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Thanks to the posts and advice here, I've gotten off to a good start with cluster analysis. On a good day I can even get R to compute one without breaking down in tears! But I'm wondering if people have tips and techniques for interpreting what the clusters they get actually mean. By this I mean that when you sit down ... |
It strikes me that the available corrections for multiple comparisons in the context of a repeated measures ANOVA are excessively conservative. Is this actually the case? If so, what are some citations I can use to support this point and learn more?
|
We perform independent Bernoulli trials with unknown probability of success P.
We perform them by series, each of 1000 trials, and stop when at least one success happens.
So the number of trials N is a multiple of 1000, and the number of successes K is 1 through 1000.
How can one estimate P?
The maximum likelihood esti... |
I'm currently a web developer with a backgound mainly in server side technologies however I've always had an interest in probability so recently I've been exploring building a dummy betting platform where people wager against insurance policies and essentially I'm aiming to use data from Google's index to set the odds ... |
I've always thought of logistic regression as simply a special case of binomial regression where the link function is the logistic function (instead of, say, a probit function).
From reading the answers on another question I had, though, it sounds like I might be confused, and there is a difference between logistic reg... |
Context
When I teach students about the correlation coefficient, I like to give students a sense of how correlations map on to common associations that might be encountered in daily life and across various topics and disciplines.
Some years back I read a psychology journal article (it might have been American Psycholo... |
Context:
Over the while I've acquired a set of heuristics on how to effectively plot the association between two numeric variables. I imagine most people who work with data would have a similar set of rules.
Examples of such rules might be:
If one of the variables is positively skewed, consider plotting that axis on a... |
Say $X_0, X_1, ...$ is a Markov chain with the state space is $S=\{0,1,2,3,...,N-1\}$ and the transition probability $P(X_{n+1}=a+1 \mod N | X_n=a)$ = $P(X_{n+1}=a \mod N | X_n=a)$ = $P(X_{n+1}=a-1 \mod N | X_n=a)$ = $1/3$. (Ie, the markov chain is a random walk on $S$ with 1/3 probability of staying put, 1/3 probab... |
I’m doing a registry based study with almost 200 000 observations and I want to perform a competing risk analysis. My problem is that the crr() in the cmprsk package is exponentially increasing with increasing number of observations. I therefore wrote a simulation for trying different approaches; check how factors, dat... |
I always use lm() in R to perform linear regression of $y$ on $x$. That function returns a coefficient $\beta$ such that $$y = \beta x.$$
Today I learned about total least squares and that princomp() function (principal component analysis, PCA) can be used to perform it. It should be good for me (more accurate). I have... |
Lets say I know what is the overall budget for some units and I want to predict share of budget each unit will get. I have historical data and could do regression analysis. Is it better to predict shares directly with logistic regression or to try to predict amount and then get calculate its share in overall prediction... |
What common methods are used for choosing the smoothing parameter for LOESS? (In R, but also in general).
|
I've got some rather messy data from a natural experiment. A number of subjects were measured (the measurements were hopefully-Poisson distributed counts and associated offsets), placed on a treatment at time T, and then measured again sometime afterward. However, there is some reason to suspect that the dependent v... |
I want to prove $[X|y] \rightarrow \delta_0(X)$, as $y$ goes to $\infty$, i.e. the distribution of $[X|y]$ converges to degenerate distribution at zero for large enough $y$.
I know the density $f(x|y)$ upto a multiplicative constant and also the fact that
$$
\frac{f(x|y)}{f(0|y)} \rightarrow 0 \quad \text{as } y \ri... |
There's a lot of discussion going on on this forum about the proper way to specify various hierarchical models using lmer.
I thought it would be great to have all the information in one place.
A couple of questions to start:
How to specify multiple levels, where one group is nested within the other: is it (1|group1:gr... |
I have a weighted sample, for which I wish to calculate quantiles.1
Ideally, where the weights are equal (whether = 1 or otherwise), the results would be consistent with those of scipy.stats.scoreatpercentile() and R's quantile(...,type=7).
One simple approach would be to "multiply out" the sample using the weights giv... |
Let, $S_{n*n}$ represent a similarity matrix, among $n$ observation, my case n = 215. and $Y=\{y_1, y_2, ...,y_n\}$ contains a response value for each $x_n$ observation. For each observation we have $t$ features,my case t = 50.
