instruction stringlengths 9 38.7k |
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I've been fitting some time series data using a Poisson general additive model using SAS's PROC GAM. Generally speaking, I've been having it's built-in generalized cross-validation procedure generate at least a decent "starting point" for my single spline, which is a non-linear function of time along with a single para... |
I have a case study where a company made new golf balls with stronger coatings than current golf balls. One of the technicians is concerned that the new coating may decrease the driving distance. An experiment was conducted in which 40 types of each ball was hit by a machine to determine mean driving distance of the tw... |
If the interest is merely estimating the parameters of a model (pointwise and/or interval estimation) and the prior information is not reliable, weak, (I know this is a bit vague but I am trying to establish an scenario where the choice of a prior is difficult) ... Why would someone choose to use the Bayesian approach ... |
What does mean by the "the cumulative frequency in the form of probits" (see diagram)? How to use this methodology when one has only the Ratio and group information. I wonder how to compute these probits for the cumulative frequencies (preferably in R). Thanks in advance for your help and time.
|
I would like to compare the curvature of two response surfaces, each of the form:
binomial ~ continuous variables1-5
I think it would be appropriate to use the effective degrees of freedom of a thin-plate spline fit to the data with generalized cross-validation as an estimate of the curvature. Is this correct? One of t... |
Study Design: I showed participants some information about sea-level rise, focusing the information in different ways, both in terms of the time-scale and the magnitude of potential rise. Thus I had a 2 (Time: 2050 or 2100) by 2 (Magnitude: Medium or High) design. There were also two control groups who received no info... |
Hi I have the following problem:
I plan to do a logistic regression on web traffic data. One of my attributes is Number of days since last visit (type numeric in R). Now lots of visitors are firs-timers and I have no data for this attribute. Should I code them as NAs, or is is valid to code them as 0s?
Thank you all
|
Using R or SAS, I want to fit the following Gaussian model:
$$
\begin{pmatrix}
y_{1j1} \\ y_{1j2} \\ y_{1j3} \\ y_{2j1} \\ y_{2j2} \\ y_{2j3}
\end{pmatrix}
\sim_{\text{i.i.d.}}
{\cal N}
\left(
\begin{pmatrix}
\mu_1 \\
\mu_1 \\
\mu_1 \\
\mu_2 \\
\mu_2 \\
\mu_2
\end{pmatrix}
, \Sigma \right), ... |
The variable is a sum of two random variable which obey gamma and uniform distributions, respectively. The parameters of the uniform distribution variable are determined, and the other's must be retrieved from real time calculation.
I want to find the boundary of the summed variable, like using a three sigma rule woul... |
I used R mvpart package to create a multivariate regression tree. This is part of the output:
CP nsplit rel error xerror xstd
1 0.02717093 0 1.0000000 1.0005358 0.03481409
2 0.01302184 2 0.9456581 0.9521266 0.03306820
Node number 1: 3479 ob... |
I begin with a matrix of features (~30000 rows) vs cases (columns). I have binary - TRUE or FALSE - data in each cell indicating whether there is an event spanning the feature for that case. Next, I sum each row to get the total number of cases from the sample set that have an event for each feature. I will call this c... |
I have data from a study with three conditions. The independent variable was within-subjects and within-items.
I did an F1 and F2 analysis (= twice a repeated measures ANOVA) on the averages, by subject (the participants) and by item (the words). I checked/corrected for sphericity and the means do differ significantly.... |
I have a signal, of varying amplitude, and after a certain point in time, I expect to see the period of this signal lengthen. I am looking for a way to measure the lengthening of this period.
Is this a way I can calculate the instantaneous period of the signal below, at any given point? For example, at index 220 I woul... |
Possible Duplicate:
Logistic regression sub-group size parameters
Someone in my lab has a sample of 500 older kids and he wants to investigate what factors are related to the probability that they will bully. Groups:
kids were bullied and go on to bully is made up of 22;
were not bullied but go on to bully is mad... |
Does normalizing data (to have zero mean and unity standard deviation) prior to performing a repeated k-fold cross-validation have any negative conquences such as overfitting?
