Design of Hamiltonian Monte Carlo for perfect simulation of general continuous distributions

Hamiltonian Monte Carlo (HMC) is an efficient method of simulating smooth distributions and has motivated the widely used No-U-turn Sampler (NUTS) and software Stan. We build on NUTS and the technique of “unbiased sampling” to design HMC algorithms that produce perfect simulation of general continuous distributions that are amenable to HMC. Our methods enable separation of Markov chain Monte Carlo convergence error from experimental error, and thereby provide much more powerful MCMC convergence diagnostics than current state-of-the-art summary statistics which confound these two errors. Objective comparison of different MCMC algorithms is provided by the number of derivative evaluations per perfect sample point. We demonstrate the methodology with applications to normal, t and normal mixture distributions up to 100 dimensions, and a 12-dimensional Bayesian Lasso regression. HMC runs effectively with a goal of 20 to 30 points per trajectory. Numbers of derivative evaluations per perfect sample point range from 390 for a univariate normal distribution to 12,000 for a 100-dimensional mixture of two normal distributions with modes separated by six standard deviations, and 22,000 for a 100-dimensional t-distribution with four degrees of freedom

Stock assessment of Australian pearl perch (Glaucosoma scapulare) with data to December 2019

Pearl perch, Glaucosoma scapulare, are endemic to sub-tropical offshore-waters along the east coast of Australia. Pearl perch form a single genetic stock in ocean waters between Rockhampton (23.20◦ S) in Queensland and Port Jackson (33.5◦ S) in New South Wales. The species live at least 25 years and have a maximum observed size of 75 cm total length. Sexual maturity is reached at 2–4 years of age (between 25 and 45 cm total length). This assessment builds on a previous assessment that estimated the stock was at 10–40% of unfished levels in 2014. This stock assessment includes updates to input data and methodology. This assessment used a single-sex, age-structured population model, fit to age and length data, constructed within the Stock Synthesis modelling framework. The assessment modelled the dynamics of the fishery across seven fishing sectors: 1) Queensland (Qld) charter line, 2) Qld commercial line, 3) Qld recreational, 4) New South Wales (NSW) charter line, 5) NSW commercial trap fishing, 6) NSW commercial line, and 7) NSW recreational. Sixteen scenarios were run, covering a range of modelling assumptions. Base case (Project Team recommended) results estimated spawning biomass to be 22% (14–46% range across scenarios) of unfished spawning biomass at the beginning of 2020

Importance of various data sources in deterministic stock assessment models

In fisheries, advice for the management of fish populations is based upon management quantities that are estimated by stock assessment models. Fisheries stock assessment is a process in which data collected from a fish population are used to generate a model which enables the effects of fishing on a stock to be quantified. This study determined the effects of various data sources, assumptions, error scenarios and sample sizes on the accuracy with which the age-structured production model and the Schaefer model (assessment models) were able to estimate key management quantities for a fish resource similar to the Cape hakes (Merluccius capensis and M. paradoxus). An age-structured production model was used as the operating model to simulate hypothetical fish resource population dynamics for which management quantities could be determined by the assessment models. Different stocks were simulated with various harvest rate histories. These harvest rates produced Downhill trip data, where harvest rates increase over time until the resource is close to collapse, and Good contrast data, where the harvest rate increases over time until the resource is at less than half of it’s exploitable biomass, and then it decreases allowing the resource to rebuild. The accuracy of the assessment models were determined when data were drawn from the operating model with various combinations of error. The age-structured production model was more accurate at estimating maximum sustainable yield, maximum sustainable yield level and the maximum sustainable yield ratio. The Schaefer model gave more accurate estimates of Depletion and Total Allowable Catch. While the assessment models were able to estimate management quantities using Downhill trip data, the estimates improved significantly when the models were tuned with Good contrast data. When autocorrelation in the spawner-recruit curve was not accounted for by the deterministic assessment model, inaccuracy in parameter estimates were high. The assessment model management quantities were not greatly affected by multinomial ageing error in the catch-at-age matrices at a sample size of 5000 otoliths. Assessment model estimates were closer to their true values when log-normal error were assumed in the catch-at-age matrix, even when the true underlying error were multinomial. However, the multinomial had smaller coefficients of variation at all sample sizes, between 1000 and 10000, of otoliths aged. It was recommended that the assessment model is chosen based on the management quantity of interest. When the underlying error is multinomial, the weighted log-normal likelihood function should be used in the catch-at-age matrix to obtain accurate parameter estimates. However, the multinomial likelihood should be used to minimise the coefficient of variation. Investigation into correcting for autocorrelation in the stock-recruitment relationship should be carried out, as it had a large effect on the accuracy of management quantities