Since, the number of observation is not enough vs features to do a nice multiply regression,... |
What would be the distribution of $y$, when:
$y = x^2$ and $x\sim\mathcal{N}(\mu, \sigma^2)$.
$y = x^2$ and $x\sim$ Log-$\mathcal{N}$.
|
I would like to use a binary logistic regression model in the context of streaming data (multidimensional time series) in order to predict the value of the dependent variable of the data (i.e. row) that just arrived, given the past observations. As far as I know, logistic regression is traditionally used for postmortem... |
I have a huge dataset of reaction times from a psycholinguistic experiment, and in separate tables, I have information that I'd like to add in about each word's frequency and things like that.
The main dataset looks something like this:
maindataset <-structure(list(item = c(101, 103, 102, 104, 104, 102, 103,
102, 101,... |
I have $N$ time series each of which can be modeled as $$y_{kt}=Ax_{kt}+b+\varepsilon_{kt}\quad(1\le k\le N,1\le t\le T),$$ where $x_{kt}\sim\text{Pois}(\lambda\Delta t)$ and $\varepsilon_{kt}\sim N(0,\sigma^2)$. Parameters $A$, $b$ and $\sigma^2$ are unknown and I want to extract the uncontamined version of all $y_{kt... |
Suppose I fit a linear regression to some data (say, weight vs. height), and all the standard linear regression assumptions are satisfied (in particular, the data is homoscedastic). For example, here's a random figure pulled from amstat.org that looks like it satisfies what I'm thinking of:
Now I'm doing some explorat... |
Hopefully this is not too subjective...
I'm looking for some direction in efforts to detect the different "parts" of a song, regardless of musical style. I have no idea where to look, but trusting in the power of the other StackOverflow sites, I figured someone here could help point the direction.
In most basic terms,... |
I have some data points, each containing 5 vectors of agglomerated discrete results, each vector's results generated by a different distribution, (the specific kind of which I am not sure, my best guess is Weibull, with shape parameter varying somewhere around exponential to power law (1 to 0, roughly).)
I am looking t... |
I have to simulate (in javascript) the likelihood that members of a certain population would have a disease, given a contextual value. All information I have comes from papers that show odds ratios with $95\%$ confidence interval.
I found Box-Muller method and other approaches to normal distribution, but I cannot reali... |
There's already been an excellent discussion on how support vector machines handle classification, but I'm very confused about how support vector machines generalize to regression.
Anyone care to enlighten me?
|
I would like to estimate a multivariate model with the following properties:
Fixed effects:
Intercept
Main effect of condition
Main effect of Task order
Task order X Condition interaction
Random effects:
Main effect of TypeOfRating
TypeOfRating X Condition interaction
TypeOfRating X Task order interaction
Type... |
What is the difference between a repeated measures ANOVA over some factor (say experimental condition) and a MANOVA?
In particular one website I stumbled across suggested that MANOVA does not make the same assumption of sphericity that repeated measures ANOVA does, is that true?
If so, why would one not just alway... |
I'm looking at some data conversion rates for an ad over time.
view clicks
Day 1 100 10
Day 2 150 13
Day 3 90 9
Day 4 130 20
Day 5 150 21
Given that there is quite a bit of variation in the conversion rate of the ad from day to day, I wa... |
Motivated by the problem of covariance estimation.
Let $\Sigma$ be a positive-definite matrix whose diagonal entries are identically 1. (i.e. $\Sigma$ is a correlation matrix.)
If $L$ is an lower-triangular matrix such that $L^T L = \Sigma$, can the entries of $L$ be bounded? (i.e. do there exist real numbers $l, u$ s... |
The problem I am trying to solve it predicting sales for an item for the next $n$ weeks.
Obviously, seasonality is a major factor for such predictions. If we use a time series based model, then we generally produce a raw forecast and multiply the raw forecast by the seasonality indices.
If we use CART to produce such f... |
I am interested in the unhealthy people across 10 different populations. Here is the raw data:
Popn Unhealthy Size Percentage
---- ---------- ------- ------------
A 170 1000 17.0%
B 2 2 100.0%
C 12 25 52.0%
D 7 20 35.... |
Assume we have a noisy system where data is available via sample() and in order to filter out the noise someone has implemented the following voting algorithm:
sample_a = sample();
sample_b = sample();
if (sample_a != sample_b) {
sample_c = sample();
if (sample_a == sample_c)
return sample_a;
else i... |
I actually know that the answer is $N(k-1)$ (where $k$ is the minimum between number of rows and number of columns).
