Perfect sampling methods for random forests

A weighted graphGis a pair (V, ℰ) containing vertex setVand edge set ℰ, where each edgee∈ ℰ is associated with a weightWe. A subgraph ofGis a forest if it has no cycles. All forests on the graphGform a probability space, where the probability of each forest is proportional to the product of the weights of its edges. This paper aims to simulate forests exactly from the target distribution. Methods based on coupling from the past (CFTP) and rejection sampling are presented. Comparisons of these methods are given theoretically and via simulation.

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Coupling from the past: A user’s guide

Microsurveys in Discrete Probability - DIMACS Series in Discrete Mathematics and Theoretical Computer Science ◽

10.1090/dimacs/041/09 ◽

1998 ◽

pp. 181-192 ◽

Cited By ~ 21

Author(s):

James Propp ◽

David Wilson

Keyword(s):

The Past ◽

Coupling From The Past

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Random flights on regular graphs

Advances in Applied Probability ◽

10.1017/s0001867800022758 ◽

1984 ◽

Vol 16 (03) ◽

pp. 618-637 ◽

Cited By ~ 2

Author(s):

Lajos Takács

Keyword(s):

Automorphism Group ◽

Transition Probabilities ◽

Finite Graph ◽

Initial Position ◽

Regular Graphs ◽

Random Flights ◽

The Past ◽

Initial Location ◽

Vertex Set

Let K be a finite graph with vertex set V = {x 0, x 1, …, xσ –1} and automorphism group G. It is assumed that G acts transitively on V. We can imagine that the vertices of K represent σ cities and a traveler visits the cities in a series of random flights. The traveler starts at a given city and in each flight, independently of the past journey, chooses a city at random as the destination. Denote by vn (n = 1, 2, …) the location of the traveler at the end of the nth flight, and by v 0 the initial location. It is assumed that the transition probabilities P{vn = xj | vn –1 = xi }, xi ϵ V, xj ϵ V, do not depend on n and are invariant under the action of G on V. The main result of this paper consists in determining p(n), the probability that the traveler returns to the initial position at the end of the nth flight.

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Relating Time and Customer Averages for Queues Using ‘forward’ Coupling from the Past

Journal of Applied Probability ◽

10.1017/s0021900200004435 ◽

2008 ◽

Vol 45 (02) ◽

pp. 568-574

Author(s):

Erol A. Peköz ◽

Sheldon M. Ross

Keyword(s):

Queueing System ◽

Steady State Distribution ◽

State Distribution ◽

The Past ◽

Coupling From The Past ◽

Poisson Arrivals ◽

Time Averages ◽

Time Average ◽

New Better Than Used ◽

Better Than

We give a new method for simulating the time average steady-state distribution of a continuous-time queueing system, by extending a ‘read-once’ or ‘forward’ version of the coupling from the past (CFTP) algorithm developed for discrete-time Markov chains. We then use this to give a new proof of the ‘Poisson arrivals see time averages’ (PASTA) property, and a new proof for why renewal arrivals see either stochastically smaller or larger congestion than the time average if interarrival times are respectively new better than used in expectation (NBUE) or new worse than used in expectation (NWUE).

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Biology and Management of Varroa destructor (Mesostigmata: Varroidae) in Apis mellifera (Hymenoptera: Apidae) Colonies

Journal of Integrated Pest Management ◽

10.1093/jipm/pmz036 ◽

2020 ◽

Vol 11 (1) ◽

Cited By ~ 2

Author(s):

Morgan A Roth ◽

James M Wilson ◽

Keith R Tignor ◽

Aaron D Gross

Keyword(s):

Apis Mellifera ◽

Honey Bee ◽

Varroa Destructor ◽

Sampling Methods ◽

Apis Cerana ◽

Varroa Mite ◽

Resistance Development ◽

Deformed Wing Virus ◽

The Past ◽

Asian Honey Bee

Abstract Varroa mite (Varroa destructor Anderson and Trueman) infestation of European honey bee (Apis mellifera L.) colonies has been a growing cause of international concern among beekeepers throughout the last 50 yr. Varroa destructor spread from the Asian honey bee (Apis cerana Fabricius [Hymenoptera: Apidae]) to A. mellifera populations in Europe in the 1970s, and subsequently traveled to the Americas. In addition to causing damage through feeding upon lipids of larval and adult bees, V. destructor also facilitates the spread of several viruses, with deformed wing virus being most prevalent. Several sampling methods have been developed for estimating infestation levels of A. mellifera colonies, and acaricide treatments have been implemented. However, overuse of synthetic acaricides in the past has led to widespread acaricide resistant V. destructor populations. The application of Integrated Pest Management (IPM) techniques is a more recent development in V. destructor control and is suggested to be more effective than only using pesticides, thereby posing fewer threats to A. mellifera colonies. When using IPM methods, informed management decisions are made based upon sampling, and cultural and mechanical controls are implemented prior to use of acaricide treatments. If acaricides are deemed necessary, they are rotated based on their mode of action, thus avoiding V. destructor resistance development.

