Diffusion limits of the random walk Metropolis algorithm in high dimensions

Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have mainly been proved for target measures with a product structure, severely limiting their applicability. The purpose of this paper is to study diffusion limits for a class of naturally occurring high-dimensional measures found from the approximation of measures on a Hilbert space which are absolutely continuous with respect to a Gaussian reference measure. The diffusion limit of a random walk Metropolis algorithm to an infinite-dimensional Hilbert space valued SDE (or SPDE) is proved, facilitating understanding of the computational complexity of the algorithm.Comment: Published in at http://dx.doi.org/10.1214/10-AAP754 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Function Space HMC Algorithm With Second Order Langevin Diffusion Limit

We describe a new MCMC method optimized for the sampling of probability measures on Hilbert space which have a density with respect to a Gaussian; such measures arise in the Bayesian approach to inverse problems, and in conditioned diffusions. Our algorithm is based on two key design principles: (i) algorithms which are well-defined in infinite dimensions result in methods which do not suffer from the curse of dimensionality when they are applied to approximations of the infinite dimensional target measure on \bbR^N; (ii) non-reversible algorithms can have better mixing properties compared to their reversible counterparts. The method we introduce is based on the hybrid Monte Carlo algorithm, tailored to incorporate these two design principles. The main result of this paper states that the new algorithm, appropriately rescaled, converges weakly to a second order Langevin diffusion on Hilbert space; as a consequence the algorithm explores the approximate target measures on \bbR^N in a number of steps which is independent of $N$. We also present the underlying theory for the limiting non-reversible diffusion on Hilbert space, including characterization of the invariant measure, and we describe numerical simulations demonstrating that the proposed method has favourable mixing properties as an MCMC algorithm.Comment: 41 pages, 2 figures. This is the final version, with more comments and an extra appendix adde

Customer driven marketing strategy of LIC international in Bahrain: a product specific study

Abstract Marketing of service product requires a slightly different strategy owing to the idiosyncratic nature of service items. The present study explores the customer oriented marketing strategy of LIC International in the Kingdom of Bahrain. The approach of the study was exploratory and personal interview was conducted to contribute major input source to the research. The company has been following a different marketing strategy in the study area different from the conventional approach in the home country. The customer focused marketing strategy was reviewed in seven Ps frame work.Service marketing, LIC international, insurance marketing, Seven Ps

Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis-Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler's exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the \emph{exact} posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this paper: when the likelihood has some \emph{local} regularity, the number of model evaluations per MCMC step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ODE and PDE inference problems, with both synthetic and real data.Comment: A major update of the theory and example

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On a young sea cow killed at Periapatnam, Gulf of Mannar

A young dugong was killed by the fishermen of Periapatnam in the inshore waters of Gulf of Mannar (depth 2 m, distance from the shore 2 km) near periapatnam. It weighed about 60 kg and had a total length of 155 cm. Meat was sold at Rs. 30.00 per kg in Periapatnam. The Dugong measuring 155 cm killed at Periapatnam, would have taken about five and a half years to attain that size

A penaeid prawn with an abnormal telson

Reported instances' of abnormalities in fishes are common 1-6, but in prawn it is limited, Deshmukh and Kuber' have reported a case of double rostrum in Parapenaeopsis styli/era. Apart from this there is no other published work on abnormalities in P. styli/era, The present note deals Witll the abnormal telson

Semi-dwarf narrow rolled leaf mutant in rice: Photosynthetic efficiency and physiological response to gibberellic acid (GA3)

Leaf is the major component for fixation of carbondioxide to produce more photoassimilates and maintains source sink relationship in plants. The present investigation was carried out to study the photosynthetic efficiency and physiological response of GA3 of semi-dwraf narrow rolled leaf mutant. Semi-dwarf narrow rolled leaf mutant exhibited reduced plant height, reduced leaf width, reduced panicle length and number of grains per panicle when compared to wild type. Photosynthetic efficiency study revealed that the mutant showed higher photosynthetic efficiency than wild type. Complementation test with GA3 clearly revealed that this mutant is sensitive to GA3 and revert to normal plant height. Scanning Electron Microscope study revealed that mutant had exhibited minimum number of inter-veins between veins, minimum distance between midrib and has slightly larger cell size. Hence, this loss of function mutant is very useful to map the regions associated with panicle length, number of grains per panicle and other traits related to enhancement of yield. The result provides an important clue for further understanding the mechanism of rice leaf development and plant architecture

Trophic model of the coastal fisheries ecosystem of the southwest coast of India

The Ecopath approach and software were used to construct a trophic model of the coastal fisheries ecosystem of the southwest (SW) coast of India. The model consisted of 11 ecological groups and used estimated landings from all areas along the southwest coast (based on the sample surveys conducted by Coastal Marine Fisheries Research Institute for the years 1994, 1995 and 1996). The trophic model suggests high catch levels, particularly for the large and medium predators, demersal feeders and detritivores. The biomass estimates in the trophic model were comparable to the biomass estimates from trawl surveys based on the swept area method for the southwest coast.Fishery resources, Demersal fisheries, Fishery surveys, Biomass, Population density, Shrimp fisheries, Catch/effort, Trawling, Mathematical models, Coastal fisheries, ISW, India,