Note: this is for a situation where #cases > total #features
I am transforming some of my data using a log transform, then normalizing all data ... |
In the following paper http://fic.wharton.upenn.edu/fic/papers/99/9914.pdf on catastrophic damage, I read a sentence the puzzled me (p. 23):
For the hurricane data the Pareto gives the heaviest tail estimates. In fact the MLE estimates of the Pareto parameters ($\lambda=177.64$, $\alpha=0.797$) indicate that the distr... |
Looking at IO latency data for a storage array. When a drive is about to fail, one indication is an increase in the IO operations 'time to complete'. The array kindly provides this data in this format:
Time Disk Channels
seconds A B C D E F G H P ... |
I have a couple things to add together- two different pools of material, and I need to know the total material. Because of various things related to the sampling, I would like to bootstrap the sampling data from each pool. So I generate a list of 100 masses for one pool, and 50 masses for the second pool. Plus, I ge... |
I always have a hard time explaining statistical techniques to audience with no statistical background. If I wanted to explain what GLM is to such audience (without throwing out statistical jargon), what would be the best or most effective way?
I usually explain GLM with three parts -- (1) the random component which is... |
In some market research consumers are asked to rank the features of a product based on priority. For example,
Rank the following features for a device based on your priority (1 being the topmost priority)
Storage capacity 6
Portability 5
Touch interface 1
Keyboard 4
Long ba... |
The traditional approach to variable selection is to find variables that contribute the most to predicting a new response. Recently I learned of an alternative to this. In modeling variables that determine the effect of a treatment--as for example in a clinical trial of a pharmaceutical--the variable is said to be qu... |
Econometrics has substantial overlap with traditional statistics, but often uses its own jargon about a variety of topics ("identification," "exogenous," etc.). I once heard an applied statistics professor in another field comment that frequently the terminology is different but the concepts are the same. Yet it also... |
When specifying a production function for regression, it is well known that one of the features of using a log-log model is that the estimated coefficients are the output elasticities w.r.t. their respective independent variables.
My question is does it then follow that if one regresses log(production) on log(price), t... |
When people speak of "simulation variance", what does this mean? Does simulation variance disappear as $N \rightarrow \infty $?
Are models that have less simulation variance for a fixed $N$ considered more "robust"?
|
What's a good example to demonstrate the difference between estimation and calibration?
Edit: I'm looking for something that has the same definition of "calibration" and "estimation" that Krugman uses here (i.e. that they are in some way substitutes):
“calibration” — which basically means tweaking the parameters of yo... |
I know that the regular bootstrap (assuming that the necessary assumptions are valid) is more efficient than the m-n bootstrap.
However, supposing that you have access to really large data (such as a 1% sample of Google's daily searches), does it ever make sense to use the regular bootstrap whose assumptions may be vio... |
I've been looking for a good explanation of the difference between running a regression with year dummies as fixed effects vs. year dummies as instrumental variables.
A prominent example of this comes from Josh Angrist's 1991 paper, "Grouped-data estimation and testing in simple labor-supply models"
http://www.science... |
What are the basic pitfalls of regressing stock price on volume of shares traded? This is a time series dataset.
The model I'm using is:
$$\ln(price)=b_0+b_1t+b_2\ln(volume)+\epsilon$$
As you can see I include a time trend $t$.
The R2 and p-value appears to come out good, but I'm more accustomed to cross-sectional ana... |
What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functions in econometrics?
|
Would it make sense to do a 2SLS regression for Nominal GDP and Money Supply (using predetermined variables of government expenditure and investment)?
If it does make theoretical sense, is this because GDP and Money Supply are endogenous? I am unsure why GDP is endogenous... For example if there is an increase in money... |
I have two time-series:
A proxy for the market risk premium (ERP; red line)
The risk-free rate, proxied by a government bond (blue line)
I want to test if the risk-free rate can explain the ERP. Hereby, I basically followed the advice of Tsay (2010, 3rd edition, p. 96): Financial Time Series:
Fit the linear regress... |
I would like to regress the influence of income, education, marital status etc. on life satisfaction. The data I use is from the SHARE survey – life satisfaction can take values of 1–10, most values are around 6–8.
OLS regression seems to be a poor choice to me, as it might produce predicted values outside the 1–10 int... |
My question is exactly the title : to whom can we report a problem with SAS ?
Below is an example. This problem is not really severe but somewhat dangerous (in fact I have just updated my example below after Aniko's comment; there was a confusion in the first version of this post).
Consider such a dataset:
> dat
tu... |
I have the following multiple linear regression model:
Call:
lm(formula = Y ~ X1 + X2 + X2 + X3 + X4 + X5 + X6 + X7,
data = my.model, na.action = na.omit)
Residuals:
Min 1Q Median 3Q Max
-43.836 -1.507 0.010 1.485 46.231
Coefficients:
Estimate Std. Error t value Pr(>|t|)... |
I understand that there are degrees of trust one can have in the output of ANOVA. However, naturally I want to maximize the amount I can trust my results.
