## Search Results: simulation (454)

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Introductory examples of Monte Carlo simulation in SAS

When I was writing Simulating Data with SAS (Wicklin, 2013), I read a lot of introductory textbooks about Monte Carlo simulation. One of my favorites is Sheldon Ross's book Simulation. (I read the 4th Edition (2006); the 5th Edition was published in 2013.) I love that the book brings together

Programming Tips
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How often do different statistical tests agree? A simulation study

Here's a fun problem to think about: Suppose that you have two different valid ways to test a statistical hypothesis. For a given sample, will both tests reject or fail to reject the hypothesis? Or might one test reject it whereas the other does not? The answer is that two

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Use simulations to evaluate the accuracy of asymptotic results

The field of probability and statistics is full of asymptotic results. The Law of Large Numbers and the Central Limit Theorem are two famous examples. An asymptotic result can be both a blessing and a curse. For example, consider a result that says that the distribution of some statistic converges

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Estimate an integral by using Monte Carlo simulation

Numerical integration is important in many areas of applied mathematics and statistics. For one-dimensional integrals on the interval (a, b), SAS software provides two important tools for numerical integration: For common univariate probability distributions, you can use the CDF function to integrate the density, thus obtaining the probability that a

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Horn's method: A simulation-based method for retaining principal components

One purpose of principal component analysis (PCA) is to reduce the number of important variables in a data analysis. Thus, PCA is known as a dimension-reduction algorithm. I have written about four simple rules for deciding how many principal components (PCs) to keep. There are other methods for deciding how

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Use simulation to estimate the power of a statistical test

A previous article about standardizing data in groups shows how to simulate data from two groups. One sample (with n1=20 observations) is simulated from an N(15, 5) distribution whereas a second (with n2=30 observations) is simulated from an N(16, 5) distribution. The sample means of the two groups are close

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A parallel implementation of Monte Carlo simulation in SAS Viya

A previous article introduces the MAPREDUCE function in the iml action. (The iml action was introduced in Viya 3.5.) The MAPREDUCE function implements the map-reduce paradigm, which is a two-step process for distributing a computation to multiple threads. The example in the previous article adds a set of numbers by

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Fast simulation of multivariate normal data with an AR(1) correlation structure

It is sometimes necessary for researchers to simulate data with thousands of variables. It is easy to simulate thousands of uncorrelated variables, but more difficult to simulate thousands of correlated variables. For that, you can generate a correlation matrix that has special properties, such as a Toeplitz matrix or a

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A zipper plot for visualizing coverage probability in simulation studies

Simulation studies are used for many purposes, one of which is to examine how distributional assumptions affect the coverage probability of a confidence interval. This article describes the "zipper plot," which enables you to compare the coverage probability of a confidence interval when the data do or do not follow

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Data-driven simulation

In a large simulation study, it can be convenient to have a "control file" that contains the parameters for the study. My recent article about how to simulate multivariate normal clusters demonstrates a simple example of this technique. The simulation in that article uses an input data set that contains

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Coverage probability of confidence intervals: A simulation approach

The article uses the SAS DATA step and Base SAS procedures to estimate the coverage probability of the confidence interval for the mean of normally distributed data. This discussion is based on Section 5.2 (p. 74–77) of Simulating Data with SAS. What is a confidence interval? Recall that a confidence

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Monte Carlo simulation for contingency tables in SAS

The FREQ procedure in SAS supports computing exact p-values for many statistical tests. For small and mid-sized problems, the procedure runs very quickly. However, even though PROC FREQ uses efficient methods to avoid unnecessary computations, the computational time required by exact tests might be prohibitively expensive for certain tables. If

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Models and simulation for 2x2 contingency tables

When modeling and simulating data, it is important to be able to articulate the real-life statistical process that generates the data. Suppose a friend says to you, "I want to simulate two random correlated variables, X and Y." Usually this means that he wants data generated from a multivariate distribution,

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Food Truck Analytics: Simulation or Queueing Model?

