A Dynamic Hierarchical Bayesian Approach for Forecasting Vegetation Condition

Agricultural drought, which occurs due to a significant reduction in the moisture required for vegetation growth, is the most complex amongst all drought categories. The onset of agriculture drought is slow and can occur over vast areas with varying spatial effects, differing in areas with a particular vegetation land cover or specific agro-ecological sub-regions. These spatial variations imply that monitoring and forecasting agricultural drought require complex models that consider the spatial variations in a given region of interest. Hierarchical Bayesian Models are suited for modelling such complex systems. Using partially pooled data with sub-groups that characterise spatial differences, these models can capture the sub-group variation while allowing flexibility and information sharing between these sub-groups. This paper's objective was to improve the accuracy and precision of agricultural drought forecast in spatially diverse regions with a Hierarchical Bayesian Model. Results showed that the Hierarchical Bayesian Model was better at capturing the variability for the different agro-ecological zones and vegetation land covers compared to a regular Bayesian Auto-Regression Distributed Lags model. The forecasted vegetation condition and associated drought probabilities were more accurate and precise with the Hierarchical Bayesian Model at 4 to 10 weeks lead times. Forecasts from the hierarchical model exhibited higher hit rates with a low probability of false alarms for drought events in semi-arid and arid zones. The Hierarchical Bayesian Model also showed good transferable forecast skills over counties not included in the training data.

Power calculator for detecting allelic imbalance using hierarchical Bayesian model

Objective Allelic imbalance (AI) is the differential expression of the two alleles in a diploid. AI can vary between tissues, treatments, and environments. Methods for testing AI exist, but methods are needed to estimate type I error and power for detecting AI and difference of AI between conditions. As the costs of the technology plummet, what is more important: reads or replicates? Results We find that a minimum of 2400, 480, and 240 allele specific reads divided equally among 12, 5, and 3 replicates is needed to detect a 10, 20, and 30%, respectively, deviation from allelic balance in a condition with power > 80%. A minimum of 960 and 240 allele specific reads divided equally among 8 replicates is needed to detect a 20 or 30% difference in AI between conditions with comparable power. Higher numbers of replicates increase power more than adding coverage without affecting type I error. We provide a Python package that enables simulation of AI scenarios and enables individuals to estimate type I error and power in detecting AI and differences in AI between conditions.

Internally Generated Time in the Rodent Hippocampus is Logarithmically Compressed

The Weber-Fechner law proposes that our perceived sensory input increases with physical input on a logarithmic scale. Hippocampal "time cells" carry a record of recent experience by firing sequentially during a circumscribed period of time after a triggering stimulus. Different cells have "time fields" at different delays up to at least tens of seconds. Past studies suggest that time cells represent a compressed timeline by demonstrating that fewer time cells fire late in the delay and their time fields are wider. This paper asks whether the compression of time cells obeys the Weber-Fechner Law. Time cells were studied with a hierarchical Bayesian model that simultaneously accounts for the firing pattern at the trial level, cell level, and population level. This procedure allows separate estimates of the within-trial receptive field width and the across-trial variability. The analysis at the trial level suggests the time cells represent an internally coherent timeline as a group. Furthermore, even after isolating across-trial variability, time field width increases linearly with delay. Finally, we find that the time cell population is distributed evenly on a logarithmic time scale. Together, these findings provide strong quantitative evidence that the internal neural temporal representation is logarithmically compressed and obeys a neural instantiation of the Weber- Fechner Law.