A preliminary assessment of the coastal fishery resources in India: socioeconomic and bioeconomic perspective

India is endowed with a continental shelf of 0.5 million km2 and an exclusive economic zone (EEZ) of about 2 million km2. Almost half (39%) of the Indian population utilizes the marine fisheries resources. India ranked sixth worldwide in total fish production (4.95 million t) and second in inland fish production (2.24 million t) during 1995 - 96. Fish production expanded from 0.75 million t in 1950 - 51 to 4.95 million t in 1995 - 96, giving a significant increase at a cumulative growth rate of 4.2% per annum. Marine fish production increased from 0.53 million t in 1950 - 51 to 2.71 million t in 1995 - 96. The contribution of the fisheries sector to the total gross domestic product (GDP) improved from 0.75% in 1980 - 81 to 1.28% in 1994 - 95, with marine fisheries providing employment opportunities both in the production and post-harvest sectors. Subsidiary employment in fishing includes boat building and repair, net mending, repair of engines and supply of diesel, kerosene and other essential items. Women are mostly engaged in post-harvest operations like net mending, fish processing, packing and selling of fish and fish products. The contribution to foreign exchange earnings by the fishery sector substantially increased from Rs46 crores in 1960 - 61 to Rs4 697 (US$121*) in 1997 - 98. India exports about 55 types of marine products to different countries in Southwest Asia, Europe and USA. The total quantity of marine product exports rose from 97 200 t in 1987 - 88 to 307 337 t in 1994 - 95 giving an equivalent export value of Rs53 000 lakhs to Rs357 500 lakhs**. The marine fishing sector can be classified into: (a) non-motorized artisanal sector using country craft with traditional gear; (b) motorized sector; (c) mechanized sector using inboard engines of 50 to 120 HP; and (d) deep sea fishing with bigger boats (25 m and above) and engines of 120 HP and above. In 1996, India had a total fishing fleet of 238 125 units comprising 160 000 traditional craft, 31 726 motorized craft (converted from traditional) and 46 918 mechanized vessels operating different gear combinations. For artisanal fishing, the use of canoe and boat seine in Kerala provided the highest net income of Rs0.10 lakh with an annual catch of 51 t and an initial investment of Rs0.85 lakh. In motorized fishing, canoe and ring seine in Kerala offered a net income of Rs0.98 lakh with an annual catch of 220 t and an initial investment of Rs5.0 lakh. All major fishing units in Kerala, Tamil Nadu and Gujarat have higher profits not because of higher levels of fish catch but due to a better fish price. In the motorized sector, the increase in the price of fish over the years is greater than the increase in fuel expenditure. Small trawlers, purse seiners, dol-netters, gillnetters, pair trawlers and sona boats are the major types of mechanized fishing units operating in the inshore waters (up to 50 m depth). Trawlers and gillnetters are mostly operated along the Indian coasts whereas the fishing fleet mentioned above is confined to certain regions only. A small trawler (32Æ - 36Æ) has a net income of Rs0.90 lakh with an annual catch of 72 t and initial investment of Rs5.2 lakh in Karnataka. A purse seiner has a net earning of Rs3.14 lakh per year with an annual catch of 280 t and an average investment of Rs10 lakh. However the average value of fish caught in a purse seiner is Rs4.29 per kg set against the break-even cost of Rs3.16 per kg. To assess the economic sustainability of Indian marine fisheries in the period 1985 to 1998, the surplus production model or Schaefer Model was applied. Based on this, the maximum sustainable yield (MSY) was estimated at 2 353 726 t with an estimated effort of 984 586 annual fishing hours (AFH). Using the Fox surplus production model, MSY was equal to 2 973 752 t with an effort of 6 126 232 AFH. Note that actual yield during that period was 2 441 043 t with an effort of 12 97 092 AFH. This is indicative of over-fishing in the Indian Sea and Bay of Bengal. A number of management strategies can be applied to reduce the fishing pressure on the coastal areas of India. These are: (a) a ban of certain fishing gear and restricted entry to over-exploited fishing grounds; (b) the promotion of alternative/subsidiary income and emphasizing the importance of mariculture/aquaculture; (c) effective implementation of small scale fishery development projects like infrastructure and service facilities; (d) coastal zone management including protection of marine habitats; and (e) information dissemination and education on the importance of fisheries resources.Fishery resources, Fishery surveys, Biomass, Population density, Shrimp fisheries, Catch/effort, Trawling, Mathematical models, Coastal fisheries, Marine fisheries, Ecosystems, Socioeconomic aspects, Artisanal fishing, Ecnonomic benefits, ISW, India,