LAISHA
Open Laisha

ICAR-IASRI MSc and PhD Statistical Computing: Simulation, Resampling & Algorithms: practice questions

ICAR-IASRI MSc and PhD (Agricultural Statistics, Computer Application, Bioinformatics) · India · ICAR-Indian Agricultural Statistics Research Institute with the IARI Graduate School

Original practice questions written to the published syllabus · not past papers
10worked here, free
21written to this exam in this subject
11syllabus units

What this subject covers

The algorithms inside modern statistics: random-number generation, Monte Carlo integration, the bootstrap and jackknife, permutation tests, the EM algorithm, MCMC and numerical linear algebra, with attention to accuracy and reproducibility.

In the exams: AICE-JRF Computer Application Unit 10 (present); GATE DA (present); PhD course in most programmes; light in national exams

Where the 21 questions fall

How our questions for ICAR-IASRI MSc and PhD spread across the units of Statistical Computing: Simulation, Resampling & Algorithms. Difficulty: 11 easy, 10 medium, 0 hard.

Pseudo-random number generation and tests of randomness2
Generating random variates: inversion, acceptance-rejection and transformation methods2
Monte Carlo integration and variance reduction2
Bootstrap: percentile and BCa intervals2
Jackknife2
Permutation and randomisation tests2
EM algorithm and its applications (missing data, mixtures)2
MCMC algorithms in practice2
Numerical linear algebra for statistics: QR and Cholesky2
Simulation studies: design and reporting2
Parallel and high-performance computing for statistics1

10 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

1 · Pseudo-random number generation and tests of randomness · easy

For the generator xₙ₊₁ = (5xₙ + 3) mod 16 with x₀ = 7, what is x₁?

  1. 38
  2. 6
  3. 2
  4. 7
Answer and working

B. 6

5 × 7 + 3 = 38, and 38 mod 16 = 6; 38 forgets the modulus.

Further reading: Robert and Casella, Monte Carlo Statistical Methods (2004); Rizzo, Statistical Computing with R (2019); Efron and Tibshirani, An Introduction to the Bootstrap (1993); Givens and Hoeting, Computational Statistics (2013)

2 · Pseudo-random number generation and tests of randomness · medium

A randomness test that a generator passes shows that:

  1. No non-randomness was detected
  2. The sequence is proven random for every purpose
  3. The generator is cryptographically secure
  4. The period is infinite
Answer and working

A. No non-randomness was detected

Tests can only fail to detect departures from randomness.

Further reading: Robert and Casella, Monte Carlo Statistical Methods (2004); Rizzo, Statistical Computing with R (2019); Efron and Tibshirani, An Introduction to the Bootstrap (1993); Givens and Hoeting, Computational Statistics (2013)

3 · Bootstrap: percentile and BCa intervals · medium

Compared with a bootstrap standard error, a bootstrap confidence interval generally needs:

  1. Fewer resamples
  2. More resamples
  3. No resamples at all
  4. Exactly 50 resamples
Answer and working

B. More resamples

Tail percentiles need 1,000–2,000 or more resamples.

Further reading: Robert and Casella, Monte Carlo Statistical Methods (2004); Rizzo, Statistical Computing with R (2019); Efron and Tibshirani, An Introduction to the Bootstrap (1993); Givens and Hoeting, Computational Statistics (2013)

4 · Permutation and randomisation tests · medium

PERMANOVA and the Mantel test are examples of:

  1. Parametric ANOVA with normal errors
  2. Bootstrap intervals
  3. Permutation methods
  4. MCMC samplers
Answer and working

C. Permutation methods

Both obtain null distributions by permutation.

Further reading: Robert and Casella, Monte Carlo Statistical Methods (2004); Rizzo, Statistical Computing with R (2019); Efron and Tibshirani, An Introduction to the Bootstrap (1993); Givens and Hoeting, Computational Statistics (2013)

5 · MCMC algorithms in practice · medium

The initial iterations discarded from an MCMC run are called:

  1. Thinning
  2. Burn-in or warm-up
  3. Proposals
  4. Effective samples
Answer and working

B. Burn-in or warm-up

They depend on starting values.

Further reading: Robert and Casella, Monte Carlo Statistical Methods (2004); Rizzo, Statistical Computing with R (2019); Efron and Tibshirani, An Introduction to the Bootstrap (1993); Givens and Hoeting, Computational Statistics (2013)

6 · Numerical linear algebra for statistics: QR and Cholesky · easy

Statistical software solves least squares preferably by:

  1. Explicitly inverting X′X
  2. Cramer's rule
  3. QR decomposition of X
  4. Random search
Answer and working

C. QR decomposition of X

QR avoids squaring the condition number.