However, I can not seem to find a simple proof for why the statistic is bounded by this. Any suggestions (or references?)
|
I'm using R to calculate the KPSS to check the stationarity.
The library that I'm using is tseries and the function is kpss.test
I have done a simple test using cars (a default matrix on R). The code is:
> k <- kpss.test(cars$dist, null="Trend")
Warning message:
In kpss.test(cars$dist, null = "Trend") :
p-value grea... |
I have a dataset with observations form a population that have been described graphically as an annual trend. For example – male infection rate per year, female infection rate per year.
The infections are aggregated count data and there are population based numerator data available.
Which statistical test would I use t... |
I've been working on solutions to my first unanswered questions and had been proposed to rather model the proportion of total count of deaths that are unnatural death counts. The reason why I want to do this, is because I want to determine the count of natural and unnatural deaths for a certain month of a year of a dis... |
I have a dependent variable: rtln (log transformed reaction time) and 3 predictors:
choicenum (ranging from 1 to 6), ifrelevant (0 and 1), and condition (0 and 1), and I have a variable with subject IDs.
I would like to estimate a model where choicenum is nested within subjects.
I use the following notation:
lmer(rtln... |
I have data from different sources that is currently in multiple data frames. They generally look something like:
TimeStamp (MS Detail Converted with strptime), Field1, Field2, Field3
In all cases the Time Stamps are irregular, and the fields are either character data or int data.
There are three types of correlation... |
If I have a $k$ successes in $n$ bernoulli trials, does the parameter $p$ of the binomial distribution follow a well-known distribution?
There are some methods to calculate confidence intervals for $p$, I'm interested in the distribution for the exact method.
|
I want to sample from a distribution with density
$$
f(\mathbf x) = \int f(c) \prod_{i=1}^n f(x_i|c) dc
$$
where $\mathbf x=(x_1,x_2,...,x_n)$. In my particular setup, is easy to sample according to the densities $f(c)$ and $f(x_i|c)$, but it is not obvious how to sample from the marginal given above.
Would the follo... |
First - very new to Statistics; about half through a basic biostats book and an R book.
I have a set of data where I"m trying to see if there is a correlation between a medication and weight gain. The dataset:
~2200 patients
A list of their primary diagnoses, weight, date's of visit, and whether they were on medicat... |
In my research there is a pretest, and a treatment followed by a posttest.
The pre and the posttests are similar but not exactly the same. A few questions were changed between the pre and posttests to avoid sensitizing the students to the questions in the pre-test, which might affect the internal validity of the study... |
My goal is to quantify dosage impact on cure probability for different patients. Let's suppose I have N patients with their charateristics such as age, gender, weight.... Also let's assume there is a known range for dosage, say from 0 to 1.
Here is what I'm currently doing:
Randomly split all patients into 3 groups
G... |
I have been asked to "construct a (normal) QQ plot" for a set of numbers. However it is not a set of pairs or a pair of sets, just a single set of numbers.
If we go ahead and assume the second probability distribution is the normal distribution, how would I go about satisfying this request?
|
Just wondering if anyone is familiar with clustering nominal inputs. I've been looking at SOM as a solution but apparently it only works with numerical features. Are there any extensions for categorical features? Specifically I was wondering about 'Days of the Week' as a possible features. Of course it is possible to c... |
Am I correct to understand that the order in which variables are specified in a multifactorial ANOVA makes a difference but that the order does not matter when doing a multiple linear regression?
So assuming an outcome such as measured blood loss y and two categorical variables
adenoidectomy method a,
tonsillectomy me... |
Lately, I have been interested in phenomenons related to omission of variables. For example, it can be shown that the expected value of the sample variance under the inclusion of one variable $x_1$ but omission of one variable $x_2$ is $\mathbb{E}(s^2|x_1,x_2)= \sigma^2 + \frac{\sigma^2}{n-1} RSS_{x_1, \beta_2 x_2}$ wh... |
I have a β-distribution(which looks like a normal distribution), for which I want to calculate the values of α and β using maximum likelihood estimation method. I am new to statistics, so would like to know if there is any tool available which can be used to compute these parameters.
PS: Similar question has been answe... |
Given a variable $X \sim N(\mu, \Sigma)$
What is the density of $X$ given $HX = d$,
$H$ and $d$ both constant
I.e. we observe $X$ with rank-deficient linear operator $H$ and obtain some value $d$. Given this knowledge how do we update our knowledge/distribution of $X$?