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On exact sampling of stochastic perpetuities

Journal of Applied Probability ◽

10.1017/s0021900200099204 ◽

2011 ◽

Vol 48 (A) ◽

pp. 165-182 ◽

Cited By ~ 6

Author(s):

Jose H. Blanchet ◽

Karl Sigman

Keyword(s):

Fixed Point ◽

Net Present Value ◽

Positive Density ◽

Simulation Algorithm ◽

Present Value ◽

The Past ◽

Coupling From The Past ◽

Fixed Point Equation ◽

Point Equation ◽

The Right

A stochastic perpetuity takes the formD∞=∑n=0∞exp(Y1+⋯+Yn)Bn, whereYn:n≥0) and (Bn:n≥0) are two independent sequences of independent and identically distributed random variables (RVs). This is an expression for the stationary distribution of the Markov chain defined recursively byDn+1=AnDn+Bn,n≥0, whereAn=eYn;D∞then satisfies the stochastic fixed-point equationD∞D̳AD∞+B, whereAandBare independent copies of theAnandBn(and independent ofD∞on the right-hand side). In our framework, the quantityBn, which represents a random reward at timen, is assumed to be positive, unbounded with EBnp<∞ for somep>0, and have a suitably regular continuous positive density. The quantityYnis assumed to be light tailed and represents a discount rate from timenton-1. The RVD∞then represents the net present value, in a stochastic economic environment, of an infinite stream of stochastic rewards. We provide an exact simulation algorithm for generating samples ofD∞. Our method is a variation ofdominated coupling from the pastand it involves constructing a sequence of dominating processes.

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Linear space direct pattern sampling using coupling from the past

Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '12 ◽

10.1145/2339530.2339545 ◽

2012 ◽

Cited By ~ 16

Author(s):

Mario Boley ◽

Sandy Moens ◽

Thomas Gärtner

Keyword(s):

Linear Space ◽

The Past ◽

Coupling From The Past

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Exact Monte Carlo simulation for fork-join networks

Advances in Applied Probability ◽

10.1017/s000186780000495x ◽

2011 ◽

Vol 43 (02) ◽

pp. 484-503 ◽

Cited By ~ 2

Author(s):

Hongsheng Dai

Keyword(s):

Monte Carlo ◽

Response Times ◽

Simulation Method ◽

Perfect Simulation ◽

Analytic Approximations ◽

The Past ◽

Coupling From The Past ◽

Service Stations ◽

Explicit Formulae ◽

Queue Lengths

In a fork-join network each incoming job is split into K tasks and the K tasks are simultaneously assigned to K parallel service stations for processing. For the distributions of response times and queue lengths of fork-join networks, no explicit formulae are available. Existing methods provide only analytic approximations for the response time and the queue length distributions. The accuracy of such approximations may be difficult to justify for some complicated fork-join networks. In this paper we propose a perfect simulation method based on coupling from the past to generate exact realisations from the equilibrium of fork-join networks. Using the simulated realisations, Monte Carlo estimates for the distributions of response times and queue lengths of fork-join networks are obtained. Comparisons of Monte Carlo estimates and theoretical approximations are also provided. The efficiency of the sampling algorithm is shown theoretically and via simulation.

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Exact Monte Carlo simulation for fork-join networks

Advances in Applied Probability ◽

10.1239/aap/1308662489 ◽

2011 ◽

Vol 43 (2) ◽

pp. 484-503 ◽

Cited By ~ 3

Author(s):

Hongsheng Dai

Keyword(s):

Monte Carlo ◽

Response Times ◽

Simulation Method ◽

Perfect Simulation ◽

Analytic Approximations ◽

The Past ◽

Coupling From The Past ◽

Service Stations ◽

Explicit Formulae ◽

Queue Lengths

In a fork-join network each incoming job is split into K tasks and the K tasks are simultaneously assigned to K parallel service stations for processing. For the distributions of response times and queue lengths of fork-join networks, no explicit formulae are available. Existing methods provide only analytic approximations for the response time and the queue length distributions. The accuracy of such approximations may be difficult to justify for some complicated fork-join networks. In this paper we propose a perfect simulation method based on coupling from the past to generate exact realisations from the equilibrium of fork-join networks. Using the simulated realisations, Monte Carlo estimates for the distributions of response times and queue lengths of fork-join networks are obtained. Comparisons of Monte Carlo estimates and theoretical approximations are also provided. The efficiency of the sampling algorithm is shown theoretically and via simulation.

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A new subterranean species and an updated checklist of Strumigenys (Hymenoptera, Formicidae) from Macao SAR, China, with a key to species of the Greater Bay Area

ZooKeys ◽

10.3897/zookeys.970.54958 ◽

2020 ◽

Vol 970 ◽

pp. 63-116

Author(s):

François Brassard ◽

Chi-Man Leong ◽

Hoi-Hou Chan ◽

Benoit Guénard

Keyword(s):

Leaf Litter ◽

Sampling Methods ◽

Secondary Forests ◽

Undescribed Species ◽

Key To Species ◽

The Past ◽

Bay Area ◽

Under Sampling ◽

Subterranean Species ◽

High Diversity

In the past few decades, sampling of leaf litter with Winkler extractors revealed how abundant and ubiquitous ants from the genus Strumigenys are. It is now known that this genus has the third greatest number of species within the Formicidae family. However, very few subterranean species are known, which may be due to the current under-sampling of the soil stratum. Here, a holistic sampling approach, including the use of subterranean traps, was employed in Macao SAR, China. Subterranean traps allowed the collection of a new cryptic ant species: Strumigenys subterranea Brassard, Leong & Guénard, sp. nov. Moreover, extensive sampling of the leaf litter in secondary forests provided four new species records for the genus. The list of Macanese Strumigenys is here updated, elevating the known diversity in Macao to nine species. Furthermore, to facilitate further research on ants of the Guangdong-Hong Kong-Macao Greater Bay Area, a key to the 29 Strumigenys species known from the region is provided. Lastly, recommendations for sampling methods to assess ant biodiversity underground are discussed. In conclusion, this study highlights the importance of using extensive sampling methods, and suggests that relatively small patches of secondary forests within cities can hold a surprisingly high diversity as well as some undescribed species.

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