Further reading: Robert and Casella, Monte Carlo Statistical Methods (2004); Rizzo, Statistical Computing with R (2019); Efron and Tibshirani, An Introduction to the Bootstrap (1993); Givens and Hoeting, Computational Statistics (2013)

7 · Numerical linear algebra for statistics: QR and Cholesky · medium

The standard, most stable way to compute a dense QR decomposition is with:

  1. Householder reflections
  2. Cramer's rule
  3. Classical Gram–Schmidt without reorthogonalisation
  4. Repeated squaring
Answer and working

A. Householder reflections

Givens rotations suit sparse matrices and updating.

Further reading: Robert and Casella, Monte Carlo Statistical Methods (2004); Rizzo, Statistical Computing with R (2019); Efron and Tibshirani, An Introduction to the Bootstrap (1993); Givens and Hoeting, Computational Statistics (2013)

8 · Simulation studies: design and reporting · easy

In the ADEMP framework for simulation studies, the 'E' stands for:

  1. Errors and residuals
  2. Estimands
  3. Experiments
  4. Exponentials
Answer and working

B. Estimands

Aims, data-generating mechanisms, estimands, methods, performance measures.

Further reading: Robert and Casella, Monte Carlo Statistical Methods (2004); Rizzo, Statistical Computing with R (2019); Efron and Tibshirani, An Introduction to the Bootstrap (1993); Givens and Hoeting, Computational Statistics (2013)

9 · Simulation studies: design and reporting · easy

Data-generating mechanisms in a good simulation study should include:

  1. Only the scenario favouring the new method
  2. A single sample size
  3. No departures from assumptions
  4. Realistic and challenging scenarios
Answer and working

D. Realistic and challenging scenarios

Factorial scenarios probe where methods break.

Further reading: Robert and Casella, Monte Carlo Statistical Methods (2004); Rizzo, Statistical Computing with R (2019); Efron and Tibshirani, An Introduction to the Bootstrap (1993); Givens and Hoeting, Computational Statistics (2013)

10 · Parallel and high-performance computing for statistics · medium

GPUs accelerate statistical computing mainly for:

  1. Reading text files from disk quickly
  2. Sequential loops with branching
  3. Printing results
  4. The same arithmetic on many data
Answer and working

D. The same arithmetic on many data

Thousands of simple cores suit array operations.

Further reading: Robert and Casella, Monte Carlo Statistical Methods (2004); Rizzo, Statistical Computing with R (2019); Efron and Tibshirani, An Introduction to the Bootstrap (1993); Givens and Hoeting, Computational Statistics (2013)

Ten here, 21 in the app. The Laisha app has every practice question we have written to ICAR-IASRI MSc and PhD in this subject, marked as you go, with timed papers, a jump-to-unanswered list and a certificate when you pass at 70 per cent.

Free for ten days, then one subscription of US$10 a month. We would rather say so here than have you find it later.

Practise the full set in Laisha →

Read the subject

Statistical Computing: Simulation, Resampling & AlgorithmsThe full study manual, free ICAR-IASRI MSc and PhDFormat, sections and how it has changed

More ICAR-IASRI MSc and PhD practice

Causal Inference, Panel Data & Efficiency AnalysisStatistical & Machine Learning for AgricultureSpatial Statistics, Geostatistics & Remote Sensing for AgricultureActuarial Statistics & Crop Insurance DesignAgriculture for StatisticiansTime Series AnalysisCrop Forecasting, Weather-Based Models & Non-linear Growth ModelsDifferential Equations, Finite Differences & Numerical AnalysisProgramming for Statistics & Data (R and Python)Data Analysis with Statistical Software & Reproducible ResearchStatistical Consulting, Research Methodology & Scientific CommunicationComputer Science Fundamentals: Architecture, Data Structures, Networks & Operating SystemsDatabases, Big Data & Agricultural Information SystemsStatistical Ecology, Environmental & Fisheries StatisticsStatistical Genomics: QTL Mapping, GWAS & Genomic SelectionBioinformatics & Computational Biology

Statistical Computing: Simulation, Resampling & Algorithms for other exams

ICAR AICE-JRF/SRF · IndiaGATE · India

Ask Laisha about this

Opens Laisha's chat with your question ready to send. Sign in or start free.