This is just one of the steps in the Kalman filte... |
When I'm dealing with time-series data I'm generally thinking about visualizing that data with a bar graph (small n) or a line plot (large n). For example, I might create something like the below:
However, is there any instance in which a dot plot can be used to visualize time-series data? ( a clevland dot-plot is wha... |
Consider $n\cdot m$ independent draws from cdf $F(x)$, which is defined over 0-1, where $n$ and $m$ are integers. Arbitrarily group the draws into $n$ groups with m values in each group. Look at the minimum value in each group. Take the group that has the greatest of these minima. Now, what is the distribution that... |
I am looking for references about the theory of linear regression or regression in general. More specifically, I am interested in knowing under what circumstances an estimated regressor is going to give accurate solutions with certain probabiltiy. For now, I am looking for the basic classical results, nothing too fancy... |
The GRS statistic is the Gibbons et al. (1989) statistic that tests whether the estimated intercepts from a multiple regression model are jointly zero.
The typical scenario involves a multivariate linear panel regression where you are explaining the returns to securities in terms of its exposures to factor return seri... |
The distribition of the rank-sum statistic U is assumed to be normal for large number of samples being considered. What is the exact distribution? I want to compare and sometimes fuse results from various tests wherein some tests might not have large number of samples. I want to have a the exact distributions in cases ... |
We know that due to LD, we can get significant p-values for markers near a causal marker (or a marker closes to the causal region) in GWAS studies. I've seen attempts looking at LD to do multiple testing correction, by counting the effective number of tests, but as far as I know, they are simply trying to fix the corre... |
I have run a simple linear regression of the natural log of 2 variables to determine if they correlate. My output is this:
R^2 = 0.0893
slope = 0.851
p < 0.001
I am confused. Looking at the $R^2$ value, I would say that the two variables are not correlated, since it is so close to $0$. However, the slope of the regr... |
If I have two variables following two different distributions and having different standard deviations... How do I need to transform two variables so that when I sum the two result is not "driven" by more volatile one.
For example... Variable A is less volatile than variable B (ranges from 0 to 3000) and variable B goe... |
Consider the following experiment: a group of people is given a list of cities, and asked to mark the corresponding locations on an (otherwise unlabeled) map of the world. For each city, you will get a scattering of points roughly centered at the respective city. Some cities, say Istanbul, will exhibit less scattering ... |
Running a crude model using Bayesian inference, I get some results > 1 (ie, more than 100% "certain") for some combinations of "evidence". For instance, for one bit of evidence the conditional probability of the null hypothesis is 0.85 while the marginal probability is 0.77. If the prior probability is 0.9, the compu... |
Please excuse me if my question is dumb but I am not a Statistics student.
I have a project where I was exploring options for time series analysis where I found some papers on cointegration.
I have 4 variables. One of them response variable. I wanted to to the forecasting using the cointegration technique. Pl... |
So as I understand it SOM is primarily a visualization tool and clustering is a logical next step after you construct a SOM from data. Typically, the clustering is subjective in that after looking at your SOM you can 'see' N clusters and then from there you would go on to cluster (k means, hierarchical etc.) the SOM no... |
I have a text corpus, from which I have computed the unigram probabilities of every word.
Now, let $p_{i}$ & $p_{j}$ be the unigram probabilities of $i$ and $j$ respectively, what will be the probability with which a pair of words $i$ and $j$ will co-occur(within a maximum gap of 1 word) when independence between $i$ a... |
I'm a novice to data mining and started to read about it. What's the exact difference between experimental data and observation data? Both are obviously data; and many say observation data can lead to errors. But I guess it's not possible to do an experiment for all data sets. I'm really confused, explain me what is ex... |
does it make sense to assume $u\sim N(0,\sigma^2)$ when I know from a histogram that $y$ is highly skewed. Because from the assumption $u\sim N(0,\sigma^2)$ it follows that $y\sim N(x\beta,\sigma^2)$ and I'm absoluteley not sure if the assumption $u\sim N(0,\sigma^2)$ makes sense in a case where I know that the distrib... |
Suppose I am building some predictive models and then creating a report detailing how "good" those models were in various ways. Is there a generic (maybe even non-technical) term for the various measures of correctness (e.g. precision, recall, etc.)? A layman might use "accuracy," but accuracy actually has a very spe... |
I am trying to understand how to use Bayes' theorem to calculate a posterior but am getting stuck with the computational approach, e.g., in the following case it is not clear to me how to take the product of the prior and likelihood and then calculate the posterior:
For this example, I am interested in calculating the ... |
I have a series of functions, each one supposedly representing the density of a random variable across agents. Each function also has a domain, which describes what values of the random variable are valid.