Question: If I have data that violate the assumption of normality (of residuals), how robust is a factorial ANOVA when cell sizes are unequal? My cell sizes range fr... |
I am actually reviewing a manuscript where the authors compare 5-6 logit regression models with AIC. However, some of the models have interaction terms without including the individual covariate terms. Does it ever make sense to do this?
For example (not specific to logit models):
M1: Y = X1 + X2 + X1*X2
M2: Y = X1 + X... |
I've been using the $K$-fold cross-validation a few times now to evaluate performance of some learning algorithms, but I've always been puzzled as to how I should choose the value of $K$.
I've often seen and used a value of $K = 10$, but this seems totally arbitrary to me, and I now just use $10$ by habit instead of th... |
Say you have an equation:
$$y = b_0 + b_1X_1 +b_2X_2$$
How would you test the hypothesis that $\frac{b1}{b2} = q$?
|
When building a vector autoregression model is there some theory that would guide me in chosing the number of variable to include? For example, I have about 3000 data points and I would like to get an idea of how many lags of explanatory variables to ues.
|
One of the things which makes econometrics unique is the use of the Generalized Method of Moments technique.
What types of problems make GMM more appropriate than other estimation techniques? What does using GMM buy you in terms of efficiency or reduced bias or more specific parameter estimation?
Conversely, what do y... |
I had a project from before I graduated from college that was effectively me acting as a research aid to a politician. The project served as my senior thesis, as well. The portion of the report that I was working on focused on determining the effect of new fuel economy legislation for heavy-duty vehicles, such as 18-wh... |
The ELO rating system and later improvements like Glicko are specifically designed, as far as I know, for mirror games. That is, we assume that no player has a systematic advantage over another. In chess, this is typically the case because a player will be black/white a roughly equal number of times.
But you can im... |
Given the following two time series (x, y; see below), what is the best method to model the relationship between the long-term trends in this data?
Both time series have significant Durbin-Watson tests when modelled as a function of time and neither are stationary (as I understand the term, or does this mean it only ... |
I must implement some Chi Square Test to test the randomness of "my" implementation, but I can't understand what this tests really say.
The tests are different but what I always do is: divide in different categories, calculate the probability to fall in these categories and then calculate this number:
$v = \sum_{i=0}^{... |
I have recently been reading a lot on this site (@Aniko, @Dikran Marsupial, @Erik) and elsewhere about the problem of overfitting occuring with cross validation - (Smialowski et al 2010 Bioinformatics, Hastie, Elements of statistical learning).
The suggestion is that any supervised feature selection (using correlation... |
Would there be any problem with using principal component analysis (e.g. for reduction of dimensionality) so that principal components scores could be used as predictors in a mixed-model? For non-mixed models this strategy is frequently applied (principal component regression) but I am not sure if it is applicable in t... |
How I got here
I was originally interested in point estimation and the Bayes risk of some distribution $\pi$
$$
r(\pi) = \mathbb{E}_{\pi(x)}[ \mathbb{E}_{\Pr(y|e,x)}[L(x,\hat x(y|e))]],
$$
where $L$ is some loss function and $\hat x$ is the posterior mean (here: Bayes estimator). Here $e$ is some experimental desig... |
Here is an exemple of fitting an ANCOVA model without intercept in R:
> k <- 40
> x <- 1:k
> sigma <- 30
> y1 <- rnorm(k, 1*x, sigma)
> y2 <- rnorm(k, 2*x, sigma)
> y3 <- rnorm(k, 3*x, sigma)
> x <- rep(x, 3)
> y <- c(y1,y2,y3)
> group <- gl(3,k)
> summary(lm(y~0+x+group:x))
Call:
lm(formula = y ~ 0 + x + group:x)
Re... |
I'm looking for an overview of some methods of variable selection.
I use datasets with around 6000 variables (the level of missing values is satisfying i.e. there are no variables with 100% missing values). There is no problem of insufficient degrees of freedom in my datasets.
In order to use some data mining technique... |
I know that Adaboost tries to generate a strong classifier using a linear combination of a set of weak classifiers.
However, I've read some papers suggesting Adaboost and SVMs work in harmony (even though SVM is a strong classifier) in certain conditions and cases.
