kind of confused about this claim.
Consider the following example, I have a data set with 200 data points and each data point is represented by a feature vector with 1000 dimensions. Assume I would like to train a map with a ... |
I understand the EM algorithm, I understand for example how we get $Q(\theta, \theta^t)$, but I have trouble translating a real-world problem into the EM framework.
For example, I'm given this problem where each document $x$ is classified into a class $y$, where there are $M$ documents and $K$ classes. $V$ is the vocab... |
I have 5 samples (from the same population). I want to calculate the Goodman-Kruskal gamma ($\gamma$) for the population, based on the gamma of the 5 samples ($G_i$).
Each data has 2 ordinal variables (X and Y), but the X's and Y's of different samples are not comparable, so I cannot put all the samples in the same b... |
Could someone provide overhead of the following model for training (With respect to input size or if there are any relevant parameters). Overhead I mean somewhat like asymptotic time complexity form.
Multiple linear regression models (Least Sqaures)
Decision Tree (C 4.5 OR ID3)
K nearest neighbor
Thank you.
|
$X_1, X_2, X_3, \ldots{}, X_n$, i.i.d., follow $\mathcal{N}(0, \theta^2)$, $\theta > 0$.
What are the UMVUEs (Uniform Minimum Variance Unbiased Estimators) of $\theta$ as well as $\Phi(\tfrac{1}{\theta})$, where $\Phi$ is the cumulative distribution function of $\mathcal{N}(0,1)$?
|
I am working with a panel data and want to perform a regression analysis (OLS, fixed effects model or random effects model). The panel data is unbalanced with $T$ varying from 7 to 13, and $N=11$. I am confused about having a small number of observations (around 100).
What is the minimum time observations and cross-se... |
Note: I am posting a question from a former student of mine unable to post on his own for technical reasons.
Given an iid sample $x_1,\ldots,x_n$ from a Weibull distribution with pdf
$$
f_k(x) = k x^{k-1} e^{-x^k} \quad x>0
$$
is there a useful missing variable representation
$$f_k(x) = \int_\mathcal{Z} g_k(x,z)\,\tex... |
Suppose we fit a proportional odds model to some data with $Y$ the response variable being ordinal. If we get 0 estimated for all the coefficients (except the intercepts), what does that mean? How would we interpret the model?
|
On the website for CRF++ http://crfpp.sourceforge.net/
they mention that marginal probabilities can be output for each possible label.
My question is, in CRF theory, what's the formula for this marginal probability? I think it's:
$$p_{_\theta}(Y_{_j} = y | X ) = \frac{\alpha_{_j}(y|X)\beta_{_j}(y|X)}{Z_{_\theta}(X)}$$
... |
In an experiment with continuous-value random variable, e.g. measuring length of cucumbers. I would like to compare the probability of getting a particular length range in two different conditions. e.g. $P1=P(0.1<L<0.2, {\rm fertilizer\ A})$, $P2=P(0.1<L<0.2, {\rm fertilizer\ B})$.
So I create 2 histograms for the leng... |
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