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 the Australian east coast tailor (Pomatomus saltatrix) fishery

Tailor is a highly migratory fish with an iconic, mainly beach-based fishery on the Australian east coast. There is a pronounced annual, close-inshore run of large schools of tailor from New South Wales, where the fishery peaks in April–June, to Queensland where the Fraser Island fishery at the northern end of the run peaks in August–September. The commercial sector of the fishery developed over the first half of the 20th century while the recreational beach line sector grew strongly from the late 1940s, facilitated by rapid developments in recreational beach-fishing gear. The recreational sector appeared to have had a pronounced peak in both harvest size and fishing effort in the mid-1990s, after which both the recreational and commercial sectors experienced big falls driven largely by cultural change. Recreational participation rates and fishing effort fell sharply while fishery management implemented measures such as bag limits on the recreational sector and harvest limits and spatial restrictions on the commercial sector. Information on the tailor fishery is relatively rich in fish length-frequency and ageing data, although data quality greatly improved from the mid-1990s with the introduction of scientific sampling methods. Prior to that time there were no reliable fish ageing data and most length-frequency data came from tagging experiments. The eastern Australian stock of tailor mainly consists of young fish with not many surviving beyond four years of age. The oldest fish aged by Fisheries Queensland’s monitoring team were just under seven years of age

Stock assessment of the Australian east coast tailor (Pomatomus saltatrix) fishery

Tailor, (Pomatomus saltatrix), is widely distributed in subtropical and temperate waters around the world. On the east coast of Australia, tailor occurs along the coasts of southern Queensland, New South Wales and Victoria and is considered a single genetic stock. This stock assessment analyses the Queensland and New South Wales component of the east coast stock. This stock assessment used the age-structured model from the previous assessment with an annual time step. Incorporated data spanned the period from 1945 to 2019 including total harvests, standardised catch rates and length and age information for Queensland and New South Wales commercial and recreational sectors. Model analyses suggested that spawning biomass was at around 51% of unfished biomass in 2019. This report provides estimates of sustainable harvests to ensure the fishery operates at sustainable levels, for commercial and recreational fishing, and supports the harvest strategy defined in Queensland’s Sustainable Fisheries Strategy 2017–2027 (Department of Agriculture and Fisheries 2017)

Stock Assessment of Queensland East Coast black jewfish (Protonibea diacanthus), Australia, with data to December 2021

Black jewfish (Protonibea diacanthus) are caught on the east coast of Queensland by commercial, recreational, charter and Indigenous fishers. The fishery is focused around Central Queensland, and has recently experienced a large shift in commercial effort and gear types. The species was historically considered a byproduct species within the inshore net fishery, but has now become a targeted line caught species. In Australia, black jewfish are found from Exmouth Gulf in Western Australia, north and east across Northern Australia, to the east coast of Queensland. Research suggests that stocks cover hundreds of kilometres. This is the first stock assessment of the Queensland East Coast stock. The stock assessment was conducted on calendar years and included input data through to December 2021. Eight model scenarios were run, covering different combinations of recreational dead catch and population steepness (productivity parameter). Base case (preferred) scenario results suggested that biomass declined gradually from the 1940s to the 1980s and has increased slightly since then. The spawning stock level at the beginning of 2022 for base-case scenarios was estimated to be between 56% and 99% with a median estimate of 79%. The estimates from other scenarios ranged from 80% to 92%. Despite high uncertainty around the exact level of biomass, the model outputs indicate that the biomass is probably at or above the target reference point of 60% unfished biomass

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

Harvest Strategies for the Torres Strait Finfish fishery

The project has provided a foundation and framework for a Harvest Strategy for both Spanish mackerel and coral trout, with both fish species supported within the project by stock assessments. An update to the Spanish mackerel assessment was conducted with direct feedback between the outputs and diagnostics of the assessment informing the process of harvest strategy development. Similarly, for coral trout the initial harvest strategy resourced the first preliminary assessment of the coral trout, also funded as part of the project. Project staff worked closely with management agencies and stakeholders, using formal committee meetings inputs and advice, which fulfilled the requirements of the guidelines for developing harvest strategies. The versions of the harvest strategies presented herein are correct up the date of the submission of the report. The current versions of the harvest strategies are adaptive, as various components need checking based on updated assessments and any new information. The project team have made a series of recommendations for future updates required to progress to the full and complete harvest strategies

Estimating the natural mortality rate of saucer scallops (Ylistrum balloti) on the Queensland east coast from tag-recaptures