I'm not able to grasp from an architectural and prog... |
I have been approaching to Support Vector Machines in this period, and I need a clarification about the use of the maximum margin hyperplane.
From a labeled point training set, we train a model that will correctly classify the future test set points.
To do this, we search for a best hyperplane that divide the training ... |
In this paper you can see equation (11), the probability density, written as:
$$S_n(\xi) = \frac{1}{N}\frac{1}{2\pi\sigma_r(n)\sigma_g(n)} \sum\limits_{i=1}^{N}\, \exp\left[-\frac{1}{2}\left(\frac{x_i^2}{\sigma_r(n)}+\frac{y_i^2}{\sigma_g(n)} \right) \right]$$
never mind what each parameter represents, my question rega... |
I'm designing a web service that will predict and recommend new items a user might like based on their expressed preferences on previous items (simple thumbs up/down interface).
I was told to look into decision trees, since they're a simple way to group things based on their characteristics, and they can be easily use... |
I'm currently analyzing data from a series of behavioral experiments that all use the following measure. The participants in this experiment are asked to select clues that (fictitious) other people could use to help solve a series of 10 anagrams. The participants are led to believe that these other people will either g... |
I have been working with glm.nb from MASS package for quite a while now. However, there are somethings I seem to not quite able to get my head around. Suppose I have a data that looks like this:
Expression Species timePoint Replicate
40 A T1 R1
60 A T1 R2
48 ... |
I'm using JMP to analyze some sample data to make predictions about the population. My sample is from a destructive QC test, so I obviously want to minimize my sample. I have a response (my Y) and a known factor (a very strong and consistent correlation that is measurable by non-destructive means) but the exact relat... |
To estimate the probability failure in medical sciences, it is not atypical to use 1-KM. However this does not account for competing risks, such as death by natural causes or causes unrelated with the disease, which preclude the event of interest. Thus 1-KM provides an inadequate measure, and cumulative incidence curve... |
I conducted a survey using a 5 point Likert scale. Firstly, I asked the respondent to select one airline out of six airlines given and then there were 20 statements regarding the services offered by the airline. The respondents have to mark their extent of agreement or disagreement on a 5 point Likert scale. So I recei... |
I have gathered information on the rate increases allowed by a government regulator over about 17 years. As background, utilities in this area must apply to the regulator if they wish to raise their rates, in exchange for being granted a quasi-monopoly in the market.
In this period, there are 65 'usable' decisions -- ... |
How do I sample from a distribution that is the product of a gaussian and an inverse-wishart distribution? I was going to use inverse transform sampling but a friend said that he thinks there is a much simpler way of doing it, a trick because the inverse-wishart is a conjugate prior of the gaussian. Does anyone know if... |
I want to model the number of users of an mobile app. This app has two kinds of users: free and paid. I thought of this autoregressive model:
$x_t = Ax_{t-1}$
with $x_t$ being a 4-dimensional vector, with quantities (all in period $t$) for the numbers of
mobile users
visitors of the app page
free users
paid users
I i... |
I would be very grateful for any ideas concerning the following problem. I would be even more grateful if someone could point me to a literature reference proposing a solution for a scenario like the one I describe below. In short, I am looking to adapt Bouackert and Frank's 2004 article on corrected repeated k-fold cv... |
Why even have non-informative priors? They don't provide information about $\theta$. So why use them? Why not only use informative priors? For example, suppose $ \theta \in [0,1]$. Then is $\theta \sim \mathcal{U}(0,1)$ a non-informative prior for $\theta$?
|
The problem:
If event $A$ happens with probability $p$, what is the probability $P[K=1]$ that, after two independent trials, $A$ happened exactly once?
Is the answer:
$P[K=1] = p(1-p)$, since we need $A$ to happen and then we need $A$ not to happen, or
$P[K=1] = 2p(1-p) = p(1-p) + (1-p)p$, since there are two cases ... |
Wikipedia's Margin of Error entry says that
a random sample of size 400 will give a margin of error, at a 95%
confidence level, of 0.98/20 or 0.049 - just under 5%
given an infinite population size. This means that if I polled 400 US citizens (randomly selected) and asked them "Obama or Romney?", the resulting pro... |
If ever there was a case where this become clear it is with the Monty Hall problem. Even the great Paul Erdős got fooled by this problem. My question, which may be difficult to answer, is what is it about probability that we can be so confident of an answer we get using an intuitive argument and yet be so wrong. Benf... |
Consider iid samples from a fixed distribution function $F(x)$ and consider its median. Now consider another median from iid samples where one half is drawn from $F_1(x)$ and the other is drawn from $F_2(x)$ with $F_1(x)+F_2(x)=2F(x)$ for all $x$. Which median has a larger variance?