Now, if I remember my stats classes correctly, if I take the integral of one of the functions across the values de... |
I was skimming through some lecture notes by Cosma Shalizi (in particular, section 2.1.1 of the second lecture), and was reminded that you can get very low $R^2$ even when you have a completely linear model.
To paraphrase Shalizi's example: suppose you have a model $Y = aX + \epsilon$, where $a$ is known. Then $\newcom... |
I need to calculate effect size for a mixed ANOVA design. I need it because I'm using GPower3 to calculate a rough sample size for a full study. I have pilot data. Based on this page:
http://www.xlstat.com/en/features/statistical-power-analysis-of-variance-anova.htm
and the GPower3 software, it looks like there are ... |
Are there any packages that supports weighted average semi-parametric regressions in R? An example of such a regression is in the links below.
I see that there is package GAM in R for Generalized Additive Models. However, it is not clear to me whether this procedure is the same as weighted average semi-parametric regre... |
After doing some reading on stochastic processes for work I've found that a proof that the specific process exists is often one of the first things presented.
Could someone please explain, in layman's terms, the purpose/necessity of this proof?
|
The basic problem I have is very similar to a classic Bayesian estimation problem: there is a real valued parameters $p\in[0,1]$, that I would like to estimate via observations $o_i$.
It is also the case that
$$
p=\lim_{N\to\infty}{1\over N}\sum_{i=1}^N o_i,
$$
so this problem is very closely analogous to estimating ... |
I'm reading a paper by Stephane Adjémian on DSGE modeling with a zero lower bound for the nominal interest rate, and he's using what he describes as the simulated method of moments / extended path. Has anyone worked with these techniques? What would you say is the next step toward gaining familiarity with them for some... |
I'm trying to finish a proof for a review exercise and I'm asked to show that
$E\left[(y-E(y|x))(E(y|x)-f(x))\right]=0$
where $y$ is the dependent variable and $f(x)$ is a linear predictor of $y$.
I'm almost finished, but I just want to check whether or not
$E\left[ E \left[ y E(y|x)\,|\,x \right] \right]=E\left[ E(y|... |
Is it OK to use the Kolmogorov-Smirnov goodness-of-fit test to compare two empirical distributions to determine whether they appear to have come from the same underlying distribution, rather than to compare one empirical distribution to a pre-specified reference distribution?
Let me try asking this another way. I coll... |
I have a hypothetical set of diet composition, showing how much of each fruit does a particular group of people eat something like:
How can I visualize in one page, all the compositions for groups A to G and more importantly, their change over the past year?
I know having more than 4 colors in design is a no-no, but... |
Does anyone know how to compute the prediction interval for ridge regression? and what's its relation with prediction interval of OLS regression?
|
Assume that I'm going to estimate a linear regression where I assume $u\sim N(0,\sigma^2)$. What is the benefit of OLS against ML estimation? I know that we need to know a distribution of $u$ when we use ML Methods, but since I assume $u\sim N(0,\sigma^2)$ whether I use ML or OLS this point seems to be irrelevant. Thus... |
I am using SAS to estimate some logistic models. Usually, I work with either MDs or social scientists, and odds ratios are the preferred metric. But I am now working with a client in economics/law and she wants the marginal effects and their standard errors, and she wants them at the means of the other variables.
This ... |
I'm currently trying to predict the probability for low probability events (~1%).
I have large DB with ~200,000 vectors (~2000 plus examples) with ~200 features.
I'm trying to find the the best features for my problem. What are the recommended method? (preferred in Python or R, but not necessarily)
|
I am interested in testing a simple mediation model with one IV, one DV, and one mediator. The indirect effect is significant as tested by the Preacher and Hayes SPSS macro, which suggests the mediator does serve to statistically mediate the relationship.
When reading about mediation I have read things such as "Note t... |
Say I have a 1-dimensional continuous random variable $X$, with PDF $f(X)$, CDF $F(X)$ and inverse CDF $F^{-1}$. What is the best way to discretize $X$?