Saucer scallops (Ylistrum balloti) were tagged and released on four occasions inside two areas closed to fishing (Hervey Bay A, HBA; and Yeppoon B, YB) on the Queensland (Australia) east coast and their subsequent recaptures over the following months were used to measure the instantaneous rate of natural mortality (M). A total of 13,295 scallops were tagged and 526 recaptured over the 15 month-long experiment (May 2018 to August 2019). Three statistical approaches were applied to the experimental design and analysis of the tagging data, based on 1) the Brownie model, 2) a modified version of the Brownie model, and 3) a binomial logistic regression model of recaptures. Estimates of M based on the Brownie model were much higher for tagged scallops that were at liberty over summer months compared to those at liberty over the winter months, possibly indicating seasonal variation. The logistic model parameter estimates indicated the proportion of recaptures differed significantly with the lunar phase at recapture, scallop size class, the number of days the scallops were at liberty and the interaction between days-at-liberty and closure. All three approaches indicated M was higher in HBA compared to YB. Mean estimates of M for the whole fishery, derived by averaging estimates from both closures, ranged from a minimum of 1.461 year–1 for the logistic model, to 1.501 year–1 for the Brownie model, to 1.548 year–1 (variable recapture rate) and 1.594 year–1 (fixed recapture rate) for the modified Brownie model. Estimates from all three approaches were higher than the previous estimate that was published over 40 years ago and possible reasons for the increase are discussed

Inhibition of Sirtuin 2 with Sulfobenzoic Acid Derivative AK1 is Non-Toxic and Potentially Neuroprotective in a Mouse Model of Frontotemporal Dementia

Tauopathies including tau-associated Frontotemporal dementia (FTD) and Alzheimer’s disease are characterized pathologically by the formation of tau-containing neurofibrillary aggregates and neuronal loss, which contribute to cognitive decline. There are currently no effective treatments to prevent or slow this neural systems failure. The rTg4510 mouse model, which expresses a mutant form of the tau protein associated with FTD with Parkinsonism-17, undergoes dramatic hippocampal and cortical neuronal loss making it an ideal model to study treatments for FTD-related neuronal loss. Sirtuins are a family of proteins involved in cell survival that have the potential to modulate neuronal loss in neurodegenerative disorders. Here we tested the hypothesis that sirtuin 2 (SIRT2) inhibition would be non-toxic and prevent neurodegeneration in rTg4510 brain. In this study we delivered SIRT2 inhibitor AK1 directly to the hippocampus with an osmotic minipump and confirmed that it reached the target region both with histological assessment of delivery of a dye and with a pharmacodynamic marker, ABCA1 transcription, which was upregulated with AK1 treatment. AK1 treatment was found to be safe in wild-type mice and in the rTg4510 mouse model, and further, it provided some neuroprotection in the rTg4510 hippocampal circuitry. This study provides proof-of-concept for therapeutic benefits of SIRT2 inhibitors in both tau-associated FTD and Alzheimer’s disease, and suggests that development of potent, brain permeable SIRT2 inhibitors is warranted

Whole Slide Image Analysis Quantification using Aperio Digital Imaging in a Mouse Lung Metastasis Model

poster abstractDigital whole slide imaging is the technique of digitizing a microscope slide at the highest resolution to produce a “digital virtual microscope slide”. This digital image can be viewed in three or four fields, from low to high power, which can be commonly used to evaluate the tissue. Many of these systems have whole slide software image analysis capability. The goal of this study was to determine if the Aperio positive pixel algorithm (image analysis) could effectively quantitate metastatic mouse lung tumors in a lung section using a H&E stain. Lung sections from a mouse lung metastasis model of 8 mice per group were evaluated: control, 50mg/kg, and 75mg/kg carboplatin. H&E and Ki67 immunostain slides were scanned using the Aperio whole slide scanning system (Scanscope CS). A single field of view from each slide representing a whole lung lobe with multiple lung metastases was selected for image analysis. The standard positive pixel algorithm was altered to read the H&E slides. Various histology slides were used to validate the altered algorithm. The immunostain (Ki67) was generated using the standard positive pixel algorithm analysis. The Aperio automated positive pixel count for a Ki67 immunostain was consistent with the H&E image analysis. The values decreased with a dose dependent treatment (control vs. 50mg/kg and 75mg/kg carboplatin) and were (H&E) 37%, 28%, and 22%, and (Ki67) 9%, 5%, and 3%. The analysis had decreasing values for both the H&E and Ki67 analysis on a dose dependent drug treatment. The metastases decreased in both treatment groups compared to controls with both the H&E and Ki67 analyses. The Aperio Image Analysis positive pixel algorithm allows large areas of the lung tissue section to be examined and not just a single 25x or 40x field like many common image analyses systems