|
I often deal with messy survey data which requires a lot of cleaning up before any statistics can be done. I used to do this "manually" in Excel, sometimes using Excel formulas, and sometimes checking entries one-by-one. I started doing more and more of these tasks by writing scripts to do them in R, which has been ver... |
In the given Image you can see a plot with error bars of different length on each upper and lower side. The bars were generated by calculating the standard error once for all points above the mean value and once for those below.
As information on this "method" is very sparse I ask myself wether it is correct to use th... |
In a previous post I’ve wondered how to deal with EQ-5D scores. Recently I stumbled upon logistic quantile regression suggested by Bottai and McKeown that introduces an elegant way to deal with bounded outcomes.
The formula is simple:
$logit(y)=log(\frac{y-y_{min}}{y_{max}-y})$
To avoid log(0) and division by 0 you ext... |
As we all know , the GLM has the structure: $G(EY)=X^{T}\beta$, in which $G(.)$ is a known
link function. What confuse me is that some people say that it's a semiparametric model. But in my opinion, it's a parametric model, because there is no nonparametric part and all we don't know in the previuos structure is $\bet... |
I currently have a setup, for which I want do do an ANOVA in spss. In my model I need to include four factors (I'll call them factor1 to factor4) each with two possible states (true and false). However not all combinations are possible. To be more precise, factor4 can only be true if one of factor1 or factor2 or both ... |
I'm trying to fit a logistic regression where there is a huge difference in the number of data points in either group (70 Vs 10,000). A statistician friend of mine has told me that this is a known problem with logistic regression and that for those kinds of numbers it overfits the data and basically doesn't work. When ... |
I was wondering if anybody had some good references on dynamic decision networks,
is there a nice recent survey on this topic?
Thanks in advance.
|
If I want to compare shooting percentages (basketball) in two conditions, what type of statistical analysis would I use? If I enter data in columns
condition 1 makes
condition 1 attempts
condition 2 makes
condition 2 attempts
Is that a bad way to do it?
Should I assign a 1, 0 to make and miss and compare by groups?
A... |
First of 2 part query: I have observed a 100 Drs and recorded the number of times they touch surfaces while in a room:
$$
\begin{array}{l|c|c|c|c}
Dr\text{ number}&Bed&Table&Chair&Door\\
Dr 1&3&2&2&1\\
Dr 2&4&1&0&1\\
\vdots&\vdots &\vdots &\vdots &\vdots\\
Dr 100& 2&3&1&1
\end{array}
$$
I would like to calculat... |
While working on some problem in bioinformatics I applied bayesian network algorithm for classification purposes. As predictors I took a window of sequence of aminoacids and for dependent variable I used some feature of interest of a central acid.
For DAG estimation I used several different algorithms which gave me ide... |
I would like to compute the measure of similarity between two ordered sets of points---the ones under User compared with the ones under Teacher:
The points are curves in 3D space, but I was thinking that the problem is simplified if I plotted them in 2 dimensions like in the picture. If the points overlap, similarity... |
Given a data, I'd like to utilize it by two different models, such as generalized linear model (GLM) and generalized partial linear model (GPLM), and my problem is how to compare the performance of these models?
Please give me some ideas!
|
I am using the package strucchange to analyze a monthly time series. I read it in as a zoo object. The series looks something like this:
date A B
2 1979-01-07 0 7
3 1979-01-14 0 4
4 1979-01-21 0 5 ... |
I want to use generalized partial linear model to fit a data. So are there
some existing functions about GPLM? I'm new about R.
|
I'm currently working on a series of Poisson time series models trying to estimate the effect of a change in how the counts were obtained (switching from one diagnostic test to another) while controlling for other trends over time (say a general increase in the incidence of disease). I've got data for a number of diffe... |
I am studying a machine learning course and the lecture slides contain information what I find contradicting with the recommended book.