To keep things clear, let $Y$ denote the discretized version of $X$, and let $g(Y)$, $G(Y)$ and $G^{-1}$ refer to the PMF, CDF and inverse CDF of $Y$.
Ideally, I wo... |
A Skellam Distribution describes the difference between two variables that have Poisson distributions. Is there a similar distribution that describes the difference between variables that follow negative binomial distributions?
My data is produced by a Poisson process, but includes a fair amount of noise, leading to o... |
I have a series of continuous probability distributions and the intervals for each distribution of possible values. Now I want to use the distributions to distribute values of a random variable among agents. I have thought of one way to do this, and I'm curious if this is an acceptable method. This is how I would do... |
In my application I'm receiving a continuous stream of 50 changing numbers, mostly these samples are contained with a nice Gaussian distribution, but now and then there are two+ distributions within the samples. The samples are always positive and within the range of 0 to 1. If there is more than one distribution prese... |
Suppose I have a questionnaire and I ask respondents how often they eat at McDonalds:
Never
Less than once a month
At least once a month but less than once a week
1-3 times a week
More than 3 times a week
I then correlate these answers with whether the respondents are wearing brown shoes.
Brown 65 -- not brown 38
Br... |
I will give my examples with R calls. First a simple example of a linear regression with a dependent variable 'lifespan', and two continuous explanatory variables.
data.frame(height=runif(4000,160,200))->human.life
human.life$weight=runif(4000,50,120)
human.life$lifespan=sample(45:90,4000,replace=TRUE)
summary(lm(lifes... |
I'm trying to extend this graph via the provided trendline formula. I'm inserting the formula into the next row and trying to assign X to be the date value, but it doesn't appear to be working. Do I need to apply a function to the date value in order for it to work? Basically I'm trying to predict what June 17th's down... |
(cross-posted from the R-sig ME list - maybe this is too basic for it)
Hello
I would like to fit piecewise linear growth curves to a number of
subjects (each with a number of observations at different abscissa),
where all the slopes for a common interval (e.g, 2 <= x < 3)
presumable arise from the same normal distribut... |
I am comparing the error between wind turbine production and predictions from 24 hours ahead. The graphs below are using the normal distribution.
But can I do better?
|
Consider the problem of randomly generating a $p \times p$ covariance matrix $\Sigma$ with the diagonal entries constrained to be 1, and the off-diagonal entries $\Sigma_{ij}=\Sigma_{ji} \sim Unif[-a,a]$. What is the maximum value of $a$, as a function of $p$, such that $\Sigma$ is positive definite with probability 1... |
I'm not that familiar with this literature, so please forgive me if this is an obvious question.
Since AIC and BIC depend on maximizing the likelihood, it seems that they can only be used to make relative comparisons between a set of models attempting to fit a given data-set. According to my understanding, it wouldn't... |
I would like to run a simulation where the sum of 20 random variables are generated 1000 times and plotted in a histogram.
I generate the random numbers using runif(20,0,1) then sum these random numbers using the sum function, but I was wondering if there is an easier method to do this 1000 then to write a for loop.
|
How do I define the distribution of a random variable $Y$ such that a draw from $Y$ has correlation $\rho$ with $x_1$, where $x_1$ is a single draw from a distribution with cumulative distribution function $F_{X}(x)$?
|
We teach supplementary lessons in nearly two dozen local schools, and have two data sets of approximately four hundred records each from pre-post tests given at these schools. Each record contains pre and post values (correct, incorrect) for questions on 12 topics as well as whether or not there was an intervention (le... |
Starting from a given sample, is it possible to estimate (roughly) automatically what kind of law the variable inducing this sample seems to follow?
|
I'm building a series of hierarchical models using R and JAGS, linked using the R2jags library. The runs are fairly long -- from several hours to several days. I've had the sad experience of running some chains that did not converge. In that case, is there a way to extend the chain, rather than starting over?
|
Andrew More defines information gain as:
$IG(Y|X) = H(Y) - H(Y|X)$
where $H(Y|X)$ is the conditional entropy. However, Wikipedia calls the above quantity mutual information.
Wikipedia on the other hand defines information gain as the Kullback–Leibler divergence (aka information divergence or relative entropy) between t... |
Suppose task performance $y$ increases with trial number $x$ ($x = 1, 2, …, 10$), so that there is a practice effect. Let’s suppose the practice effect is linear. Subjects have a long break, and then provide another observation of $y$ (for $x = 11$).
I have reason to believe that subjects get better at the task during... |
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