In a previous post, I discussed using discrete-event simulation to validate an optimization model and its underlying assumptions.  A similar approach can be used to validate queueing models as well.  And when it is found that the assumptions required for a queueing model are not a good fit for the

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Monitor convergence during simulation studies in SAS

Ugh! Your favorite regression procedure just printed a warning to the SAS log. Something is wrong, and your attempt to fit a model to the data has not succeeded. A typical message is "WARNING: The validity of the model fit is questionable," perhaps followed by some additional diagnostic messages about

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Using simulation to help Duke Hospital's tiniest patients

Last year, my SAS Simulation Studio R&D team began a discrete-event simulation modeling project of a neonatal intensive care unit (NICU) with two doctors from Duke University’s Division of Neonatal-Perinatal Medicine.  After several initial meetings discussing such things as necrotizing enterocolitis (NEC), retinopathy of prematurity (ROP), patent ductus arteriosis (PDA), and

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How discrete-event simulation can help project prison populations

In 2011, the passage of the federal Justice Reinvestment Act (JRA) brought significant changes to North Carolina’s criminal sentencing practices, particularly in relation to the supervision of offenders released into the community on probation or post-release supervision. A recent New York Times article highlighted how NC has used the implementation

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SAS author's tip: the basic structure of efficient simulations in SAS

This week's SAS tip is from Rick Wicklin and his powerful new book Simulating Data with SAS. Rick is a principal researcher in computational statistics at SAS, where he develops and supports the IML procedure and the SAS/IML Studio application. Chances are you're already familiar with Rick's work - whether you've seen him

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Using simulation to compute a power curve

Last week I showed how to use simulation to estimate the power of a statistical test. I used the two-sample t test to illustrate the technique. In my example, the difference between the means of two groups was 1.2, and the simulation estimated a probability of 0.72 that the t

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Using simulation to estimate the power of a statistical test

The power of a statistical test measures the test's ability to detect a specific alternate hypothesis. For example, educational researchers might want to compare the mean scores of boys and girls on a standardized test. They plan to use the well-known two-sample t test. The null hypothesis is that the

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Turn off ODS when running simulations in SAS

In my article "Simulation in SAS: The slow way or the BY way," I showed how to use BY-group processing rather than a macro loop in order to efficiently analyze simulated data with SAS. In the example, I analyzed the simulated data by using PROC MEANS, and I use the

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Efficient acceptance-rejection simulation: Part II

Last week I wrote about using acceptance-rejection algorithms in vector languages to simulate data. The main point I made is that in a vector language it is efficient to generate many more variates than are needed, with the knowledge that a certain proportion will be rejected. In last week's article,

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Efficient acceptance-rejection simulation

A few days ago on the SAS/IML Support Community, there was an interesting discussion about how to simulate data from a truncated Poisson distribution. The SAS/IML user wanted to generate values from a Poisson distribution, but discard any zeros that are generated. This kind of simulation is known as an

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Using macro loops for simulation

Last week I wrote an article in which I pointed out that many SAS programmers write a simulation in SAS by writing a macro loop. This approach is extremely inefficient, so I presented a more efficient technique. Not only is the macro loop approach slow, but there are other undesirable

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Simulation in SAS: The slow way or the BY way

Over the past few years, and especially since I posted my article on eight tips to make your simulation run faster, I have received many emails (often with attached SAS programs) from SAS users who ask for advice about how to speed up their simulation code. For this reason, I

Programming Tips
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Eight tips to make your simulation run faster

"Help! My simulation is taking too long to run! How can I make it go faster?" I frequently talk with statistical programmers who claim that their "simulations are too slow" (by which they mean, "they take too long"). They suspect that their program is inefficient, but they aren't sure why.

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How to lie with a simulation

In my article on Buffon's needle experiment, I showed a graph that converges fairly nicely and regularly to the value π, which is the value that the simulation is trying to estimate. This graph is, indeed, a typical graph, as you can verify by running the simulation yourself. However, notice

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Simulation of Buffon's needle in SAS

Buffon's needle experiment for estimating π is a classical example of using an experiment (or a simulation) to estimate a probability. This example is presented in many books on statistical simulation and is famous enough that Brian Ripley in his book Stochastic Simulation states that the problem is "well known

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