Perfect simulation from unbiased simulation

We show that any application of the technique of unbiased simulation becomes perfect simulation when coalescence of the two coupled Markov chains can be practically assured in advance. This happens when a fixed number of iterations is high enough that the probability of needing any more to achieve coalescence is negligible; we suggest a value of $10^{-20}$. This finding enormously increases the range of problems for which perfect simulation, which exactly follows the target distribution, can be implemented. We design a new algorithm to make practical use of the high number of iterations by producing extra perfect sample points with little extra computational effort, at a cost of a small, controllable amount of serial correlation within sample sets of about 20 points. Different sample sets remain completely independent. The algorithm includes maximal coupling for continuous processes, to bring together chains that are already close. We illustrate the methodology on a simple, two-state Markov chain and on standard normal distributions up to 20 dimensions. Our technical formulation involves a nonzero probability, which can be made arbitrarily small, that a single perfect sample point may have its place taken by a "string" of many points which are assigned weights, each equal to $\pm 1$, that sum to~$1$. A point with a weight of $-1$ is a "hole", which is an object that can be cancelled by an equivalent point that has the same value but opposite weight $+1$.Comment: 17 pages, 4 figures; for associated R scripts, see https://github.com/George-Leigh/PerfectSimulatio

Towards an Initial Quota for the Queensland Mud Crab Fishery

Mud crabs in Queensland (principally Scylla serrata) are captured by baited pots. They are found mostly in estuaries and adjacent foreshores. Their populations are spatially variable and separated between the east coast and the Gulf of Carpentaria. No previous stock assessment has evaluated the sustainability of mud crab harvests in Queensland. This stock assessment is new, using the modified catch-MSY method of Haddon et al. (2018) from Martell and Froese (2013). The model used data from 1988/89 to 2017/18. This comprised of annual commercial harvests, and an estimate of recreational harvest derived from state-wide phone-diary surveys. The assessment provides estimates of exploitable biomass in 2017-18 and recommends Total Allowable Catches for the east coast and Gulf of Carpentaria stocks. The recommendations considered the biological sustainability of the stocks. Other objectives, such as social and economic, were not addressed in the analysis. However, they are important considerations when setting limits on harvests

Environmental proteomics reveals taxonomic and functional changes in an enriched aquatic ecosystem

Aquatic ecosystem enrichment can lead to distinct and irreversible changes to undesirable states. Understanding changes in active microbial community function and composition following organic matter loading in enriched ecosystems can help identify biomarkers of such state changes. In a field experiment, we enriched replicate aquatic ecosystems in the pitchers of the northern pitcher plant, Sarracenia purpurea. Shotgun metaproteomics using a custom metagenomic database identified proteins, molecular pathways, and contributing microbial taxa that differentiated control ecosystems from those that were enriched. The number of microbial taxa contributing to protein expression was comparable between treatments; however, taxonomic evenness was higher in controls. Functionally active bacterial composition differed significantly among treatments and was more divergent in control pitchers than in enriched pitchers. Aerobic and facultative anaerobic bacteria contributed most to identified proteins in control and enriched ecosystems, respectively. The molecular pathways and contributing taxa in enriched pitcher ecosystems were similar to those found in larger enriched aquatic ecosystems and are consistent with microbial processes occurring at the base of detrital food webs. Detectable differences between protein profiles of enriched and control ecosystems suggest that a time series of environmental proteomics data may identify protein biomarkers of impending state changes to enriched states

Not All Kinds of Revegetation Are Created Equal: Revegetation Type Influences Bird Assemblages in Threatened Australian Woodland Ecosystems

The value for biodiversity of large intact areas of native vegetation is well established. The biodiversity value of regrowth vegetation is also increasingly recognised worldwide. However, there can be different kinds of revegetation that have different origins. Are there differences in the richness and composition of biotic communities in different kinds of revegetation? The answer remains unknown or poorly known in many ecosystems. We examined the conservation value of different kinds of revegetation through a comparative study of birds in 193 sites surveyed over ten years in four growth types located in semi-cleared agricultural areas of south-eastern Australia. These growth types were resprout regrowth, seedling regrowth, plantings, and old growth