The problem is the following: there are three classifiers:
classifier A providing better performance in the lower range of the thresholds,
classifier B providing better performance in... |
The relative asymptotic power of non-parametric tests is reported to be high. What is the power of tests such as Wilcoxon Signed Rank Test and Mann-Whitney U with N's of 10, 20, 50, for example, as compared with t-tests?
|
In order to explain why I have those stupid question you'll find below I have to say that I am more a machine-learning person. While I worked on problems in bioinformatics everything was fine. When I heard words like "regression" or "kurtosis and skewness", in first case I just smiled, in second case I just made some c... |
Possible Duplicate:
Analysis of part of Likert scale
My survey consist of 6 airlines (non metric) and 10 attributes for rating these airlines. The questionnaire uses 5 point likert scale. Only one airline can be rated using one questionnaire. The questionnaire has 10 questions, each one regarding one attributes.
My ... |
A contractor has submitted bid on four state jobs: a car parking garage, an office building, a theater, and a shopping mall. State rules do not allow a contractor to be offered more than one of these jobs. If this contractor is awarded any of these jobs, the profits earned from these contracts are: RM2 million from the... |
I have a sample (n=200) that I have collected questionnaire data from. Each participant will complete 5 questionnaires that capture different behaviours and all of my 5 questionnaires include between 10 and 27 items.
I am planning to use SEM to construct a model that investigates whether scores on 4 of my questionnair... |
I may be mixing up my time series and non time series concepts, but what is the difference between a regression model that exhibits serial correlation and a model that exhibits a unit root?
In addition, why is it that you can use a Durbin-Watson test to test for serial correlation, but must use a Dickey-Fuller test f... |
I can't seem to find this anywhere on the internet or in my books. I'm putting together a construct for an underlying variable.
Is it acceptable to have a construct with two variables if that produces a bigger Cronbach alpha than the construct with 3 variables in a professional statistical analysis?
Using 2 variables s... |
I 'm looking to find a general formula for the following problem:
The events:
Let each event have two possible outcomes (e.g. success and failure)
The events are independent
Scenario:
Let the number of trials be Y
Let the number of successes be N
Here's the tough part:
Over Y trials, what is the probability of the... |
I'm reading the paper Optimal Rates of Convergence for Sparse Covariance Matrix Estimation by T. Cai and H. Zhou.
They refer to a specific version of Assouad's Lemma (see lemma 2, p. 6 of the linked paper), which differs from the one I've found in Yu [1] and Le Cam [2]. I've also ordered van der Vaart [3], but it has y... |
Data
An experiment was run with 40 subjects. 20 subjects are in condition 1 and 20 in condition 2. Over the course of the experiment, subjects went through 60 trials. 20 trials with stimuli of type A, 20 with stimuli of type B and 20 trials with stimuli of type C. In each trial, 6 scores are measured (secondwise).
Ima... |
How can one obtain the gamma distribution through convolution of two different distributions? Could the gamma distribution be created as a non-trivial sum of $N$ random variables $X$ which have the same distribution and parameters?
Trivial case is summation of fixed number $N$ of variables with gamma distribution as de... |
Suppose A is a fixed factor and B is a random factor. A and B are crossed. Another random factor C is nested in B. Taking into account the AB and AC interactions, how should I fit the model using lme function in the nlme package? Thanks.
|
I wonder if you can help me to get the right answer to a question about structural equation modeling. Imagine someone trying to validate a questionnaire using component factor analysis that highlighted 5 subscales. Is it right to use the total score of the questionnaire in a model created by structural equation modelin... |
In reviewing some market research, I came across a study which decided to weight the results/outcomes of the control group so the distribution of participants in the control sub-groups (0,1,2,3,4,5 - a measure of their pre-experiment activity of a certain activity) would equate with that of the treatment group. The exp... |
I've learned sum of exponential random variables follows Gamma distribution.
But everywhere I read the parametrization is different. For instance, Wiki describes the relationship, but don't say what their parameters actually mean? Shape, scale, rate, 1/rate?
Exponential distribution: $x$~$exp(\lambda)$
$$f(x|\lambda... |
Let $(n_1,...,n_k)$ be a sample from a Binomial$(N,p)$ where both parameters are unknown. In many cases, the profile likelihood of $N$ is asymptotic in the sense that it never decays to $0$. An example of this is given here. The following code shows the profile likelihood of $N$ for this data set.
data = c(16, 18, 22, ... |
In the Metropolis–Hastings algorithm for sampling a target distribution, let:
$\pi_{i}$ be the target density at state $i$,
$\pi_j$ be the target density at the proposed state $j$,
$h_{ij}$ be the proposal density for transition to state $j$ given current state $i$,
$a_{ij}$ be the accept probability of proposed sta... |
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